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Information gain (decision tree) : In general terms, the expected information gain is the reduction in information entropy Ξ from a prior state to a state that takes some information as given: I G ( T , a ) = H ( T ) β H ( T | a ) , -\mathrm , where H ( T | a ) is the conditional entropy of T given the value of at... |
Information gain (decision tree) : Let T denote a set of training examples, each of the form ( x , y ) = ( x 1 , x 2 , x 3 , . . . , x k , y ) ,y)=(x_,x_,x_,...,x_,y) where x a β v a l s ( a ) \in \mathrm (a) is the value of the a th attribute or feature of example x and y is the corresponding class label. The infor... |
Information gain (decision tree) : For a better understanding of information gain, let us break it down. As we know, information gain is the reduction in information entropy, what is entropy? Basically, entropy is the measure of impurity or uncertainty in a group of observations. In engineering applications, informatio... |
Information gain (decision tree) : Information gain is the basic criterion to decide whether a feature should be used to split a node or not. The feature with the optimal split i.e., the highest value of information gain at a node of a decision tree is used as the feature for splitting the node. The concept of informat... |
Information gain (decision tree) : Although information gain is usually a good measure for deciding the relevance of an attribute, it is not perfect. A notable problem occurs when information gain is applied to attributes that can take on a large number of distinct values. For example, suppose that one is building a de... |
Information gain (decision tree) : Information gain more broadly Decision tree learning Information content, the starting point of information theory and the basis of Shannon entropy Information gain ratio ID3 algorithm C4.5 algorithm Surprisal analysis |
Information gain (decision tree) : Nowozin, Sebastion (2012-06-18). "Improved Information Gain Estimates for Decision Tree Induction". arXiv:1206.4620v1 [cs.LG]. Shouman, Mai (2011). "Using decision tree for diagnosing heart disease patients" (PDF). Proceedings of the Ninth Australasian Data Mining Conference. 121: 23β... |
Information gain ratio : In decision tree learning, information gain ratio is a ratio of information gain to the intrinsic information. It was proposed by Ross Quinlan, to reduce a bias towards multi-valued attributes by taking the number and size of branches into account when choosing an attribute. Information gain is... |
Information gain ratio : Information gain is the reduction in entropy produced from partitioning a set with attributes a and finding the optimal candidate that produces the highest value: IG ( T , a ) = H ( T ) β H ( T | a ) , (T,a)=\mathrm -\mathrm , where T is a random variable and H ( T | a ) is the entropy of... |
Information gain ratio : The split information value for a test is defined as follows: SplitInformation ( X ) = β β i = 1 n N ( x i ) N ( x ) β log β‘ 2 N ( x i ) N ( x ) (X)=-\sum _^ (x_) (x)*\log (x_) (x) where X is a discrete random variable with possible values x 1 , x 2 , . . . , x i ,x_,...,x_ and N ( x i ) ) be... |
Information gain ratio : The information gain ratio is the ratio between the information gain and the split information value: IGR ( T , a ) = IG ( T , a ) / SplitInformation ( T ) (T,a)=(T,a)/(T) IGR ( T , a ) = β β i = 1 n P ( T ) log β‘ P ( T ) β ( β β i = 1 n P ( T | a ) log β‘ P ( T | a ) ) β β i = 1 n N ( t i ) N (... |
Information gain ratio : Using weather data published by Fordham University, the table was created below: Using the table above, one can find the entropy, information gain, split information, and information gain ratio for each variable (outlook, temperature, humidity, and wind). These calculations are shown in the tab... |
Information gain ratio : Information gain ratio biases the decision tree against considering attributes with a large number of distinct values. For example, suppose that we are building a decision tree for some data describing a business's customers. Information gain ratio is used to decide which of the attributes are ... |
Information gain ratio : Although information gain ratio solves the key problem of information gain, it creates another problem. If one is considering an amount of attributes that have a high number of distinct values, these will never be above one that has a lower number of distinct values. |
Information gain ratio : Information gain's shortcoming is created by not providing a numerical difference between attributes with high distinct values from those that have less. Example: Suppose that we are building a decision tree for some data describing a business's customers. Information gain is often used to deci... |
