Base_JSON/prefixD/json/D14/D14-1039.json

{
    "paper_id": "D14-1039",
    "header": {
        "generated_with": "S2ORC 1.0.0",
        "date_generated": "2023-01-19T15:55:13.100962Z"
    },
    "title": "Hierarchical Discriminative Classification for Text-Based Geolocation",
    "authors": [
        {
            "first": "Benjamin",
            "middle": [],
            "last": "Wing",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "University of Texas at Austin",
                "location": {}
            },
            "email": ""
        },
        {
            "first": "Jason",
            "middle": [],
            "last": "Baldridge",
            "suffix": "",
            "affiliation": {
                "laboratory": "",
                "institution": "University of Texas at Austin",
                "location": {}
            },
            "email": "jbaldrid@utexas.edu"
        }
    ],
    "year": "",
    "venue": null,
    "identifiers": {},
    "abstract": "Text-based document geolocation is commonly rooted in language-based information retrieval techniques over geodesic grids. These methods ignore the natural hierarchy of cells in such grids and fall afoul of independence assumptions. We demonstrate the effectiveness of using logistic regression models on a hierarchy of nodes in the grid, which improves upon the state of the art accuracy by several percent and reduces mean error distances by hundreds of kilometers on data from Twitter, Wikipedia, and Flickr. We also show that logistic regression performs feature selection effectively, assigning high weights to geocentric terms.",
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        "abstract": [
            {
                "text": "Text-based document geolocation is commonly rooted in language-based information retrieval techniques over geodesic grids. These methods ignore the natural hierarchy of cells in such grids and fall afoul of independence assumptions. We demonstrate the effectiveness of using logistic regression models on a hierarchy of nodes in the grid, which improves upon the state of the art accuracy by several percent and reduces mean error distances by hundreds of kilometers on data from Twitter, Wikipedia, and Flickr. We also show that logistic regression performs feature selection effectively, assigning high weights to geocentric terms.",
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                "section": "Abstract",
                "sec_num": null
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            {
                "text": "Document geolocation is the identification of the location-a specific latitude and longitude-that forms the primary focus of a given document. This assumes that a document can be adequately associated with a single location, which is only valid for certain documents, generally of fairly small size. Nonetheless, there are many natural situations in which such collections arise. For example, a great number of articles in Wikipedia have been manually geotagged; this allows those articles to appear in their geographic locations in geobrowsers like Google Earth. Images in social networks such as Flickr may be geotagged by a camera and their textual tags can be treated as documents. Likewise, tweets in Twitter are often geotagged; in this case, it is possible to view either an individual tweet or the collection of tweets for a given user as a document, respectively identifying the location as the place from which the tweet was sent or the home location of the user.",
                "cite_spans": [],
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                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "Early work on document geolocation used heuristic algorithms, predicting locations based on toponyms in the text (named locations, determined with the aid of a gazetteer) (Ding et al., 2000; Smith and Crane, 2001) . More recently, various researchers have used topic models for document geolocation (Ahmed et al., 2013; Hong et al., 2012; Eisenstein et al., 2011; Eisenstein et al., 2010) or other types of geographic document summarization (Mehrotra et al., 2013; Adams and Janowicz, 2012; Hao et al., 2010) . A number of researchers have used metadata of various sorts for document or user geolocation, including document links and social network connections. This research has sometimes been applied to Wikipedia (Overell, 2009) or Facebook (Backstrom et al., 2010) but more commonly to Twitter, focusing variously on friends and followers (McGee et al., 2013; Sadilek et al., 2012) , time zone (Mahmud et al., 2012) , declared location (Hecht et al., 2011) , or a combination of these (Schulz et al., 2013) .",
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                        "start": 171,
                        "end": 190,
                        "text": "(Ding et al., 2000;",
                        "ref_id": "BIBREF14"
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                        "start": 191,
                        "end": 213,
                        "text": "Smith and Crane, 2001)",
                        "ref_id": "BIBREF46"
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                    {
                        "start": 299,
                        "end": 319,
                        "text": "(Ahmed et al., 2013;",
                        "ref_id": "BIBREF2"
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                    {
                        "start": 320,
                        "end": 338,
                        "text": "Hong et al., 2012;",
                        "ref_id": "BIBREF25"
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                    {
                        "start": 339,
                        "end": 363,
                        "text": "Eisenstein et al., 2011;",
                        "ref_id": "BIBREF16"
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                        "start": 364,
                        "end": 388,
                        "text": "Eisenstein et al., 2010)",
                        "ref_id": "BIBREF15"
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                    {
                        "start": 441,
                        "end": 464,
                        "text": "(Mehrotra et al., 2013;",
                        "ref_id": "BIBREF32"
                    },
                    {
                        "start": 465,
                        "end": 490,
                        "text": "Adams and Janowicz, 2012;",
                        "ref_id": "BIBREF0"
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                    {
                        "start": 491,
                        "end": 508,
                        "text": "Hao et al., 2010)",
                        "ref_id": "BIBREF23"
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                    {
                        "start": 716,
                        "end": 731,
                        "text": "(Overell, 2009)",
                        "ref_id": "BIBREF37"
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                    {
                        "start": 744,
                        "end": 768,
                        "text": "(Backstrom et al., 2010)",
                        "ref_id": "BIBREF4"
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                        "start": 843,
                        "end": 863,
                        "text": "(McGee et al., 2013;",
                        "ref_id": "BIBREF31"
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                        "start": 864,
                        "end": 885,
                        "text": "Sadilek et al., 2012)",
                        "ref_id": "BIBREF41"
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                        "start": 898,
                        "end": 919,
                        "text": "(Mahmud et al., 2012)",
                        "ref_id": "BIBREF29"
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                        "start": 940,
                        "end": 960,
                        "text": "(Hecht et al., 2011)",
                        "ref_id": "BIBREF24"
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                        "text": "(Schulz et al., 2013)",
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                "section": "Introduction",
                "sec_num": "1"
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            {
                "text": "We tackle document geolocation using supervised methods based on the textual content of documents, ignoring their metadata. Metadatabased approaches can achieve great accuracy (e.g. Schulz et al. (2013) obtain 79% accuracy within 100 miles for a US-based Twitter corpus, compared with 49% using our methods on a comparable corpus), but are very specific to the particular corpus and the types of metadata it makes available. For Twitter, the metadata includes the user's declared location and time zone, information which greatly simplifies geolocation and which is unavailable for other types of corpora, such as Wikipedia. In many cases essentially no metadata is available at all, as in historical corpora in the digital humanities (Lunenfeld et al., 2012) , such as those in the Perseus project (Crane, 2012) . Text-based approaches can be applied to all types of corpora; metadata can be additionally incorporated when available (Han and Cook, 2013) .",
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                        "text": "Schulz et al. (2013)",
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                        "text": "(Lunenfeld et al., 2012)",
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                        "text": "(Crane, 2012)",
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                "section": "Introduction",
                "sec_num": "1"
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            {
                "text": "We introduce a hierarchical discriminative classification method for text-based geotagging. We apply this to corpora in three languages (English, German and Portuguese) . This method scales well to large training sets and greatly improves results across a wide variety of corpora, beating current state-of-the-art results by wide margins, including Twitter users (Han et al., 2014, henceforth Han14; Roller et al., 2012, henceforth Roller12) ; Wikipedia articles (Roller12; Wing and Baldridge, 2011, henceforth WB11) ; and Flickr images (O'Hare and Murdock, 2013, henceforth OM13) . Importantly, this is the first method that improves upon straight uniform-grid Naive Bayes on all of these corpora, in contrast with k-d trees (Roller12) and the current state-of-the-art technique for Twitter users of geographically-salient feature selection (Han14).",
                "cite_spans": [
                    {
                        "start": 136,
                        "end": 168,
                        "text": "(English, German and Portuguese)",
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                    {
                        "start": 363,
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                        "text": "(Han et al., 2014, henceforth Han14;",
                        "ref_id": null
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                    {
                        "start": 400,
                        "end": 441,
                        "text": "Roller et al., 2012, henceforth Roller12)",
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                        "start": 474,
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                        "text": "Wing and Baldridge, 2011, henceforth WB11)",
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                        "text": "(O'Hare and Murdock, 2013, henceforth OM13)",
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                "section": "Introduction",
                "sec_num": "1"
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                "text": "We also show, contrary to Han14, that logistic regression when properly optimized is more accurate than state-of-the-art techniques, including feature selection, and fast enough to run on large corpora. Logistic regression itself very effectively picks out words with high geographic significance. In addition, because logistic regression does not assume feature independence, complex and overlapping features of various sorts can be employed.",
                "cite_spans": [],
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                "section": "Introduction",
                "sec_num": "1"
            },
            {
                "text": "We work with six large datasets: two of geotagged tweets, three of Wikipedia articles, and one of Flickr photos. One of the two Twitter datasets is primarily localized to the United States, while the remaining datasets cover the whole world.",
                "cite_spans": [],
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                "section": "Data",
                "sec_num": "2"
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            {
                "text": "TWUS is a dataset of tweets compiled by Roller12. A document in this dataset is the concatenation of all tweets by a single user, as long as at least one of the user's tweets is geotagged with specific, GPS-assigned latitude/longitude coordinates. The earliest such tweet determines the user's location. Tweets outside of a bounding box covering the contiguous United States (including parts of Canada and Mexico) were discarded, as well as users that may be spammers or robots (based on the number of followers, followees and tweets). The resulting dataset contains 38M tweets from 450K users, of which 10,000 each are reserved for the development and test sets.",
                "cite_spans": [],
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                "section": "Data",
                "sec_num": "2"
            },
            {
                "text": "TWWORLD is a dataset of tweets compiled by Han et al. (2012) . It was collected in a similar fashion to TWUS but differs in that it covers the entire Earth instead of primarily the United States, and consists only of geotagged tweets.",
                "cite_spans": [
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                        "start": 43,
                        "end": 60,
                        "text": "Han et al. (2012)",
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                "section": "Data",
                "sec_num": "2"
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                "text": "Non-English tweets and those not near a city were removed, and non-alphabetic, overly short and overly infrequent words were filtered. The resulting dataset consists of 1.4M users, with 10,000 each reserved for the development and test sets.",
                "cite_spans": [],
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                "section": "Data",
                "sec_num": "2"
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            {
                "text": "ENWIKI13 is a dataset consisting of the 864K geotagged articles (out of 14M articles in all) in the November 4, 2013 English Wikipedia dump. It is comparable to the dataset used in WB11 and was processed using an analogous fashion. The articles were randomly split 80/10/10 into training, development and test sets.",
                "cite_spans": [],
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                "section": "Data",
                "sec_num": "2"
            },
            {
