Supplementary Materials: Self-Paced Learning with Diversity

This is the supplementary material for the paper entitled “Self-Paced Learning with Diversity”. The material is organized as follows: Section 1 gives the proof of Theorem 1. Section 2.1 and Section 2.2 present the detailed experimental settings and results on the MED (Multimedia Event Detection) dataset. Section 2.3 and Section 2.4 present the settings and detailed results on the Hollywood2 and Olympic datasets. Section 3 briefly discusses our practical lessons and the observed deficiency of the SPL/SPLD models. 1 Proof of Theorem 1 We present the proof of Theorem 1 in the paper. Given the training dataset D = {(x1, y1), · · · , (xn, yn)}, where xi ∈ R denotes the i observed sample and yi denotes its label. Assume that the training samplesX = [x1, · · · ,xn] are with b groups: X, · · · ,X, where X (j) = (x (j) 1 , · · · ,x (j) nj ) ∈ Rm×nj corresponds to samples in the j group, nj is the sample number in this group and ∑b j=1 nj = n. Accordingly, denote the weight vector as v = [v , · · · ,v], where v = (v (j) 1 , · · · , v (j) nj ) T ∈ Rj . The following theorem proves that Algorithm 1 can get the global solution of the following non-convex optimization problem: min v∈[0,1]n E(w,v;λ, γ) = n ∑ i=1 viL(yi, f(xi,w))− λ n ∑ i=1 vi − γ‖v‖2,1, (1) where L(yi, f(xi,w)) denotes the loss function which calculates the cost between the ground truth label yi and the estimated label f(xi,w), and the l2,1-norm ‖v‖2,1 is the group sparsity of v: ‖v‖2,1 = b ∑