A Problem of Dimensionality: A Simple Example

Trunk, G. V.

doi:10.1109/tpami.1979.4766926

Cited by 339 publications

(182 citation statements)

References 1 publication

Supporting

Mentioning

176

Contrasting

Unclassified

Order By: Relevance

“…However, relatively small sample size (compared to dimensionality d) may cause LDA's performance to decrease when adding more dimensions, even though the extra dimensions contain discriminative information. Trunk (1979) affirmed this phenomenon by investigating an illuminating simple example. Chang (1983), Dillon, Mulani, and Frederick (1989), Kshirsagar, Kocherlakota, and Kocherlakota (1990) all established a statistic θ k for the kth principal component (PC) and use θ k to decide which PCs should be used in discrimination.…”

Section: Introductionmentioning

confidence: 85%

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Cardinal-Stakenas

Park

et al. 2010

J Classif

View full text Add to dashboard Cite

Abstract:We consider the problem of combining multiple dissimilarity representations via the Cartesian product of their embeddings. For concreteness, we choose the inferential task at hand to be classification. The high dimensionality of this Cartesian product space implies the necessity of dimensionality reduction before training a classifier. We propose a supervised dimensionality reduction method, which utilizes the class label information, to help achieve a favorable combination. The simulation and real data results show that our approach can improve classification accuracy compared to the alternatives of principal components analysis and no dimensionality reduction at all.

show abstract

Section: Introductionmentioning

confidence: 85%

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Cardinal-Stakenas

Park

et al. 2010

J Classif

View full text Add to dashboard Cite

show abstract

“…This phenomenon is also known as the curse ofdimensionality. Generally, the number of training samples per class should be at least five to ten times the number offeatures used for computing the decision surfaces (Trunk, 1979).…”

Section: Parametric Methodsmentioning

confidence: 99%

Multistrategy Learning for Document Recognition

Esposito

Malerba

Semeraro

1994

Applied Artificial Intelligence

View full text Add to dashboard Cite

show abstract

“…The accuracy of learned models tends to deteriorate in high dimensions, a phenomenon called the 'curse of dimensionality' (Duda et al, 2001). This phenomenon is illustrated for classification by an example by Trunk (1979). Consider two equally probable, normally distributed classes with common variance in each dimension.…”

Section: Predictive Classificationmentioning

confidence: 98%

Approaches to working in high-dimensional data spaces: gene expression microarrays

2008

View full text Add to dashboard Cite

This review provides a focused summary of the implications of high-dimensional data spaces produced by gene expression microarrays for building better models of cancer diagnosis, prognosis, and therapeutics. We identify the unique challenges posed by high dimensionality to highlight methodological problems and discuss recent methods in predictive classification, unsupervised subclass discovery, and marker identification.

show abstract

A Problem of Dimensionality: A Simple Example

Cited by 339 publications

References 1 publication

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

Multistrategy Learning for Document Recognition

Approaches to working in high-dimensional data spaces: gene expression microarrays

Contact Info

Product

Resources

About