                "text": "DEWIKI14 is a similar dataset consisting of the 324K geotagged articles (out of 1.71M articles in all) in the July 5, 2014 German Wikipedia dump.",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Data",
                "sec_num": "2"
            },
            {
                "text": "PTWIKI14 is a similar dataset consisting of the 131K geotagged articles (out of 817K articles in all) in the June 24, 2014 Portuguese Wikipedia dump.",
                "cite_spans": [],
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                "section": "Data",
                "sec_num": "2"
            },
            {
                "text": "COPHIR (Bolettieri et al., 2009 ) is a large dataset of images from the photo-sharing social network Flickr. It consists of 106M images, of which 8.7M are geotagged. Most images contain user-provided tags describing them. We follow algorithms described in OM13 in order to make direct comparison possible. This involves removing photos with empty tag sets and performing bulk upload filtering, retaining only one of a set of photos from a given user with identical tag sets. The resulting reduced set of 2.8M images is then divided 80/10/10 into training, development and test sets. The tag set of each photo is concatenated into a single piece of text (in the process losing usersupplied tag boundary information in the case of multi-word tags).",
                "cite_spans": [
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                        "start": 7,
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                        "text": "(Bolettieri et al., 2009",
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                "section": "Data",
                "sec_num": "2"
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            {
                "text": "Our code and processed corpora are available for download. 1",
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                "section": "Data",
                "sec_num": "2"
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                "text": "The dominant approach for text-based geolocation comes from language modeling approaches in information retrieval (Ponte and Croft, 1998; Manning et al., 2008) . For this general strategy, the Earth is sub-divided into a grid, and then each training set document is associated with the cell that contains it. Some model (typically Naive Bayes) is then used to characterize each cell and enable new documents to be assigned a latitude and longitude based on those characterizations. There are several options for constructing the grid and for modeling, which we review next.",
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                        "text": "(Ponte and Croft, 1998;",
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                        "text": "Manning et al., 2008)",
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                "section": "Supervised models for document geolocation",
                "sec_num": "3"
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            {
                "text": "The simplest grid is a uniform rectangular one with cells of equal-sized degrees, which was used by Serdyukov et al. (2009) for Flickr images and WB11 for Twitter and Wikipedia. This has two problems. Compared to a grid that takes document density into account, it over-represents rural areas at the expense of urban areas. Furthermore, the rectangles are not equal-area, but shrink in width away from the equator (although the shrinkage is mild until near the poles). Roller12 tackle the former issue by using an adaptive grid based on k-d trees, while Dias et al. (2012) handle the latter issue with an equal-area quaternary triangular mesh. An additional issue with geodesic grids is that a single metro area may be divided between two or more cells. This can introduce a statistical bias known as the modifiable areal unit problem (Gehlke and Biehl, 1934; Openshaw, 1983) . One way to mitigate this, implemented in Roller12's code but not investigated in their paper, is to divide a cell in a k-d tree in such a way as to produce the maximum margin between the dividing line and the nearest document on each side.",
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                        "text": "Serdyukov et al. (2009)",
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                        "text": "Dias et al. (2012)",
                        "ref_id": "BIBREF13"
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                        "text": "(Gehlke and Biehl, 1934;",
                        "ref_id": "BIBREF17"
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                        "text": "Openshaw, 1983)",
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                "section": "Geodesic grids",
                "sec_num": "3.1"
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                "text": "A more direct method is to use a city-based representation, either with a full set of sufficientlysized cities covering the Earth and taken from a comprehensive gazetteer (Han14) or a limited, pre-specified set of cities (Kinsella et al., 2011; Sadilek et al., 2012) . Han14 amalgamate cities into nearby larger cities within the same state (or equivalent); an even more direct method would use census-tract boundaries when available. Disadvantages of these methods are the dependency on time-specific population data, making them unsuitable for some corpora (e.g. 19th-century documents); the difficulty in adjusting grid resolution in a principled fashion; and the fact that not all documents are near a city (Han14 find that 8% of tweets are \"rural\" and cannot predicted by their model).",
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                        "start": 221,
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                        "text": "(Kinsella et al., 2011;",
                        "ref_id": "BIBREF26"
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                        "start": 245,
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                        "text": "Sadilek et al., 2012)",
                        "ref_id": "BIBREF41"
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                "section": "Geodesic grids",
                "sec_num": "3.1"
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                "text": "We construct rectangular grids, since they are very easy to implement and Dias et al. (2012)'s triangular mesh did not yield consistently better results over Wikipedia. We use both uniform grids and k-d tree grids with midpoint splitting.",
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                "section": "Geodesic grids",
                "sec_num": "3.1"
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                "text": "A geodesic grid of sufficient granularity creates a large decision space, when each cell is viewed as a label to be predicted by some classifier. This situation naturally lends itself to simple, scalable language-modeling approaches. For this general strategy, each cell is characterized by a pseudodocument constructed from the training documents that it contains. A test document's location is then chosen based on the cell with the most similar language model according to standard measures such as Kullback-Leibler (KL) divergence (Zhai and Lafferty, 2001) , which seeks the cell whose language model is closest to the test document's, or Naive Bayes (Lewis, 1998), which chooses the cell that assigns the highest probability to the test document.",
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                        "start": 535,
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                        "text": "(Zhai and Lafferty, 2001)",
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                "section": "Naive Bayes",
                "sec_num": "3.2"
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                "text": "Han14, Roller12 and WB11 follow this strategy, using KL divergence in preference to Naive Bayes. However, we find that Naive Bayes in conjunction with Dirichlet smoothing (Smucker and Allan, 2006) works at least as well when appropriately tuned. Dirichlet smoothing is a type of discounting model that interpolates between the unsmoothed (maximum-likelihood) document distribution\u03b8 d i of a document d i and the unsmoothed distribution\u03b8 D over all documents. A general interpolation model for the smoothed distribution \u03b8 d i has the following form:",
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                "section": "Naive Bayes",
                "sec_num": "3.2"
            },
            {
                "text": "EQUATION",
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                        "raw_str": "P (w|\u03b8 d i ) = (1 \u2212 \u03bb d i )P (w|\u03b8 d i ) + \u03bb d i P (w|\u03b8D)",
                        "eq_num": "(1)"
                    }
                ],
                "section": "Naive Bayes",
                "sec_num": "3.2"
            },
            {
                "text": "where the discount factor \u03bb d i indicates how much probability mass to reserve for unseen words. For Dirichlet smoothing, \u03bb d i is set as:",
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                "eq_spans": [],
                "section": "Naive Bayes",
                "sec_num": "3.2"
            },
            {
                "text": "\u03bb d i = 1 \u2212 |d i | |d i | + m (2)",
                "cite_spans": [],
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                "eq_spans": [],
                "section": "Naive Bayes",
                "sec_num": "3.2"
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                "text": "where |d i | is the size of the document and m is a tunable parameter. This has the effect of relying more on d i 's distribution and less on the global distribution for larger documents that provide more evidence than shorter ones. Naive Bayes models are estimated easily, which allows them to handle fine-scale grid resolutions with potentially thousands or even hundreds of thousands of non-empty cells to choose among. Figure 1 shows a choropleth map of the behavior of Naive Bayes, plotting the rank of cells for the test document Pennsylvania Avenue (Washington, DC) in ENWIKI13, for a uniform 0.1 \u2022 grid. The top-ranked cell is the correct one.",
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                        "start": 423,
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                        "text": "Figure 1",
                        "ref_id": "FIGREF0"
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                "section": "Naive Bayes",
                "sec_num": "3.2"
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                "text": "The use of discrete cells over the Earth's surface allows any classification strategy to be employed, including discriminative classifiers such as logistic regression. Logistic regression often produces produces better results than generative classifiers at the cost of more time-consuming training, which limits the size of the problems it may be applied to. Training is generally unable to scale to encompass several thousand or more distinct labels, as is the case with fine-scale grids of the sort we may employ. Nonetheless we find flat logistic regression to be effective on most of our largescale corpora, and the hierarchical classification strategy discussed in \u00a74 allows us to take advantage of logistic regression without incurring such a high training cost.",
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                "section": "Logistic regression",
                "sec_num": "3.3"
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                "text": "Naive Bayes assumes that features are independent, which penalizes models that must accommodate many features that are poor indicators and which can gang up on the good features. Large improvements have been obtained by reducing the set of words used as features to those that are geographically salient. Cheng et al. (2010; model word locality using a unimodal distribution taken from Backstrom et al. (2008) and train a classifier to identify geographically local words based on this distribution. This unfortunately requires a large hand-annotated cor-pus for training. Han14 systematically investigate various feature selection methods for finding geo-indicative words, such as information gain ratio (IGR) (Quinlan, 1993 ), Ripley's K statistic (O'Sullivan and Unwin, 2010) and geographic density (Chang et al., 2012) , showing significant improvements on TWUS and TWWORLD ( \u00a72).",
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                        "text": "Cheng et al. (2010;",
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                        "text": "Backstrom et al. (2008)",
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                        "text": "(Quinlan, 1993",
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                "section": "Feature selection",
                "sec_num": "3.4"
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                "text": "For comparison with Han14, we test against an additional baseline: Naive Bayes combined with feature selection done using IGR. Following Han14, we first eliminate words which occur less than 10 times, have non-alphabetic characters in them or are shorter than 3 characters. We then compute the IGR for the remaining words across all cells at a given cell size or bucket size, select the top N % for some cutoff percentage N (which we vary in increments of 2%), and then run Naive Bayes at the same cell size or bucket size.",
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                "section": "Feature selection",
                "sec_num": "3.4"
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            {
                "text": "To overcome the limitations of discriminative classifiers in terms of the maximum number of cells they can handle, we introduce hierarchical classification (Silla Jr. and Freitas, 2011) for geolocation. Dias et al. (2012) use a simple two-level generative hierarchical approach using Naive Bayes, but to our knowledge no previous work implements a multi-level discriminative hierarchical model with beam search for geolocation.",
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                        "text": "(Silla Jr. and Freitas, 2011)",
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                "section": "Hierarchical classification",
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            },
            {
                "text": "To construct the hierarchy, we start with a root cell c root that spans the entire Earth and from there build a tree of cells at different scales, from coarse to fine. A cell at a given level is subdivided to create smaller cells at the next level of resolution that altogether cover the same area as their parent.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "We use the local classifier per parent approach to hierarchical classification (Silla Jr. and Freitas, 2011) in which an independent classifier is learned for every node of the hierarchy above the leaf nodes. The probability of any node in the hierarchy is the product of the probabilities of that node and all of its ancestors, up to the root. This is defined recursively as:",
                "cite_spans": [
                    {
                        "start": 79,
                        "end": 108,
                        "text": "(Silla Jr. and Freitas, 2011)",
