Содержание
- 2. The Origin of ICA: Factor Analysis Multivariate data are often thought to be indirect measurements arising
- 3. Latent Variables and Factor Analysis Latent variable model: or, Observed variable Latent components Mixing matrix Factor
- 4. Latent Variables and Factor Analysis… Typically we require the latent variables to have unit variance and
- 5. Classical Factor Analysis Model: ε’s are zero mean, uncorrelated Gaussian noise. q the number of observed
- 6. Independent Component Analysis Step 1: Center data: Step 2: Whiten data: compute SVD of the centered
- 7. Example: PCA and ICA Blind source separation (cocktail party problem) Model:
- 8. PCA vs. ICA PCA: Find projections to minimize reconstruction error Variance of projected data is as
- 9. Computing ICA Step 3: Find out orthogonal A and unit variance, non-Gaussian and independent S. The
- 10. ICA: KL Divergence Criterion x is zero-mean and whitened KL divergence measures “distance” between two probability
- 11. ICA: KL Divergence Criterion… Theorem for random variable transformation says: So, Hence, Minimize with respect to
- 12. ICA: Negentropy Criterion Differential entropy H(.) is not invariant to scaling of variable Negentropy is a
- 13. ICA: Negentropy Criterion… Approximate the negentropy from data by: FastICA (http://www.cis.hut.fi/projects/ica/fastica/) is based on negentropy. Free
- 14. ICA Filter Bank for Image Processing An image patch is modeled as a weighted sum of
- 15. Texture and ICA Filter Bank Training textures 12x12 ICA basis functions or ICA filters Jenssen and
- 16. Segmentation By ICA FB Image, I ICA Filter Bank With n filters I1, I2,…, In Clustering
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