Publication 2004 Issue No. 4 - July/August Abstract - Robust Linear Dimensionality Reduction
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Robust Linear Dimensionality Reduction
July/August 2004 (vol. 10 no. 4)
pp. 459-470
 ASCII Text x Yehuda Koren, Liran Carmel, "Robust Linear Dimensionality Reduction," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, pp. 459-470, July/August, 2004.
 BibTex x @article{ 10.1109/TVCG.2004.17,author = {Yehuda Koren and Liran Carmel},title = {Robust Linear Dimensionality Reduction},journal ={IEEE Transactions on Visualization and Computer Graphics},volume = {10},number = {4},issn = {1077-2626},year = {2004},pages = {459-470},doi = {http://doi.ieeecomputersociety.org/10.1109/TVCG.2004.17},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on Visualization and Computer GraphicsTI - Robust Linear Dimensionality ReductionIS - 4SN - 1077-2626SP459EP470EPD - 459-470A1 - Yehuda Koren, A1 - Liran Carmel, PY - 2004KW - Dimensionality reductionKW - visualizationKW - classificationKW - feature extractionKW - projectionKW - linear transformationKW - principal component analysisKW - Fisher's linear discriminant analysis.VL - 10JA - IEEE Transactions on Visualization and Computer GraphicsER -

Abstract—We present a novel family of data-driven linear transformations, aimed at finding low-dimensional embeddings of multivariate data, 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 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.

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Index Terms:
Dimensionality reduction, visualization, classification, feature extraction, projection, linear transformation, principal component analysis, Fisher's linear discriminant analysis.
Citation:
Yehuda Koren, Liran Carmel, "Robust Linear Dimensionality Reduction," IEEE Transactions on Visualization and Computer Graphics, vol. 10, no. 4, pp. 459-470, July-Aug. 2004, doi:10.1109/TVCG.2004.17