Optimal Predictive Linear Discriminants

Enis, Peter; Geisser, Seymour

doi:10.1214/aos/1176342677

Cited by 14 publications

(18 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Also, any sensible Bayesian rule will not lead to this approach, except either asymptotically or under very restrictive conditions [Enis and Geisser (1974)]. …”

Section: Discriminant Analysismentioning

confidence: 99%

Regularized Discriminant Analysis

Friedman

1989

Journal of the American Statistical Association

1,000

651

View full text Add to dashboard Cite

“…Also, any sensible Bayesian rule will not lead to this approach, except either asymptotically or under very restrictive conditions [Enis and Geisser (1974)]. …”

Section: Discriminant Analysismentioning

confidence: 99%

Regularized Discriminant Analysis

Friedman

1989

Journal of the American Statistical Association

1,000

651

View full text Add to dashboard Cite

“…Although the estimates of the covariance may be considered optimal in some sense, this does not mean that the resulting discriminant obtained by substituting these values is optimal in any sense, even if the assumption of normally distributed classes is correct (Anderson, 1984). Also, any sensible Bayesian rule will not lead to this approach, except either asymptotically or under very restrictive conditions (Enis and Geisser, 1986). Additionally, we have to estimate a priori probabilities.…”

Section: Linear Discriminant Analysismentioning

confidence: 99%

Linear discriminant analysis with a generalization of the Moore–Penrose pseudoinverse

Górecki

Łuczak

2013

International Journal of Applied Mathematics and Computer Science

View full text Add to dashboard Cite

The Linear Discriminant Analysis (LDA) technique is an important and well-developed area of classification, and to date many linear (and also nonlinear) discrimination methods have been put forward. A complication in applying LDA to real data occurs when the number of features exceeds that of observations. In this case, the covariance estimates do not have full rank, and thus cannot be inverted. There are a number of ways to deal with this problem. In this paper, we propose improving LDA in this area, and we present a new approach which uses a generalization of the Moore-Penrose pseudoinverse to remove this weakness. Our new approach, in addition to managing the problem of inverting the covariance matrix, significantly improves the quality of classification, also on data sets where we can invert the covariance matrix. Experimental results on various data sets demonstrate that our improvements to LDA are efficient and our approach outperforms LDA.

show abstract

“…2 The paper demonstrates that full-dimensionality classification is not only possible but of equivalent accuracy to more sophisticated subspace classifiers. (ii) While the input feature space of contemporary face-image classifiers is often something other than raw pixels (e.g.…”

Section: Introductionmentioning

confidence: 97%

“…But the ''curse of dimensionality" means that huge numbers of training samples are required to exploit the plug-ins' asymptotic optimality. In practice, they are inaccurate, unreliable and different from any Bayesian modification of any reasonable prior [2]. For this reason, plug-in estimates must be improved before use in a probability model, usually by Regularization.…”

Section: Introductionmentioning

confidence: 99%

“…The samplecovariance is sometimes called the scatter matrix. 2 Dimensionality reduction is so common as a first stage that appearance-based classification is almost synonymous with subspace methods. For face processing, for example, Shakhnarovich and Moghaddam begin their review chapter [4] (titled ''Face Recognition in Subspaces") with the statement that faces are within a submanifold of low intrinsic dimensionality, while Penev and Sirovich [5] seek to discover this intrinsic dimensionality by experiment.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation