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Cluster analysis : Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task of exploratory data analys... |
Cluster analysis : The notion of a "cluster" cannot be precisely defined, which is one of the reasons why there are so many clustering algorithms. There is a common denominator: a group of data objects. However, different researchers employ different cluster models, and for each of these cluster models again different ... |
Cluster analysis : As listed above, clustering algorithms can be categorized based on their cluster model. The following overview will only list the most prominent examples of clustering algorithms, as there are possibly over 100 published clustering algorithms. Not all provide models for their clusters and can thus no... |
Cluster analysis : Evaluation (or "validation") of clustering results is as difficult as the clustering itself. Popular approaches involve "internal" evaluation, where the clustering is summarized to a single quality score, "external" evaluation, where the clustering is compared to an existing "ground truth" classifica... |
Archetypal analysis : Archetypal analysis in statistics is an unsupervised learning method similar to cluster analysis and introduced by Adele Cutler and Leo Breiman in 1994. Rather than "typical" observations (cluster centers), it seeks extremal points in the multidimensional data, the "archetypes". The archetypes are... |
Archetypal analysis : Adele Cutler and Leo Breiman. Archetypal analysis. Technometrics, 36(4):338–347, November 1994. Manuel J. A. Eugster: Archetypal Analysis, Mining the Extreme. HIIT seminar, Helsinki Institute for Information Technology, 2012 Anil Damle, Yuekai Sun: A geometric approach to archetypal analysis and n... |
Behavioral clustering : Behavioral clustering is a statistical analysis method used in retailing to identify consumer purchase trends and group stores based on consumer buying behaviors. |
Behavioral clustering : Erickson, D., and Weber, W. (2009). "Five Pitfalls To Avoid When Clustering". Chain Store Age.: CS1 maint: multiple names: authors list (link) |
Behavioral clustering : Behavioural Clustering 101: Here's What You Need To Know Personalize Content on Your Website with Behavioral Clustering A two-step segmentation algorithm for behavioral clustering of naturalistic driving styles |
Biclustering : Biclustering, block clustering, Co-clustering or two-mode clustering is a data mining technique which allows simultaneous clustering of the rows and columns of a matrix. The term was first introduced by Boris Mirkin to name a technique introduced many years earlier, in 1972, by John A. Hartigan. Given a ... |
Biclustering : Biclustering was originally introduced by John A. Hartigan in 1972. The term "Biclustering" was then later used and refined by Boris G. Mirkin. This algorithm was not generalized until 2000, when Y. Cheng and George M. Church proposed a biclustering algorithm based on the mean squared residue score (MSR)... |
Biclustering : The complexity of the Biclustering problem depends on the exact problem formulation, and particularly on the merit function used to evaluate the quality of a given Bicluster. However, the most interesting variants of this problem are NP-complete. NP-complete has two conditions. In the simple case that th... |
Biclustering : Bicluster with constant values (a) When a Biclustering algorithm tries to find a constant-value Bicluster, it reorders the rows and columns of the matrix to group together similar rows and columns, eventually grouping Biclusters with similar values. This method is sufficient when the data is normalized. ... |
Biclustering : There are many Biclustering algorithms developed for bioinformatics, including: block clustering, CTWC (Coupled Two-Way Clustering), ITWC (Interrelated Two-Way Clustering), δ-bicluster, δ-pCluster, δ-pattern, FLOC, OPC, Plaid Model, OPSMs (Order-preserving submatrixes), Gibbs, SAMBA (Statistical-Algorith... |
Biclustering : Formal concept analysis Biclique Galois connection |
Biclustering : FABIA: Factor Analysis for Bicluster Acquisition, an R package —software |
Calinski–Harabasz index : The Calinski–Harabasz index (CHI), also known as the Variance Ratio Criterion (VRC), is a metric for evaluating clustering algorithms, introduced by Tadeusz Caliński and Jerzy Harabasz in 1974. It is an internal evaluation metric, where the assessment of the clustering quality is based solely ... |
Calinski–Harabasz index : Given a data set of n points: , and the assignment of these points to k clusters: , the Calinski–Harabasz (CH) Index is defined as the ratio of the between-cluster separation (BCSS) to the within-cluster dispersion (WCSS), normalized by their number of degrees of freedom: C H = B C S S / ( k −... |
Calinski–Harabasz index : The numerator of the CH index is the between-cluster separation (BCSS) divided by its degrees of freedom. The number of degrees of freedom of BCSS is k - 1, since fixing the centroids of k - 1 clusters also determines the kth centroid, as its value makes the weighted sum of all centroids match... |
Calinski–Harabasz index : Similar to other clustering evaluation metrics such as Silhouette score, the CH index can be used to find the optimal number of clusters k in algorithms like k-means, where the value of k is not known a priori. This can be done by following these steps: Perform clustering for different values ... |
Calinski–Harabasz index : The scikit-learn Python library provides an implementation of this metric in the sklearn.metrics module. R provides a similar implementation in its fpc package. |
