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Semi-supervised dimensionality reduction using pairwise equivalence constraints

By Hakan Cevikalp, Jakob Verbeek, Frédéric Jurie, Er Kläser and Lear Team

Abstract

• In classification problems of high dimensional data lack of labeled data can be problematic, and explicit labeling is expensive. • We propose CLPP: a dimension reduction method that exploits pairwise class information (easy labeling of pairs: same class or not). • Our method is based on a neighborhood graph to reflect the intuition that nearby examples tend to have the same label. • Classification and clustering performance is improved, more so than unsupervised dimension reduction followed by metric learning. Datasets ETH-80 (top row) and Birds (the second and third rows, 2 illustrative images per category). Semi-supervised dimensionality reduction • As input for the semi-supervised problem we have: – data points X = {x1, x2,..., xn}, – pairs of the same class S = { (i, j) | xi and xj belong to the same class}, – pairs of the different classes D = { (i, j) | xi and xj belong to different classes}. • High dimensional data is often embedded on a low dimensional manifold, therefore we construct neighborhood graph to capture local data structure. • We modify the Locality Preserving Projection (LPP) method [1] to take into account the class information in the form of pairwise constraints. Locality Preserving Projections • LPP is an unsupervised dimension reduction method that is based on a neighborhood graph over a set of points X. A pair of points xi and xj are connected by an edge if they are nearest neighbors in the input space; the associated edge weight Wij ∈ [0, 1] depends on their distance. • The objective of LPP is to find a linear projections of the inputs y = a ⊤ x that minimize E(a) =

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.173.3321
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