Robust linear dimensionality reduction

Yehuda Koren*, Liran Carmel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

123 Scopus citations

Abstract

We present a novel family of data-driven linear transformations, aimed at finding low-dimensional embeddings of multlvariate data, In a way that optimally preserves the structure of the data. The well-studied PCA and Fisher's IDA 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 palrwlse relationships between the data elements. Even more so, when information on the clustering (labeling) decomposition of the data Is known, this information can also be Integrated in the linear transformation, resulting in embeddings that clearly show the separation between the clusters, as well as their internal structure. All of 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
Pages (from-to)459-470
Number of pages12
JournalIEEE Transactions on Visualization and Computer Graphics
Volume10
Issue number4
DOIs
StatePublished - Jul 2004
Externally publishedYes

Keywords

  • Classification
  • Dimensionality reduction
  • Feature extraction
  • Fisher's linear discriminant analysis
  • Linear transformation
  • Principal component analysis
  • Projection
  • Visualization

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