Principal Component Analysis (PCA)

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<strong>PCA</strong> vs. Discrimination • variance maximization or compression are different from discrimination! • consider this data coming stemming from two classes? • which direction has max. variance, which discriminates between the two clusters? Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 18
Application: <strong>PCA</strong> on face images • 120 × 100 pixel grayscale 2D images of faces. Each image is considered to be a single point in face space (a single sample from a random vector): ⎡↑⎤ ⎢ ⎥ ⎢x⎥ ⎢ ⎥ ⎣↓⎦ • How many dimensions is the vector x ? n = 120 • 100 = 12000 • Each dimension (each pixel) can take values between 0 and 255 (8 bit grey scale images). • You can easily visualize points in this 12000 dimensional space! Jochen Triesch, UC San Diego, http://cogsci.ucsd.edu/~triesch 19
Page 1 and 2: Principal Component Analysis (PCA)
Page 3 and 4: Example: • consider projecting x
Page 5 and 6: • continuing with some linear alg
Page 7 and 8: Notes: • if v is an eigenvector o
Page 9 and 10: What are the variances of the PCA p
Page 11 and 12: PCA for multinomial Gaussian • We
Page 13 and 14: Transformation matrix for PCA • L
Page 15 and 16: • PCA expresses the mean-subtract
Page 17: • Equivalent view: To compress n-
Page 21 and 22: The mean face Jochen Triesch, UC Sa
Page 23 and 24: The transpose trick The eigenvector
Page 25 and 26: Eigenfaces • Eigenfaces (the prin
Page 27 and 28: PCA for low-dimensional low dimensi
Page 29 and 30: The mean face Jochen Triesch, UC Sa
Page 31 and 32: Approximating a face using the firs
Page 33 and 34: Approximating a face using all 97 e
Page 35: Eigenfaces in 3D • Blanz and Vett

Principal Component Analysis (PCA)

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