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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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This note was uploaded on 11/24/2010 for the course STAT 201a taught by Professor Wu during the Spring '10 term at Pasadena City College.
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