Calinski–Harabasz index : Cluster analysis Silhouette score Davies–Bouldin index Dunn index == References == |
Clustering high-dimensional data : Clustering high-dimensional data is the cluster analysis of data with anywhere from a few dozen to many thousands of dimensions. Such high-dimensional spaces of data are often encountered in areas such as medicine, where DNA microarray technology can produce many measurements at once,... |
Clustering high-dimensional data : Four problems need to be overcome for clustering in high-dimensional data: Multiple dimensions are hard to think in, impossible to visualize, and, due to the exponential growth of the number of possible values with each dimension, complete enumeration of all subspaces becomes intracta... |
Clustering high-dimensional data : Approaches towards clustering in axis-parallel or arbitrarily oriented affine subspaces differ in how they interpret the overall goal, which is finding clusters in data with high dimensionality. An overall different approach is to find clusters based on pattern in the data matrix, oft... |
Clustering high-dimensional data : ELKI includes various subspace and correlation clustering algorithms FCPS includes over fifty clustering algorithms == References == |
Clustering illusion : The clustering illusion is the tendency to erroneously consider the inevitable "streaks" or "clusters" arising in small samples from random distributions to be non-random. The illusion is caused by a human tendency to underpredict the amount of variability likely to appear in a small sample of ran... |
Clustering illusion : Using this cognitive bias in causal reasoning may result in the Texas sharpshooter fallacy, in which differences in data are ignored and similarities are overemphasized. More general forms of erroneous pattern recognition are pareidolia and apophenia. Related biases are the illusion of control whi... |
Clustering illusion : Daniel Kahneman and Amos Tversky explained this kind of misprediction as being caused by the representativeness heuristic (which itself they also first proposed). |
Clustering illusion : Apophenia Alignments of random points Complete spatial randomness Confirmation bias List of cognitive biases Numeracy bias Poisson distribution Statistical randomness |
Clustering illusion : Skeptic's Dictionary: The clustering illusion Hot Hand website: Statistical analysis of sports streakiness |
Consensus clustering : Consensus clustering is a method of aggregating (potentially conflicting) results from multiple clustering algorithms. Also called cluster ensembles or aggregation of clustering (or partitions), it refers to the situation in which a number of different (input) clusterings have been obtained for a... |
Consensus clustering : Current clustering techniques do not address all the requirements adequately. Dealing with large number of dimensions and large number of data items can be problematic because of time complexity; Effectiveness of the method depends on the definition of "distance" (for distance-based clustering) I... |
Consensus clustering : There are potential shortcomings for all existing clustering techniques. This may cause interpretation of results to become difficult, especially when there is no knowledge about the number of clusters. Clustering methods are also very sensitive to the initial clustering settings, which can cause... |
Consensus clustering : The Monti consensus clustering algorithm is one of the most popular consensus clustering algorithms and is used to determine the number of clusters, K . Given a dataset of N total number of points to cluster, this algorithm works by resampling and clustering the data, for each K and a N × N c... |
Consensus clustering : Monti consensus clustering can be a powerful tool for identifying clusters, but it needs to be applied with caution as shown by Şenbabaoğlu et al. It has been shown that the Monti consensus clustering algorithm is able to claim apparent stability of chance partitioning of null datasets drawn from... |
Consensus clustering : Clustering ensemble (Strehl and Ghosh): They considered various formulations for the problem, most of which reduce the problem to a hyper-graph partitioning problem. In one of their formulations they considered the same graph as in the correlation clustering problem. The solution they proposed is... |
Consensus clustering : This approach by Strehl and Ghosh introduces the problem of combining multiple partitionings of a set of objects into a single consolidated clustering without accessing the features or algorithms that determined these partitionings. They discuss three approaches towards solving this problem to ob... |
Consensus clustering : Punera and Ghosh extended the idea of hard clustering ensembles to the soft clustering scenario. Each instance in a soft ensemble is represented by a concatenation of r posterior membership probability distributions obtained from the constituent clustering algorithms. We can define a distance mea... |
Consensus clustering : Aristides Gionis, Heikki Mannila, Panayiotis Tsaparas. Clustering Aggregation. 21st International Conference on Data Engineering (ICDE 2005) Hongjun Wang, Hanhuai Shan, Arindam Banerjee. Bayesian Cluster Ensembles, SIAM International Conference on Data Mining, SDM 09 Nguyen, Nam; Caruana, Rich (2... |
Constrained clustering : In computer science, constrained clustering is a class of semi-supervised learning algorithms. Typically, constrained clustering incorporates either a set of must-link constraints, cannot-link constraints, or both, with a data clustering algorithm. A cluster in which the members conform to all ... |
