Visualization of labeled data using linear transformations

Yehuda Koren*, Liran Carmel

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

46 Scopus citations

Abstract

We present a novel family of data-driven linear transformations, aimed at visualizing multivariate data in a low-dimensional space in a way that optimally preserves the structure of the data. The well-studied PCA and Fisher's LDA are shown to be special members in this family of transformations, and we demonstrate how to generalize these two methods such as to enhance their performance. Furthermore, our technique is the only one, to the best of our knowledge, that reflects in the resulting embedding both the data coordinates and pairwise similarities and/or dissimilarities between the data elements. Even more so, when information on the clustering (labeling) decomposition of the data is known, this information can be integrated in the linear transformation, resulting in embeddings that clearly show the separation between the clusters, as well as their intra-structure. All this makes our technique very flexible and powerful, and lets us cope with kinds of data that other techniques fail to describe properly.

Original languageAmerican English
Title of host publicationIEEE Symposium on Information Visualization 2003, InfoVis 2003
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages121-130
Number of pages10
ISBN (Print)0780381548, 9780780381544
DOIs
StatePublished - 2003
Externally publishedYes

Publication series

NameProceedings - IEEE Symposium on Information Visualization, INFO VIS
ISSN (Print)1522-404X

Keywords

  • Classification
  • Dimensionality-reduction
  • Eigenprojection
  • Fisher's linear discriminant analysis
  • Principal component analysis
  • Projection
  • Visualization

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