                        "ref_id": "BIBREF44"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "EQUATION",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [
                    {
                        "start": 0,
                        "end": 8,
                        "text": "EQUATION",
                        "ref_id": "EQREF",
                        "raw_str": "P (c root ) = 1.0 P (c j ) = P (c j |\u2191c j )P (\u2191c j )",
                        "eq_num": "(3)"
                    }
                ],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "where \u2191c j indicates c j 's parent in the hierarchy.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "In addition to allowing one to use many classifiers that each have a manageable number of outcomes, the hierarchical approach naturally lends itself to beam search. Rather than computing the probability of every leaf cell using equation 3, we use a stratified beam search: starting at the root cell, keep the b highest-probability cells at each level until reaching the leaf node level. With a tight beam-which we show to be very effectivethis dramatically reduces the number of model evaluations that must be performed at test time.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "Grid size parameters Two factors determine the size of the grids at each level. The first-level grid is constructed the same as for Naive Bayes or flat logistic regression and is controlled by its own parameter. In addition, the subdivision factor N determines how we subdivide each cell to get from one level to the next. Both factors must be optimized appropriately.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "For the uniform grid, we subdivide each cell into N xN subcells. In practice, there may actually be fewer subcells, because some of the potential subcells may be empty (contain no documents).",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "For the k-d grid, if level 1 is created using a bucket size B (i.e. we recursively divide cells as long as their size exceeds B), then level 2 is created by continuing to recursively divide cells that exceed a smaller bucket size B/N . At this point, the subcells of a given level-1 cell are the leaf cells contained with the cell's geographic area. The construction of level 3 proceeds similarly using bucket size B/N 2 , etc.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "Note that the subdivision factor has a different meaning for uniform and k-d tree grids. Furthermore, because creating the subdividing cells for a given cell involves dividing by N 2 for the uniform grid but N for the k-d tree grid, greater subdivision factors are generally required for the k-d tree grid to achieve similar-scale resolution. Figure 2 shows the behavior of hierarchical LR using k-d trees for the test document Pennsylvania Avenue (Washington, DC) in ENWIKI13. After ranking the first level, the beam zooms in on the top-ranked cells and constructs a finer k-d tree under each one (one such subtree is shown in the top-right map callout).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 343,
                        "end": 351,
                        "text": "Figure 2",
                        "ref_id": "FIGREF1"
                    }
                ],
                "eq_spans": [],
                "section": "Hierarchical classification",
                "sec_num": "4"
            },
            {
                "text": "Configurations. We experiment with several methods for configuring the grid and selecting the best cell. For grids, we use either a uniform or k-d tree grid. For uniform grids, the main tunable parameter is grid size (in degrees), while for k-d trees it is bucket size (BK), i.e. the number of documents above which a node is divided in two. 3) For Dirichlet smoothing in conjunction with Naive Bayes, we set the Dirichlet parameter m = 1, 000, 000, which we found worked well in preliminary experiments. For hierarchical classification, there are additional parameters: subdivision factor (SF) and beam size (BM) ( \u00a74), and hierarchy depth (D) ( \u00a76.4). All of our test-set results use a depth of three levels.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Experimental Setup",
                "sec_num": "5"
            },
            {
                "text": "Due to its speed and flexibility, we use Vowpal Wabbit (Agarwal et al., 2014) for logistic regression, estimating parameters with limited-memory BFGS (Nocedal, 1980; Byrd et al., 1995) . Unless otherwise mentioned, we use 26-bit feature hashing (Weinberger et al., 2009) and 40 passes over the data (optimized based on early experiments on development data) and turn off the hold-out mechanism. For the subcell classifiers in hierarchical classification, which have fewer classes and much less data, we use 24-bit features and 12 passes.",
                "cite_spans": [
                    {
                        "start": 55,
                        "end": 77,
                        "text": "(Agarwal et al., 2014)",
                        "ref_id": "BIBREF1"
                    },
                    {
                        "start": 150,
                        "end": 165,
                        "text": "(Nocedal, 1980;",
                        "ref_id": "BIBREF33"
                    },
                    {
                        "start": 166,
                        "end": 184,
                        "text": "Byrd et al., 1995)",
                        "ref_id": "BIBREF8"
                    },
                    {
                        "start": 245,
                        "end": 270,
                        "text": "(Weinberger et al., 2009)",
                        "ref_id": "BIBREF48"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Experimental Setup",
                "sec_num": "5"
            },
            {
                "text": "Evaluation. To measure geolocation performance, we use three standard metrics based on error distance, i.e. the distance between the correct location and the predicted location. These metrics are mean and median error distance (Eisenstein et al., 2010) and accuracy at 161 km (acc@161), i.e. within a 161-km radius, which was introduced by Cheng et al. (2010) as a proxy for accuracy within a metro area. All of these metrics are independent of cell size, unlike the measure of cell accuracy (fraction of cells correctly predicted) used in Serdyukov et al. (2009) . Following Han14, we use acc@161 on development sets when choosing algorithmic parameter values such as cell and bucket sizes.",
                "cite_spans": [
                    {
                        "start": 227,
                        "end": 252,
                        "text": "(Eisenstein et al., 2010)",
                        "ref_id": "BIBREF15"
                    },
                    {
                        "start": 540,
                        "end": 563,
                        "text": "Serdyukov et al. (2009)",
                        "ref_id": "BIBREF43"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Experimental Setup",
                "sec_num": "5"
            },
            {
                "text": "We show the effect of varying cell size in Table 1 and k-d tree bucket size in Figure 3 . The number of non-empty cells is shown for each cell size and bucket size. For NB, this is the number of cells against which a comparison must be made for each test document; for FlatLR, this is the number of classes that must be distinguished. For HierLR, no figure is given because it varies from level to level and from classifier to classifier. For example, with a uniform grid and subdivision factor of 3, each level-2 subclassifier will have between 1 and 9 labels to choose among, depending on which cells are empty. FlatLR does much better than NB and IGR, and HierLR is still better. This is despite logistic regression needing to operate at a much lower resolution. 2 Interestingly, uniform-grid 2-level Hi-erLR does better at 4 \u2022 with a subdivision factor 2 The limiting factor for resolution for us was the 24-hour per job limit on our computing cluster. Table 2 shows the test set results for the various methods and metrics described in \u00a75, on both TWUS and TWWORLD. 3 HierLR is the best across all metrics; the best acc@161km and median error is obtained with a uniform grid, while HierLR with k-d trees obtains the best mean error.",