Constrained clustering : Both a must-link and a cannot-link constraint define a relationship between two data instances. Together, the sets of these constraints act as a guide for which a constrained clustering algorithm will attempt to find chunklets (clusters in the dataset which satisfy the specified constraints). A... |
Constrained clustering : Examples of constrained clustering algorithms include: COP K-means PCKmeans (Pairwise Constrained K-means) CMWK-Means (Constrained Minkowski Weighted K-Means) == References == |
Correlation clustering : Clustering is the problem of partitioning data points into groups based on their similarity. Correlation clustering provides a method for clustering a set of objects into the optimum number of clusters without specifying that number in advance. |
Correlation clustering : In machine learning, correlation clustering or cluster editing operates in a scenario where the relationships between the objects are known instead of the actual representations of the objects. For example, given a weighted graph G = ( V , E ) where the edge weight indicates whether two nodes ... |
Correlation clustering : Let G = ( V , E ) be a graph with nodes V and edges E . A clustering of G is a partition of its node set Π = ,\dots ,\pi _\ with V = π 1 ∪ ⋯ ∪ π k \cup \dots \cup \pi _ and π i ∩ π j = ∅ \cap \pi _=\emptyset for i ≠ j . For a given clustering Π , let δ ( Π ) = ∈ E ∣ ⊈ π ∀ π ∈ Π \in E... |
Correlation clustering : Bansal et al. discuss the NP-completeness proof and also present both a constant factor approximation algorithm and polynomial-time approximation scheme to find the clusters in this setting. Ailon et al. propose a randomized 3-approximation algorithm for the same problem. CC-Pivot(G=(V,E+,E−)) ... |
Correlation clustering : In 2011, it was shown by Bagon and Galun that the optimization of the correlation clustering functional is closely related to well known discrete optimization methods. In their work they proposed a probabilistic analysis of the underlying implicit model that allows the correlation clustering fu... |
Correlation clustering : Correlation clustering also relates to a different task, where correlations among attributes of feature vectors in a high-dimensional space are assumed to exist guiding the clustering process. These correlations may be different in different clusters, thus a global decorrelation cannot reduce t... |
Dendrogram : A dendrogram is a diagram representing a tree. This diagrammatic representation is frequently used in different contexts: in hierarchical clustering, it illustrates the arrangement of the clusters produced by the corresponding analyses. in computational biology, it shows the clustering of genes or samples,... |
Dendrogram : For a clustering example, suppose that five taxa ( a to e ) have been clustered by UPGMA based on a matrix of genetic distances. The hierarchical clustering dendrogram would show a column of five nodes representing the initial data (here individual taxa), and the remaining nodes represent the clusters to... |
Dendrogram : Cladogram Distance matrices in phylogeny Hierarchical clustering MEGA, a freeware for drawing dendrograms yEd, a freeware for drawing and automatically arranging dendrograms Taxonomy |
Dendrogram : Iris dendrogram - Example of using a dendrogram to visualize the 3 clusters from hierarchical clustering using the "complete" method vs the real species category (using R). |
Determining the number of clusters in a data set : Determining the number of clusters in a data set, a quantity often labelled k as in the k-means algorithm, is a frequent problem in data clustering, and is a distinct issue from the process of actually solving the clustering problem. For a certain class of clustering a... |
Determining the number of clusters in a data set : The elbow method looks at the percentage of explained variance as a function of the number of clusters: One should choose a number of clusters so that adding another cluster does not give much better modeling of the data. More precisely, if one plots the percentage of ... |
Determining the number of clusters in a data set : In statistics and data mining, X-means clustering is a variation of k-means clustering that refines cluster assignments by repeatedly attempting subdivision, and keeping the best resulting splits, until a criterion such as the Akaike information criterion (AIC) or Baye... |
Determining the number of clusters in a data set : Another set of methods for determining the number of clusters are information criteria, such as the Akaike information criterion (AIC), Bayesian information criterion (BIC), or the deviance information criterion (DIC) — if it is possible to make a likelihood function f... |
Determining the number of clusters in a data set : Rate distortion theory has been applied to choosing k called the "jump" method, which determines the number of clusters that maximizes efficiency while minimizing error by information-theoretic standards. The strategy of the algorithm is to generate a distortion curve ... |
Determining the number of clusters in a data set : The average silhouette of the data is another useful criterion for assessing the natural number of clusters. The silhouette of a data instance is a measure of how closely it is matched to data within its cluster and how loosely it is matched to data of the neighboring ... |
Determining the number of clusters in a data set : One can also use the process of cross-validation to analyze the number of clusters. In this process, the data is partitioned into v parts. Each of the parts is then set aside at turn as a test set, a clustering model computed on the other v − 1 training sets, and the v... |