Information gain ratio : Information gain in decision trees Entropy (information theory) == References == |
Jackknife variance estimates for random forest : In statistics, jackknife variance estimates for random forest are a way to estimate the variance in random forest models, in order to eliminate the bootstrap effects. |
Jackknife variance estimates for random forest : The sampling variance of bagged learners is: V ( x ) = V a r [ ΞΈ ^ β ( x ) ] ^(x)] Jackknife estimates can be considered to eliminate the bootstrap effects. The jackknife variance estimator is defined as: V ^ j = n β 1 n β i = 1 n ( ΞΈ ^ ( β i ) β ΞΈ Β― ) 2 _=\sum _^(_-)^ I... |
Jackknife variance estimates for random forest : E-mail spam problem is a common classification problem, in this problem, 57 features are used to classify spam e-mail and non-spam e-mail. Applying IJ-U variance formula to evaluate the accuracy of models with m=15,19 and 57. The results shows in paper( Confidence Interv... |
Jackknife variance estimates for random forest : When using Monte Carlo MSEs for estimating V I J β ^ and V J β ^ , a problem about the Monte Carlo bias should be considered, especially when n is large, the bias is getting large: E [ V ^ I J B ] β V ^ I J β β n β b = 1 B ( t b β β t Β― β ) 2 B _^]-_^\approx ^(t_^-^)^ To... |
Large margin nearest neighbor : Large margin nearest neighbor (LMNN) classification is a statistical machine learning algorithm for metric learning. It learns a pseudometric designed for k-nearest neighbor classification. The algorithm is based on semidefinite programming, a sub-class of convex optimization. The goal o... |
Large margin nearest neighbor : The main intuition behind LMNN is to learn a pseudometric under which all data instances in the training set are surrounded by at least k instances that share the same class label. If this is achieved, the leave-one-out error (a special case of cross validation) is minimized. Let the tra... |
Large margin nearest neighbor : Large margin nearest neighbors optimizes the matrix M with the help of semidefinite programming. The objective is twofold: For every data point x β i _ , the target neighbors should be close and the impostors should be far away. Figure 1 shows the effect of such an optimization on an i... |
Large margin nearest neighbor : LMNN was extended to multiple local metrics in the 2008 paper. This extension significantly improves the classification error, but involves a more expensive optimization problem. In their 2009 publication in the Journal of Machine Learning Research, Weinberger and Saul derive an efficien... |
Large margin nearest neighbor : Matlab Implementation ICML 2010 Tutorial on Metric Learning |
Latent class model : In statistics, a latent class model (LCM) is a model for clustering multivariate discrete data. It assumes that the data arise from a mixture of discrete distributions, within each of which the variables are independent. It is called a latent class model because the class to which each data point b... |
Latent class model : Within each latent class, the observed variables are statistically independent. This is an important aspect. Usually the observed variables are statistically dependent. By introducing the latent variable, independence is restored in the sense that within classes variables are independent (local ind... |
Latent class model : There are a number of methods with distinct names and uses that share a common relationship. Cluster analysis is, like LCA, used to discover taxon-like groups of cases in data. Multivariate mixture estimation (MME) is applicable to continuous data, and assumes that such data arise from a mixture of... |
Latent class model : LCA may be used in many fields, such as: collaborative filtering, Behavior Genetics and Evaluation of diagnostic tests. |
Latent class model : Linda M. Collins; Stephanie T. Lanza (2010). Latent class and latent transition analysis for the social, behavioral, and health sciences. New York: Wiley. ISBN 978-0-470-22839-5. Allan L. McCutcheon (1987). Latent class analysis. Quantitative Applications in the Social Sciences Series No. 64. Thous... |
Latent class model : Statistical Innovations, Home Page, 2016. Website with latent class software (Latent GOLD 5.1), free demonstrations, tutorials, user guides, and publications for download. Also included: online courses, FAQs, and other related software. The Methodology Center, Latent Class Analysis, a research cent... |
Linear classifier : In machine learning, a linear classifier makes a classification decision for each object based on a linear combination of its features. Such classifiers work well for practical problems such as document classification, and more generally for problems with many variables (features), reaching accuracy... |
