Machine Learning for Multimedia Content Analysis (Multimedia by Yihong Gong, Wei Xu

By Yihong Gong, Wei Xu

This quantity introduces laptop studying options which are quite robust and potent for modeling multimedia facts and customary initiatives of multimedia content material research. It systematically covers key computing device studying ideas in an intuitive type and demonstrates their purposes via case reports. insurance comprises examples of unsupervised studying, generative versions and discriminative versions. moreover, the ebook examines greatest Margin Markov (M3) networks, which try to mix the benefits of either the graphical versions and help Vector Machines (SVM).

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Xj−1 , the quotient xT Ax is minimized by the next smallest eigenvector xj , and its minimum value xT x is the corresponding eigenvalue λj . Applying this theorem to the above four criterion functions, we obtain the following solutions. Average Weight FAW ≤ λ1 + . . 16) where λ1 , . . 12) are the eigenvectors of the largest eigenvalues. Ratio Cut FRC ≥ λN + . . 17) where λN , . . 13) are the eigenvectors of the smallest eigenvalues. Normalized Cut FN C ≥ K − (λ1 + . . 18) where λ1 , .

Maximizing these metrics can be achieved using the standard gradient decent algorithm and its variations. 13) can be found in [12]. 3 shows the subspace obtained by applying the ICA algorithm to the synthetic data set shown in Fig. 1. The data distribution in the figure confirms that the two axes of this subspace correspond to the two directions that provide the maximum statistical independence. 4 Dimension Reduction by Locally Linear Embedding Many complex data represented by high-dimensional spaces typically have a much more compact description.

13) where yg is a Gaussian variable with zero mean and unit variable, and G(y) = 1 a log cosh(ay) for 1 ≤ a ≤ 2. 3 Independent Component Analysis 23 Mutual Information The mutual information I between the components of a random vector y = [y1 , y2 , . . , yn ]T is defined as n H(yi ) − H(y) . I(y1 , y2 , . . 14) i=1 The quantity I(y1 , y2 , . . , yn ) is equivalent to the famous Kullback-Leibler divergence between the joint density p(y) and the product of its marginal n densities i=1 p(yi ), which is an independent version of p(y).

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