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Unformatted text preview: 1 Lecture 4: Dimension Reduction I One common method is to assume smooth density functions in empty spaces, e.g. Lecture notes Stat 231CS276A S.C. Zhu Dimension reduction techniques The other method is to reduce the dimension of the feature space, for example by projecting a feature vector to a lower dimensional space. Common techniques for dimension reduction: 1. Principle component analysis (PCA) 2. Fisher linear discriminant analysis 3. Independent component analysis (ICA) 4. Multidimensional scaling (MDS) Lecture notes Stat 231CS276A S.C. Zhu 5. Overcomplete bases coding 6. Transformed component analysis (TCA) Some features are generative and some are discriminative. 2 Overview: what are the real dimensions of your data? For a human face image of 128 x 128 pixels, what is the dimension of all images of a same person under varying illumination? It must be quite small. Lecture notes Stat 231CS276A S.C. Zhu Other variations: glass, expression add more dimensions to the face Lecture notes Stat 231CS276A S.C. Zhu 3 A wide spectrum of categories from low to high entropy Entropy ~ Dimension ~ Log volume( manifold ) Take 16x16 image patches (256 space), run PCA for each category, and plot the eigen values in decreasing order....
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 Spring '10
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