Topic
Linear discriminant analysis
About: Linear discriminant analysis is a research topic. Over the lifetime, 18361 publications have been published within this topic receiving 603195 citations. The topic is also known as: Linear discriminant analysis & LDA.
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TL;DR: In this article, the authors consider the problem of combining a collection of general regression fit vectors to obtain a better predictive model and develop a general framework for this problem and examine a cross-validation-based proposal called "model mix" or "stacking" in this context.
Abstract: We consider the problem of how to combine a collection of general regression fit vectors to obtain a better predictive model. The individual fits may be from subset linear regression, ridge regression, or something more complex like a neural network. We develop a general framework for this problem and examine a cross-validation—based proposal called “model mix” or “stacking” in this context. We also derive combination methods based on the bootstrap and analytic methods and compare them in examples. Finally, we apply these ideas to classification problems where the estimated combination weights can yield insight into the structure of the problem.
318 citations
IBM1
TL;DR: This paper reviews statistical, adaptive, and heuristic techniques used in laboratory investigations of pattern recognition problems and includes correlation methods, discriminant analysis, maximum likelihood decisions minimax techniques, perceptron-like algorithms, feature extraction, preprocessing, clustering and nonsupervised learning.
Abstract: This paper reviews statistical, adaptive, and heuristic techniques used in laboratory investigations of pattern recognition problems. The discussion includes correlation methods, discriminant analysis, maximum likelihood decisions minimax techniques, perceptron-like algorithms, feature extraction, preprocessing, clustering and nonsupervised learning. Two-dimensional distributions are used to illustrate the properties of the various procedures. Several experimental projects, representative of prospective applications, are also described.
317 citations
20 Oct 2007
TL;DR: It is argued that robust recognition requires several different kinds of appearance information to be taken into account, suggesting the use of heterogeneous feature sets, and combining two of the most successful local face representations, Gabor wavelets and Local Binary Patterns, gives considerably better performance than either alone.
Abstract: Extending recognition to uncontrolled situations is a key challenge for practical face recognition systems Finding efficient and discriminative facial appearance descriptors is crucial for this Most existing approaches use features of just one type Here we argue that robust recognition requires several different kinds of appearance information to be taken into account, suggesting the use of heterogeneous feature sets We show that combining two of the most successful local face representations, Gabor wavelets and Local Binary Patterns (LBP), gives considerably better performance than either alone: they are complimentary in the sense that LBP captures small appearance details while Gabor features encode facial shape over a broader range of scales Both feature sets are high dimensional so it is beneficial to use PCA to reduce the dimensionality prior to normalization and integration The Kernel Discriminative Common Vector method is then applied to the combined feature vector to extract discriminant nonlinear features for recognition The method is evaluated on several challenging face datasets including FRGC 104, FRGC 204 and FERET, with promising results
314 citations
Posted Content•
TL;DR: Linear dimensionality reduction methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted as discussed by the authors.
Abstract: Linear dimensionality reduction methods are a cornerstone of analyzing high dimensional data, due to their simple geometric interpretations and typically attractive computational properties. These methods capture many data features of interest, such as covariance, dynamical structure, correlation between data sets, input-output relationships, and margin between data classes. Methods have been developed with a variety of names and motivations in many fields, and perhaps as a result the connections between all these methods have not been highlighted. Here we survey methods from this disparate literature as optimization programs over matrix manifolds. We discuss principal component analysis, factor analysis, linear multidimensional scaling, Fisher's linear discriminant analysis, canonical correlations analysis, maximum autocorrelation factors, slow feature analysis, sufficient dimensionality reduction, undercomplete independent component analysis, linear regression, distance metric learning, and more. This optimization framework gives insight to some rarely discussed shortcomings of well-known methods, such as the suboptimality of certain eigenvector solutions. Modern techniques for optimization over matrix manifolds enable a generic linear dimensionality reduction solver, which accepts as input data and an objective to be optimized, and returns, as output, an optimal low-dimensional projection of the data. This simple optimization framework further allows straightforward generalizations and novel variants of classical methods, which we demonstrate here by creating an orthogonal-projection canonical correlations analysis. More broadly, this survey and generic solver suggest that linear dimensionality reduction can move toward becoming a blackbox, objective-agnostic numerical technology.
313 citations