Determining the number of clusters in a data set : When clustering text databases with the cover coefficient on a document collection defined by a document by term D matrix (of size m×n, where m is the number of documents and n is the number of terms), the number of clusters can roughly be estimated by the formula m n ... |
Determining the number of clusters in a data set : Kernel matrix defines the proximity of the input information. For example, in Gaussian radial basis function, it determines the dot product of the inputs in a higher-dimensional space, called feature space. It is believed that the data become more linearly separable in... |
Determining the number of clusters in a data set : Robert Tibshirani, Guenther Walther, and Trevor Hastie proposed estimating the number of clusters in a data set via the gap statistic. The gap statistics, based on theoretical grounds, measures how far is the pooled within-cluster sum of squares around the cluster cent... |
Determining the number of clusters in a data set : Clustergram – cluster diagnostic plot – for visual diagnostics of choosing the number of (k) clusters (R code) Eight methods for determining an optimal k value for k-means analysis – Answer on stackoverflow containing R code for several methods of computing an optimal ... |
Farthest-first traversal : In computational geometry, the farthest-first traversal of a compact metric space is a sequence of points in the space, where the first point is selected arbitrarily and each successive point is as far as possible from the set of previously-selected points. The same concept can also be applie... |
Farthest-first traversal : A farthest-first traversal is a sequence of points in a compact metric space, with each point appearing at most once. If the space is finite, each point appears exactly once, and the traversal is a permutation of all of the points in the space. The first point of the sequence may be any point... |
Farthest-first traversal : Rosenkrantz, Stearns & Lewis (1977) used the farthest-first traversal to define the farthest-insertion heuristic for the travelling salesman problem. This heuristic finds approximate solutions to the travelling salesman problem by building up a tour on a subset of points, adding one point at ... |
Farthest-first traversal : Lloyd's algorithm, a different method for generating evenly spaced points in geometric spaces == References == |
Frequent pattern discovery : Frequent pattern discovery (or FP discovery, FP mining, or Frequent itemset mining) is part of knowledge discovery in databases, Massive Online Analysis, and data mining; it describes the task of finding the most frequent and relevant patterns in large datasets. The concept was first introd... |
Frequent pattern discovery : Techniques for FP mining include: market basket analysis cross-marketing catalog design clustering classification recommendation systems For the most part, FP discovery can be done using association rule learning with particular algorithms Eclat, FP-growth and the Apriori algorithm. Other s... |
Geographical cluster : A geographical cluster is a localized anomaly, usually an excess of something given the distribution or variation of something else. Often it is considered as an incidence rate that is unusual in that there is more of some variable than might be expected. Examples would include: a local excess di... |
Geographical cluster : Identifying geographical clusters can be an important stage in a geographical analysis. Mapping the locations of unusual concentrations may help identify causes of these. Some techniques include the Geographical Analysis Machine and Besag and Newell's cluster detection method. == References == |
GeWorkbench : geWorkbench (genomics Workbench) is an open-source software platform for integrated genomic data analysis. It is a desktop application written in the programming language Java. geWorkbench uses a component architecture. As of 2016, there are more than 70 plug-ins available, providing for the visualization... |
GeWorkbench : Computational analysis tools such as t-test, hierarchical clustering, self-organizing maps, regulatory network reconstruction, BLAST searches, pattern-motif discovery, protein structure prediction, structure-based protein annotation, etc. Visualization of gene expression (heatmaps, volcano plot), molecula... |
GeWorkbench : geWorkbench is open-source software that can be downloaded and installed locally. A zip file of the released version Java source is also available. Prepackaged installer versions also exist for Windows, Macintosh, and Linux. |
GeWorkbench : Official website, includes installation, tutorials, FAQs, known issues - geworkbench release downloads - geWorkbench plugins |
Latent space : A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge ... |
Latent space : Several embedding models have been developed to perform this transformation to create latent space embeddings given a set of data items and a similarity function. These models learn the embeddings by leveraging statistical techniques and machine learning algorithms. Here are some commonly used embedding ... |
Latent space : Multimodality refers to the integration and analysis of multiple modes or types of data within a single model or framework. Embedding multimodal data involves capturing relationships and interactions between different data types, such as images, text, audio, and structured data. Multimodal embedding mode... |
