Multiclass SVM with graph path coding regularization for face classification

We consider the problem of learning graphs in a sparse multiclass support vector machines framework. For such a problem, sparse graph penalty is useful to select the significant features and interpret the results. Classical ℓ
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-norm learns a sparse solution without considering the structure between the features. In this paper, a structural knowledge is encoded as directed acyclic graph and a graph path penalty is incorporated to multiclass SVM. The learned classifiers not only improve the performance, but also help in the interpretation of the learned features. The performance of the proposed method highly depends on an initialization graph. Two generic ways to initialize the graph between the features are considered: one is built from similarities while the other one uses Graphical Lasso. The experiments of face classification task on Extended YaleB database verify that: i) graph regularization with multiclass SVM improves the performance and also leads to a more sparse solution compared to ℓ
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-norm.