                "cite_spans": [
                    {
                        "start": 857,
                        "end": 858,
                        "text": "2",
                        "ref_id": null
                    }
                ],
                "ref_spans": [
                    {
                        "start": 43,
                        "end": 50,
                        "text": "Table 1",
                        "ref_id": "TABREF1"
                    },
                    {
                        "start": 79,
                        "end": 87,
                        "text": "Figure 3",
                        "ref_id": "FIGREF2"
                    },
                    {
                        "start": 957,
                        "end": 964,
                        "text": "Table 2",
                        "ref_id": "TABREF3"
                    }
                ],
                "eq_spans": [],
                "section": "Twitter",
                "sec_num": "6.1"
            },
            {
                "text": "Compared with vanilla NB, our implementation of NB using IGR feature selection obtains large gains for TWUS and moderate gains for TWWORLD, showing that IGR can be an effective geolocation method for Twitter. This agrees in general with Han14's findings. We can only compare our figures directly with Han14 for k-d trees-in this case they use a version of the same software we use and report figures within 1% of ours for TWUS. Their remaining results are computed using a city-based grid and an NB implementation with add-one smoothing, and are significantly worse than our uniform-grid NB and IGR figures using Dirichlet smoothing, which is known to significantly outperform add-one smoothing (Smucker and Allan, 2006) . For example, for NB they report 30.8% acc@161 for TWUS and 20.0% for TWWORLD, compared with our 36.2% and 30.2% respectively. We suspect an additional reason for the discrepancy is due to the limitations of their city-based grid, which has no tunable parameter to optimize the grid size and requires that test instances not near a city be reported as incorrect.",
                "cite_spans": [
                    {
                        "start": 695,
                        "end": 720,
                        "text": "(Smucker and Allan, 2006)",
                        "ref_id": "BIBREF47"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Twitter",
                "sec_num": "6.1"
            },
            {
                "text": "Our ference in smoothing methods. Table 3 shows results on the test set of ENWIKI13 for various methods. Table 5 shows the corresponding results for DEWIKI14 and PTWIKI14. In all cases, the best parameters for each method were determined using acc@161 on the development set, as above. HierLR is clearly the stand-out winner among all methods and metrics, and particularly so for the k-d tree grid. This is achieved through a high subdivision factor, especially in a 2-level hierarchy, where a factor of 36 is best, as shown in Figure 4 for ENWIKI13. (For a 3-level hierarchy, the best subdivision factor is 12.)",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 34,
                        "end": 41,
                        "text": "Table 3",
                        "ref_id": "TABREF7"
                    },
                    {
                        "start": 105,
                        "end": 112,
                        "text": "Table 5",
                        "ref_id": "TABREF9"
                    },
                    {
                        "start": 528,
                        "end": 536,
                        "text": "Figure 4",
                        "ref_id": "FIGREF3"
                    }
                ],
                "eq_spans": [],
                "section": "Twitter",
                "sec_num": "6.1"
            },
            {
                "text": "Unlike for TWUS, FlatLR simply cannot com- pete with NB in the larger Wikipedias (ENWIKI13 and DEWIKI14). ENWIKI13 especially has dense coverage across the entire world, whereas TWUS only covers the United States and parts of Canada and Mexico. Thus, there are a much larger number of non-empty cells at a given resolution and much coarser resolution required, especially with the uniform grid. For example, at 7.5 \u2022 there are 933 non-empty cells, comparable to 1 \u2022 for TWUS. Table 4 shows the number of classes and runtime for FlatLR and HierLR at different parameter values. The hierarchical classification approach is clearly essential for allowing us to scale the discriminative approach for a large, dense dataset across the whole world.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 476,
                        "end": 483,
                        "text": "Table 4",
                        "ref_id": "TABREF5"
                    }
                ],
                "eq_spans": [],
                "section": "Wikipedia",
                "sec_num": "6.2"
            },
            {
                "text": "Moving from larger to smaller Wikipedias, FlatLR becomes more competitive. In particular, FlatLR outperforms NB and is close to HierLR for PTWIKI14, the smallest of the three (and significantly smaller than TWUS). In this case, the relatively small size of the dataset and its greater geographic specificity (many articles are located in Brazil or Portugal) allows for a fine enough resolution to make FlatLR perform well-comparable to or even finer than NB.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Wikipedia",
                "sec_num": "6.2"
            },
            {
                "text": "In all of the Wikipedias, NB k-d outperforms older English Wikipedia corpus were are noticeably higher than our figures: They report 90.3% acc@161, compared with our 84.5%. We verified that this is due to corpus differences: we obtain their performance when we run on their Wikipedia corpus. This suggests that the various differences may be due to vagaries of the individual corpora, e.g. the presence of differing numbers of geotagged stub articles, which are very short and thus hard to geolocate. As for IGR, though it is competitive for Twitter, it performs badly here-in fact, it is even worse than plain Naive Bayes for all three Wikipedias (likewise for COPHIR, in the next section). Table 3 shows results on the test set of COPHIR for various methods, similarly to the ENWIKI13 results. HierLR is again the clear winner. Unlike for ENWIKI13, FlatLR is able to do fairly well. IGR performs poorly, especially when combined with k-d.",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 692,
                        "end": 699,
                        "text": "Table 3",
                        "ref_id": "TABREF7"
                    }
                ],
                "eq_spans": [],
                "section": "Wikipedia",
                "sec_num": "6.2"
            },
            {
                "text": "In general, as can be seen, for COPHIR the median figures are very low but the mean figures very high, meaning there are many images that can be very accurately placed while the remainder are very difficult to place. (The former images likely have the location mentioned in the tags, while the latter do not.)",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "CoPhIR",
