2. (PCA and kernel PCA) Given a data matrix X = [2₁₂ %], where x (1, 0)”, x2 = (0, −−1)”, x − (−)" and x − (√)". (a) Find the first principal component w€ R², and then compute (b) Let K(,): R² × R² → R given by Note that K() is a reproducing kernel, and thus there is a corresponding RKHS, denoted by (H. (-)). 1 1. Use this kernel to perform kernel PCA, and find the first principal com- ponente € H. . Recall that this first principal componente can be expressed as v(x)-(,), satisfying (, ) 1. Calculate K()-(K(·)) w

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