Linear classifier : If the input feature vector to the classifier is a real vector x β , then the output score is y = f ( w β β
x β ) = f ( β j w j x j ) , \cdot )=f\left(\sum _w_x_\right), where w β is a real vector of weights and f is a function that converts the dot product of the two vectors into the desired outp... |
Linear classifier : There are two broad classes of methods for determining the parameters of a linear classifier w β . They can be generative and discriminative models. Methods of the former model joint probability distribution, whereas methods of the latter model conditional density functions P ( c l a s s | x β ) |)... |
Linear classifier : Backpropagation Linear regression Perceptron Quadratic classifier Support vector machines Winnow (algorithm) |
Linear classifier : Y. Yang, X. Liu, "A re-examination of text categorization", Proc. ACM SIGIR Conference, pp. 42β49, (1999). paper @ citeseer R. Herbrich, "Learning Kernel Classifiers: Theory and Algorithms," MIT Press, (2001). ISBN 0-262-08306-X |
Linear discriminant analysis : Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that cha... |
Linear discriminant analysis : The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936. It is different from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. Discriminant funct... |
Linear discriminant analysis : Consider a set of observations x β (also called features, attributes, variables or measurements) for each sample of an object or event with known class y . This set of samples is called the training set in a supervised learning context. The classification problem is then to find a good ... |
Linear discriminant analysis : The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables. Multivariate normality: Independent variables are normal for each level of the g... |
Linear discriminant analysis : Discriminant analysis works by creating one or more linear combinations of predictors, creating a new latent variable for each function. These functions are called discriminant functions. The number of functions possible is either N g β 1 -1 where N g = number of groups, or p (the numbe... |
Linear discriminant analysis : Maximum likelihood: Assigns x to the group that maximizes population (group) density. Bayes Discriminant Rule: Assigns x to the group that maximizes Ο i f i ( x ) f_(x) , where Οi represents the prior probability of that classification, and f i ( x ) (x) represents the population densit... |
Linear discriminant analysis : An eigenvalue in discriminant analysis is the characteristic root of each function. It is an indication of how well that function differentiates the groups, where the larger the eigenvalue, the better the function differentiates. This however, should be interpreted with caution, as eigenv... |
Linear discriminant analysis : Some suggest the use of eigenvalues as effect size measures, however, this is generally not supported. Instead, the canonical correlation is the preferred measure of effect size. It is similar to the eigenvalue, but is the square root of the ratio of SSbetween and SStotal. It is the corre... |
Linear discriminant analysis : Canonical discriminant analysis (CDA) finds axes (k β 1 canonical coordinates, k being the number of classes) that best separate the categories. These linear functions are uncorrelated and define, in effect, an optimal k β 1 space through the n-dimensional cloud of data that best separate... |
Linear discriminant analysis : The terms Fisher's linear discriminant and LDA are often used interchangeably, although Fisher's original article actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances. Suppo... |
Linear discriminant analysis : In the case where there are more than two classes, the analysis used in the derivation of the Fisher discriminant can be extended to find a subspace which appears to contain all of the class variability. This generalization is due to C. R. Rao. Suppose that each of C classes has a mean ΞΌ ... |
Linear discriminant analysis : The typical implementation of the LDA technique requires that all the samples are available in advance. However, there are situations where the entire data set is not available and the input data are observed as a stream. In this case, it is desirable for the LDA feature extraction to hav... |
Linear discriminant analysis : In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the cova... |
Linear discriminant analysis : In addition to the examples given below, LDA is applied in positioning and product management. |
Linear discriminant analysis : Discriminant function analysis is very similar to logistic regression, and both can be used to answer the same research questions. Logistic regression does not have as many assumptions and restrictions as discriminant analysis. However, when discriminant analysisβ assumptions are met, it ... |