                "sec_num": "6.3"
            },
            {
                "text": "For COPHIR, and also TWWORLD, HierLR performs best when the root level is significantly coarser than the cell or bucket size that is best for FlatLR. The best setting for the root level appears to be correlated with cell accuracy, which in general increases with larger cell sizes. The intuition here is that HierLR works by drilling down from a single top-level child of the root cell. Thus, the higher the cell accuracy, the greater the fraction of test instances that can be improved in this fashion, and in general the better the ultimate values of the main metrics. (The above discussion isn't strictly true for beam sizes above 1, but these tend to produce marginal improvements, with little if any gain from going above a beam size of 5.) The large size of a coarse root-child cell, and correspondingly poor results for acc@161, can be offset by a high subdivision factor, which does not materially slow down the training process.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "CoPhIR",
                "sec_num": "6.3"
            },
            {
                "text": "Our NB results are not directly comparable with OM13's results on COPHIR because they use various cell-based accuracy metrics while we use cell-size-independent metrics. The closest to our acc@161 metric is their Ac1 metric, which at a cell size of 100 km corresponds to a 300km-perside square at the equator, roughly comparable to our 161-km-radius circle. They report Ac1 figures of 57.7% for term frequency and 65.3% for user frequency, which counts the number of distinct users in a cell using a given term and is intended to offset bias resulting from users who upload a large batch of similar photos at a given location. Our term frequency figure of 65.0% significantly beats theirs, but we found that user frequency actually degraded our dev set results by 5%. The reason for this discrepancy is unclear.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "CoPhIR",
                "sec_num": "6.3"
            },
            {
                "text": "Optimizing for median. Note that better values for the other metrics, especially median, can be achieved by specifically optimizing for these metrics. In general, the best parameters for median are finer-scale than those for acc@161: smaller grid sizes and bucket sizes, and greater subdivision factors. This is especially revealing in ENWIKI13 and COPHIR. For example, on the ENWIKI13 Hierarchy depth. We use a 3-level hierarchy throughout for the test set results. Evaluation on development data showed that 2-level hierarchies perform comparably for several data sets, but are less effective overall. We did not find improvements from using more than three levels. When using a simple local classifier per parent approach as we do, which chains together spines of related but independently trained classifiers when assigning a probability to a leaf cell, most of the benefit presumably comes from simply enabling logistic regression to be used with fine-grained leaf cells, overcoming the limitations of FlatLR. Further benefits of the hierarchical approach might be achieved with the data-biasing and bottom-up error propagation techniques of Bennett and Nguyen (2009) or the hierarchical Bayesian approach of Gopal et al. (2012) , which is able to handle largescale corpora and thousands of classes.",
                "cite_spans": [
                    {
                        "start": 1147,
                        "end": 1172,
                        "text": "Bennett and Nguyen (2009)",
                        "ref_id": "BIBREF5"
                    },
                    {
                        "start": 1214,
                        "end": 1233,
                        "text": "Gopal et al. (2012)",
                        "ref_id": "BIBREF18"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Parameterization variations",
                "sec_num": "6.4"
            },
            {
                "text": "The main focus of Han14 is identifying geographically salient words through feature selection. Logistic regression performs feature selection naturally by assigning higher weights to features that better discriminate among the target classes. Table 6 shows the top 20 features ranked by feature weight for a number of different cells, labeled by the largest city in the cell. The features were produced using a uniform 5 \u2022 grid, trained using 27-bit features and 40 passes over TWUS. The high number of bits per feature were chosen to ensure as few collisions as possible of different features (as it would be impossible to distinguish two words that were hashed together).",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 243,
                        "end": 250,
                        "text": "Table 6",
                        "ref_id": "TABREF13"
                    }
                ],
                "eq_spans": [],
                "section": "Feature Selection",
                "sec_num": "6.5"
            },
            {
                "text": "Most words are clearly region specific, consisting of cities, states and abbreviations, sports teams (broncos, texans, niners, saints), wellknown streets (bourbon, folsom), characteristic features (desert, bayou, earthquake, temple), local brands (whataburger, soopers, heb), local foods (gumbo, poutine), and dialect terms (hella, buku). Angeles  utah  sacramento  orleans  tucson  denver  houston  montreal  seattle  tulsa  knotts  slc  hella  jtfo  az  colorado  antonio  mtl  portland  okc  sd  salt  sac  prelaw  phoenix  broncos  texans  quebec  tacoma  oklahoma pasadena  byu  niners  saints  arizona  aurora  sa  magrib  wa  wichita  diego  provo  berkeley  louisiana  asu  amarillo  corpus  rue  vancouver ou  ucla  ut  safeway  bourbon  tempe  soopers  whataburger habs  bellevue  kansas  disneyland  utes  oakland  kmsl  scottsdale colfax  heb  canadian  oregon  ku  irvine which have geographic significance, while the bottom words are quite common. To some extent this is a feature of IGR, since it divides by the binary entropy of each word, which is directly related to its frequency. However, it shows why cutoffs around 90% of the original feature set are necessary to achieve good performance on the Twitter corpora. (IGR does not perform well on Wikipedia or COPHIR, as shown above.)",
                "cite_spans": [],
                "ref_spans": [
                    {
                        "start": 339,
                        "end": 884,
                        "text": "Angeles  utah  sacramento  orleans  tucson  denver  houston  montreal  seattle  tulsa  knotts  slc  hella  jtfo  az  colorado  antonio  mtl  portland  okc  sd  salt  sac  prelaw  phoenix  broncos  texans  quebec  tacoma  oklahoma pasadena  byu  niners  saints  arizona  aurora  sa  magrib  wa  wichita  diego  provo  berkeley  louisiana  asu  amarillo  corpus  rue  vancouver ou  ucla  ut  safeway  bourbon  tempe  soopers  whataburger habs  bellevue  kansas  disneyland  utes  oakland  kmsl  scottsdale colfax  heb  canadian  oregon  ku  irvine",
                        "ref_id": null
                    }
                ],
                "eq_spans": [],
                "section": "Feature Selection",
                "sec_num": "6.5"
            },
            {