Latent space : Embedding latent space and multimodal embedding models have found numerous applications across various domains: Information retrieval: Embedding techniques enable efficient similarity search and recommendation systems by representing data points in a compact space. Natural language processing: Word embed... |
Latent space : == References == |
Medoid : Medoids are representative objects of a data set or a cluster within a data set whose sum of dissimilarities to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on dat... |
Medoid : Let X := :=\,x_,\dots ,x_\ be a set of n points in a space with a distance function d. Medoid is defined as x medoid = arg min y ∈ X ∑ i = 1 n d ( y , x i ) . =\arg \min _\sum _^d(y,x_). |
Medoid : Medoids are a popular replacement for the cluster mean when the distance function is not (squared) Euclidean distance, or not even a metric (as the medoid does not require the triangle inequality). When partitioning the data set into clusters, the medoid of each cluster can be used as a representative of each ... |
Medoid : From the definition above, it is clear that the medoid of a set X can be computed after computing all pairwise distances between points in the ensemble. This would take O ( n 2 ) ) distance evaluations (with n = | X | | ). In the worst case, one can not compute the medoid with fewer distance evaluations. Howe... |
Medoid : An implementation of RAND, TOPRANK, and trimed can be found here. An implementation of Meddit can be found here and here. An implementation of Correlated Sequential Halving can be found here. |
Medoid : Medoids can be applied to various text and NLP tasks to improve the efficiency and accuracy of analyses. By clustering text data based on similarity, medoids can help identify representative examples within the dataset, leading to better understanding and interpretation of the data. |
Medoid : As a versatile clustering method, medoids can be applied to a variety of real-world issues in numerous fields, stretching from biology and medicine to advertising and marketing, and social networks. Its potential to handle complex data sets with a high degree of perplexity makes it a powerful device in modern-... |
Medoid : A common problem with k-medoids clustering and other medoid-based clustering algorithms is the "curse of dimensionality," in which the data points contain too many dimensions or features. As dimensions are added to the data, the distance between them becomes sparse, and it becomes difficult to characterize clu... |
Medoid : StatQuest k-means video used for visual reference in #Visualization_of_the_medoid-based_clustering_process section |
Mixture model : In statistics, a mixture model is a probabilistic model for representing the presence of subpopulations within an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to the mix... |
Mixture model : Identifiability refers to the existence of a unique characterization for any one of the models in the class (family) being considered. Estimation procedures may not be well-defined and asymptotic theory may not hold if a model is not identifiable. |
Mixture model : Parametric mixture models are often used when we know the distribution Y and we can sample from X, but we would like to determine the ai and θi values. Such situations can arise in studies in which we sample from a population that is composed of several distinct subpopulations. It is common to think of ... |
Mixture model : In a Bayesian setting, additional levels can be added to the graphical model defining the mixture model. For example, in the common latent Dirichlet allocation topic model, the observations are sets of words drawn from D different documents and the K mixture components represent topics that are shared a... |
Mixture model : Mixture distributions and the problem of mixture decomposition, that is the identification of its constituent components and the parameters thereof, has been cited in the literature as far back as 1846 (Quetelet in McLachlan, 2000) although common reference is made to the work of Karl Pearson (1894) as ... |
Mixture model : Nielsen, Frank (23 March 2012). "K-MLE: A fast algorithm for learning statistical mixture models". 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). pp. 869–872. arXiv:1203.5181. Bibcode:2012arXiv1203.5181N. doi:10.1109/ICASSP.2012.6288022. ISBN 978-1-4673-0046-9. S... |
WACA clustering algorithm : WACA is a clustering algorithm for dynamic networks. WACA (Weighted Application-aware Clustering Algorithm) uses a heuristic weight function for self-organized cluster creation. The election of clusterheads is based on local network information only. == References == |
Calibration (statistics) : There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. Calibration can mean a reverse process to regression, where instead of a future dependent variable being predicted from known explanatory variables, a known observation o... |
Calibration (statistics) : Calibration in classification means transforming classifier scores into class membership probabilities. An overview of calibration methods for two-class and multi-class classification tasks is given by Gebel (2009). A classifier might separate the classes well, but be poorly calibrated, meani... |
Calibration (statistics) : The calibration problem in regression is the use of known data on the observed relationship between a dependent variable and an independent variable to make estimates of other values of the independent variable from new observations of the dependent variable. This can be known as "inverse reg... |
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