Linear discriminant analysis : Geometric anomalies in higher dimensions lead to the well-known curse of dimensionality. Nevertheless, proper utilization of concentration of measure phenomena can make computation easier. An important case of these blessing of dimensionality phenomena was highlighted by Donoho and Tanner... |
Linear discriminant analysis : Data mining Decision tree learning Factor analysis Kernel Fisher discriminant analysis Logit (for logistic regression) Linear regression Multiple discriminant analysis Multidimensional scaling Pattern recognition Preference regression Quadratic classifier Statistical classification |
Linear discriminant analysis : Duda, R. O.; Hart, P. E.; Stork, D. H. (2000). Pattern Classification (2nd ed.). Wiley Interscience. ISBN 978-0-471-05669-0. MR 1802993. Hilbe, J. M. (2009). Logistic Regression Models. Chapman & Hall/CRC Press. ISBN 978-1-4200-7575-5. Mika, S.; et al. (1999). "Fisher discriminant analysi... |
Linear discriminant analysis : Discriminant Correlation Analysis (DCA) of the Haghighat article (see above) ALGLIB contains open-source LDA implementation in C# / C++ / Pascal / VBA. LDA in Python- LDA implementation in Python LDA tutorial using MS Excel Biomedical statistics. Discriminant analysis StatQuest: Linear Di... |
Margin classifier : In machine learning (ML), a margin classifier is a type of classification model which is able to give an associated distance from the decision boundary for each data sample. For instance, if a linear classifier is used, the distance (typically Euclidean, though others may be used) of a sample from t... |
Margin classifier : The margin for an iterative boosting algorithm given a dataset with two classes can be defined as follows: the classifier is given a sample pair ( x , y ) , where x β X is a domain space and y β Y = is the sample's label. The algorithm then selects a classifier h j β C \in C at each iteration j ... |
Margin classifier : Many classifiers can give an associated margin for each sample. However, only some classifiers utilize information of the margin while learning from a dataset. Many boosting algorithms rely on the notion of a margin to assign weight to samples. If a convex loss is utilized (as in AdaBoost or LogitBo... |
Margin classifier : One theoretical motivation behind margin classifiers is that their generalization error may be bound by the algorithm parameters and a margin term. An example of such a bound is for the AdaBoost algorithm. Let S be a set of m data points, sampled independently at random from a distribution D . As... |
Margin-infused relaxed algorithm : Margin-infused relaxed algorithm (MIRA) is a machine learning algorithm, an online algorithm for multiclass classification problems. It is designed to learn a set of parameters (vector or matrix) by processing all the given training examples one-by-one and updating the parameters acco... |
Margin-infused relaxed algorithm : adMIRAble β MIRA implementation in C++ Miralium β MIRA implementation in Java MIRA implementation for Mahout in Hadoop |
Multi-label classification : In machine learning, multi-label classification or multi-output classification is a variant of the classification problem where multiple nonexclusive labels may be assigned to each instance. Multi-label classification is a generalization of multiclass classification, which is the single-lab... |
Multi-label classification : Several problem transformation methods exist for multi-label classification, and can be roughly broken down into: |
Multi-label classification : Some classification algorithms/models have been adapted to the multi-label task, without requiring problem transformations. Examples of these including for multi-label data are k-nearest neighbors: the ML-kNN algorithm extends the k-NN classifier to multi-label data. decision trees: "Clare"... |
Multi-label classification : Based on learning paradigms, the existing multi-label classification techniques can be classified into batch learning and online machine learning. Batch learning algorithms require all the data samples to be available beforehand. It trains the model using the entire training data and then p... |
Multi-label classification : Data streams are possibly infinite sequences of data that continuously and rapidly grow over time. Multi-label stream classification (MLSC) is the version of multi-label classification task that takes place in data streams. It is sometimes also called online multi-label classification. The ... |