                "text": "This paper demonstrates that major performance improvements to geolocation based only on text can be obtained by using a hierarchy of logistic regression classifiers. Logistic regression also allows for the use of complex, interdependent features, beyond the simple unigram models commonly employed. Our preliminary experiments did not show noticeable improvements from bigram or character-based features, but it is possible that higher-level features such as morphological, part-of-speech or syntactic features could yield further performance gains. And, of course, these improved text-based models may help decrease error even further when metadata (e.g. time zone and declared location) are available. An interesting extension of this work is to rely upon the natural clustering of related documents. Joint modeling of geographic topics and locations has been attempted (see \u00a71), but has generally been applied to much smaller corpora than those considered here. Skiles (2012) found sig-nificant improvements by clustering the training documents of large-scale corpora using K-means, training separate models from each cluster, and estimating a test document's location with the cluster model returning the best overall similarity (e.g. through KL divergence). Bergsma et al. (2013) likewise cluster tweets using K-means but predict location only at the country level. Such methods could be combined with hierarchical classification to yield further gains.",
                "cite_spans": [
                    {
                        "start": 966,
                        "end": 979,
                        "text": "Skiles (2012)",
                        "ref_id": "BIBREF45"
                    },
                    {
                        "start": 1264,
                        "end": 1285,
                        "text": "Bergsma et al. (2013)",
                        "ref_id": "BIBREF6"
                    }
                ],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Conclusion",
                "sec_num": "7"
            },
            {
                "text": "https://github.com/utcompling/ textgrounder/wiki/WingBaldridge_ EMNLP2014",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            },
            {
                "text": "Note that for TWWORLD, it was necessary to modify the parameters normally passed to Vowpal Wabbit, moving up to 27-bit features and 96 passes, and 24-bit features with 24 passes in sublevels of HierLR.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "",
                "sec_num": null
            }
        ],
        "back_matter": [
            {
                "text": "We would like to thank Grant Delozier for assistance in generating choropleth graphs, and the three anonymous reviewers for their feedback. This research was supported by a grant from the Morris Memorial Trust Fund of the New York Community Trust.",
                "cite_spans": [],
                "ref_spans": [],
                "eq_spans": [],
                "section": "Acknowledgments",
                "sec_num": null
            }
        ],
        "bib_entries": {
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        "ref_entries": {
            "FIGREF0": {
                "text": "Relative Naive Bayes rank of cells for ENWIKI13 test document Pennsylvania Avenue (Washington, DC), surrounding the true location.",
                "num": null,
                "type_str": "figure",
                "uris": null
            },
            "FIGREF1": {
                "text": "Relative hierarchical LR rank of cells for ENWIKI13 test document Pennsylvania Avenue (Washington, DC), surrounding the true location. The first callout simply expands a portion of level 1, while the second callout shows a level 1 cell subdivided down to level 2. For cell choice, the options are: \u2022 NB: Naive Bayes baseline \u2022 IGR: Naive Bayes using features selected by information gain ratio \u2022 FlatLR: logistic regression model over all leaf nodes \u2022 HierLR: product of logistic regression models at each node in a hierarchical grid (eq.",
                "num": null,
                "type_str": "figure",
                "uris": null
            },
            "FIGREF2": {
                "text": "Dev set performance for TWUS, with k-d tree grids. of 2 than the equivalent FlatLR run at 2 \u2022 .",
                "num": null,
                "type_str": "figure",
                "uris": null
            },
            "FIGREF3": {
                "text": "Plot of subdivision factor vs. acc@161 for the ENWIKI13 dev set with 2-level k-d tree HierLR, bucket size 1500. Beam sizes above 2 yield little improvement.",
                "num": null,
                "type_str": "figure",
                "uris": null
            },
            "TABREF1": {
                "num": null,
                "content": "<table><tr><td>: Dev set performance for TWUS, with</td></tr><tr><td>uniform grids. HierLR and IGR parameters op-</td></tr><tr><td>timized using acc@161. Best metric numbers for</td></tr><tr><td>a given method are underlined, except that overall</td></tr><tr><td>best numbers are in bold.</td></tr></table>",
                "type_str": "table",
                "text": "",
                "html": null
            },
            "TABREF3": {
                "num": null,
                "content": "<table/>",
                "type_str": "table",
                "text": "Performance on the test sets of TWUS and TWWORLD for different methods and metrics.",
                "html": null
            },
            "TABREF5": {
                "num": null,
                "content": "<table/>",
                "type_str": "table",
                "text": "Performance/runtime for FlatLR and 3level HierLR on the ENWIKI13 dev set, with varying parameters.",
                "html": null
            },
            "TABREF7": {
                "num": null,
                "content": "<table><tr><td>NB uniform, and HierLR outperforms both, but</td></tr><tr><td>by greatly varying amounts, with only a 1% differ-</td></tr><tr><td>ence for DEWIKI14 but 12% for PTWIKI14. It's</td></tr><tr><td>unclear what causes these variations, although it's</td></tr><tr><td>worth noting that Roller12's NB k-d figures on an</td></tr></table>",
                "type_str": "table",
                "text": "Performance on the test sets of ENWIKI13 and COPHIR for different methods and metrics.",
                "html": null
            },
            "TABREF9": {
                "num": null,
                "content": "<table><tr><td>dev set, the \"best\" uniform NB parameter of 1.5 \u2022 ,</td></tr><tr><td>as optimized on acc@161, yields a median error</td></tr><tr><td>of 56.1 km, but an error of just 16.7 km can be</td></tr><tr><td>achieved with the parameter setting 0.25 \u2022 (which,</td></tr><tr><td>however, drops acc@161 from 83.8% to 78.3%</td></tr><tr><td>in the process). Similarly, for the COPHIR dev</td></tr><tr><td>set, the optimized uniform 2-level HierLR median</td></tr><tr><td>error of 46.6 km can be reduced to just 8.1 km</td></tr><tr><td>by dropping from 7 \u2022 to 3.5 \u2022 and bumping up the</td></tr><tr><td>subdivision factor from 4 to 35-again, causing a</td></tr><tr><td>drop in acc@161 from 68.6% to 65.5%.</td></tr></table>",
                "type_str": "table",
                "text": "Performance on the test sets of DEWIKI14 and PTWIKI14 for different methods and metrics.",
                "html": null
            },
            "TABREF11": {
                "num": null,
                "content": "<table><tr><td>Salt Lake San Francisco New Orleans Phoenix</td><td>Denver</td><td>Houston</td><td>Montreal</td><td>Seattle</td><td>Tulsa</td><td>Los</td></tr></table>",
                "type_str": "table",
                "text": "Top and bottom 40 features selected using IGR for TWUS with a uniform 1.5 \u2022 grid.As a comparison,Table 7shows the top and bottom 40 features selected using IGR on the same corpus. Unlike for logistic regression, the top IGR features are mostly obscure words, only some of",
                "html": null
            },
            "TABREF13": {
                "num": null,
                "content": "<table/>",
                "type_str": "table",
                "text": "Top 20 features selected for various regions using logistic regression on TWUS with a uniform 5",
                "html": null
            }
        }
    }
}