Penalized Discriminant Analysis

Hastie, Trevor; Buja, Andreas; Tibshirani, Robert

doi:10.1214/aos/1176324456

Cited by 715 publications

(479 citation statements)

References 16 publications

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“…Curve discrimination Different alternatives have been proposed for the curve discrimination problem, although mainly for univariate functions. Two of the first methods were a regularized version of LDA called penalized discriminant analysis (PDA) proposed by Hastie et al (1995), and a generalized linear regression approach proposed by Marx and Eilers (1999). More recently, some non-parametric alternatives have been proposed, such as the kernel one by Ferraty and Vieu (2003), the k-NN one by Burba et al (2009) or the local linear one by Barrientos-Marin et al (2010).…”

Section: Comparison Of the Three Approachesmentioning

confidence: 99%

Functional data analysis in shape analysis

Epifanio

Ventura‐Campos

2011

Computational Statistics & Data Analysis

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Mid-level processes on images often return outputs in functional form. In this context the use of functional data analysis (FDA) in image analysis is considered. In particular, attention is focussed on shape analysis, where the use of FDA in the functional approach (contour functions) shows its superiority over other approaches, such as the landmark based approach or the set theory approach, on two different problems (principal component analysis and discriminant analysis) in a well-known database of bone outlines. Furthermore, a problem that has hardly ever been considered in the literature is dealt with: multivariate functional discrimination. A discriminant function based on independent component analysis for indicating where the differences between groups are and what their level of discrimination is, is proposed. The classification results obtained with the methodology are very promising. Finally, an analysis of hippocampal differences in Alzheimer's disease is carried out.

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Section: Comparison Of the Three Approachesmentioning

confidence: 99%

Functional data analysis in shape analysis

Epifanio

Ventura‐Campos

2011

Computational Statistics & Data Analysis

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“…We, instead, adopt a direct, many-fold cross-validation approach ignoring smoothing at the regression stage by using misclassification rate as the figure-of-merit during crossvalidation. This is particularly convenient in the current formulation because, as shown in [24], the Mahalanobis distance from class centroids (adjusted for class prior distribution) can be simply and quickly computed in canonical variates by the following expression:…”

Section: Sparse Multinomial Kernel Discriminant Analysis (Smkda)mentioning

confidence: 99%

“…Our intention was then to apply a regressor selection technique such as OLS to the least-squares stage. Subsequently, a more convenient formulation [21] based on penalized optimal scoring was shown via canonical correlation analysis to be able to provide exactly the canonical variates [24], i.e. identical direction and scaling to LDA.…”

Section: Introductionmentioning

confidence: 99%

Sparse multinomial kernel discriminant analysis (sMKDA)

Harrison

Pasupa

2009

Pattern Recognition

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Dimensionality reduction via canonical variate analysis (CVA) is important for pattern recognition and has been extended variously to permit more flexibility, e.g. by "kernelizing" the formulation. This can lead to over-fitting, usually ameliorated by regularization. Here, a method for sparse, multinomial kernel discriminant analysis (sMKDA) is proposed, using a sparse basis to control complexity. It is based on the connection between CVA and least-squares, and uses forward selection via orthogonal least-squares to approximate a basis, generalizing a similar approach for binomial problems. Classification can be performed directly via minimum Mahalanobis distance in the canonical variates. sMKDA achieves state-of-the-art performance in terms of accuracy and sparseness on 11 benchmark datasets.

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“…In Sec. 4, the classification behavior 15 of the combination of three feature extraction methods (no feature extraction, FDA and quadratic FDA) together with a classifier based on Linear Discriminant Analy-17 sis (LDA), will be compared. Six experiments will be performed using six standard data sets encountered in pattern recognition literature.…”

mentioning

confidence: 99%

“…LDA is directly applied to data. Next, FDA is used as feature extraction 15 and finally QFDA is used a feature extraction method. From Table 1 we can deduce that feature extraction positively affects the clas-17 sifier behavior and QFDA introduces an improvement of 4% in the classification rate if compared with the cases with no feature extraction or when using FDA.…”

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confidence: 99%

Nonlinear Feature Extraction Using Fisher Criterion

Bustos

Duarte‐Mermoud

Beltrán

2008

Int. J. Patt. Recogn. Artif. Intell.

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13In this paper the problem of nonlinear feature extraction based on the optimization of the Fisher criterion is analyzed. A new nonlinear feature extraction method is proposed. The 15 method does not make use of numerical algorithms and it has an analytical (closed-form) solution. Moreover, no assumptions on the class probability distribution functions are 17 imposed. The proposed method is applied to some standard pattern recognition problems and compared with other classical methodologies already proposed in the literature. The 19 performance of the proposed method turned out to be superior when compared with the other methods studied. 21

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Penalized Discriminant Analysis

Cited by 715 publications

References 16 publications

Functional data analysis in shape analysis

Functional data analysis in shape analysis

Sparse multinomial kernel discriminant analysis (sMKDA)

Nonlinear Feature Extraction Using Fisher Criterion

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