Multi-label classification : Considering Y i to be a set of labels for i t h data sample (do not confuse it with a one-hot vector; it is simply a collection of all of the labels that belong to this sample), the extent to which a dataset is multi-label can be captured in two statistics: Label cardinality is the averag... |
Multi-label classification : Java implementations of multi-label algorithms are available in the Mulan and Meka software packages, both based on Weka. The scikit-learn Python package implements some multi-labels algorithms and metrics. The scikit-multilearn Python package specifically caters to the multi-label classifi... |
Multi-label classification : Multiclass classification Multiple-instance learning Structured prediction Life-time of correlation |
Multi-label classification : Madjarov, Gjorgji; Kocev, Dragi; Gjorgjevikj, Dejan; DΕΎeroski, SaΕ‘o (2012). "An extensive experimental comparison of methods for multi-label learning". Pattern Recognition. 45 (9): 3084β3104. Bibcode:2012PatRe..45.3084M. doi:10.1016/j.patcog.2012.03.004. S2CID 14064264. |
Multiclass classification : In machine learning and statistical classification, multiclass classification or multinomial classification is the problem of classifying instances into one of three or more classes (classifying instances into one of two classes is called binary classification). For example, deciding on whet... |
Multiclass classification : The existing multi-class classification techniques can be categorised into transformation to binary extension from binary hierarchical classification. |
Multiclass classification : Based on learning paradigms, the existing multi-class classification techniques can be classified into batch learning and online learning. Batch learning algorithms require all the data samples to be available beforehand. It trains the model using the entire training data and then predicts t... |
Multiclass classification : The performance of a multi-class classification system is often assessed by comparing the predictions of the system against reference labels with an evaluation metric. Common evaluation metrics are Accuracy or macro F1. |
Multiclass classification : Binary classification One-class classification Multi-label classification Multiclass perceptron Multi-task learning |
Multinomial logistic regression : In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes. That is, it is a model that is used to predict the probabilities of the different possible outcomes... |
Multinomial logistic regression : Multinomial logistic regression is used when the dependent variable in question is nominal (equivalently categorical, meaning that it falls into any one of a set of categories that cannot be ordered in any meaningful way) and for which there are more than two categories. Some examples ... |
Multinomial logistic regression : The multinomial logistic model assumes that data are case-specific; that is, each independent variable has a single value for each case. As with other types of regression, there is no need for the independent variables to be statistically independent from each other (unlike, for exampl... |
Multinomial logistic regression : When using multinomial logistic regression, one category of the dependent variable is chosen as the reference category. Separate odds ratios are determined for all independent variables for each category of the dependent variable with the exception of the reference category, which is o... |
Multinomial logistic regression : The observed values y i β \in \ for i = 1 , β¦ , n of the explained variables are considered as realizations of stochastically independent, categorically distributed random variables Y 1 , β¦ , Y n ,\dots ,Y_ . The likelihood function for this model is defined by L = β i = 1 n P ( Y i ... |
Multinomial logistic regression : In natural language processing, multinomial LR classifiers are commonly used as an alternative to naive Bayes classifiers because they do not assume statistical independence of the random variables (commonly known as features) that serve as predictors. However, learning in such a model... |
Multinomial logistic regression : Logistic regression Multinomial probit == References == |
Multispectral pattern recognition : Multispectral remote sensing is the collection and analysis of reflected, emitted, or back-scattered energy from an object or an area of interest in multiple bands of regions of the electromagnetic spectrum (Jensen, 2005). Subcategories of multispectral remote sensing include hypersp... |
Multispectral pattern recognition : Remote sensing systems gather data via instruments typically carried on satellites in orbit around the Earth. The remote sensing scanner detects the energy that radiates from the object or area of interest. This energy is recorded as an analog electrical signal and converted into a d... |
Multispectral pattern recognition : A variety of methods can be used for the multispectral classification of images: Algorithms based on parametric and nonparametric statistics that use ratio-and interval-scaled data and nonmetric methods that can also incorporate nominal scale data (Duda et al., 2001), Supervised or u... |
Multispectral pattern recognition : In this classification method, the identity and location of some of the land-cover types are obtained beforehand from a combination of fieldwork, interpretation of aerial photography, map analysis, and personal experience. The analyst would locate sites that have similar characterist... |
Multispectral pattern recognition : Unsupervised classification (also known as clustering) is a method of partitioning remote sensor image data in multispectral feature space and extracting land-cover information. Unsupervised classification require less input information from the analyst compared to supervised classif... |
Multispectral pattern recognition : Ball, Geoffrey H., Hall, David J. (1965) Isodata: a method of data analysis and pattern classification, Stanford Research Institute, Menlo Park, United States. Office of Naval Research. Information Sciences Branch Duda, R. O., Hart, P. E., & Stork, D. G. (2001). Pattern Classificatio... |
Naive Bayes classifier : In statistics, naive (sometimes simple or idiot's) Bayes classifiers are a family of "probabilistic classifiers" which assumes that the features are conditionally independent, given the target class. In other words, a naive Bayes model assumes the information about the class provided by each va... |
Naive Bayes classifier : Naive Bayes is a simple technique for constructing classifiers: models that assign class labels to problem instances, represented as vectors of feature values, where the class labels are drawn from some finite set. There is not a single algorithm for training such classifiers, but a family of a... |
Naive Bayes classifier : Abstractly, naive Bayes is a conditional probability model: it assigns probabilities p ( C k β£ x 1 , β¦ , x n ) \mid x_,\ldots ,x_) for each of the K possible outcomes or classes C k given a problem instance to be classified, represented by a vector x = ( x 1 , β¦ , x n ) =(x_,\ldots ,x_) encod... |
Naive Bayes classifier : A class's prior may be calculated by assuming equiprobable classes, i.e., p ( C k ) = 1 K )= , or by calculating an estimate for the class probability from the training set: prior for a given class = no. of samples in that class total no. of samples =\, To estimate the parameters for a feature'... |
Naive Bayes classifier : Despite the fact that the far-reaching independence assumptions are often inaccurate, the naive Bayes classifier has several properties that make it surprisingly useful in practice. In particular, the decoupling of the class conditional feature distributions means that each distribution can be ... |
Naive Bayes classifier : AODE Anti-spam techniques Bayes classifier Bayesian network Bayesian poisoning Email filtering Linear classifier Logistic regression Markovian discrimination Mozilla Thunderbird mail client with native implementation of Bayes filters Perceptron Random naive Bayes Take-the-best heuristic |
Naive Bayes classifier : Domingos, Pedro; Pazzani, Michael (1997). "On the optimality of the simple Bayesian classifier under zero-one loss". Machine Learning. 29 (2/3): 103β137. doi:10.1023/A:1007413511361. Webb, G. I.; Boughton, J.; Wang, Z. (2005). "Not So Naive Bayes: Aggregating One-Dependence Estimators". Machine... |
Naive Bayes classifier : Book Chapter: Naive Bayes text classification, Introduction to Information Retrieval Naive Bayes for Text Classification with Unbalanced Classes |
Nearest centroid classifier : In machine learning, a nearest centroid classifier or nearest prototype classifier is a classification model that assigns to observations the label of the class of training samples whose mean (centroid) is closest to the observation. When applied to text classification using word vectors c... |
Nearest centroid classifier : Cluster hypothesis k-means clustering k-nearest neighbor algorithm Linear discriminant analysis == References == |
Nearest neighbor search : Nearest neighbor search (NNS), as a form of proximity search, is the optimization problem of finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the less similar the objects, the larger the ... |
Nearest neighbor search : The nearest neighbor search problem arises in numerous fields of application, including: Pattern recognition β in particular for optical character recognition Statistical classification β see k-nearest neighbor algorithm Computer vision β for point cloud registration Computational geometry β s... |
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