Multi-Label Learning with Missing Labels via Common and Label-Specific Features

Abstract

In multi-label learning with missing labels, previous works usually only consider all features, or only consider label-specific features. It is obviously inappropriate to select a subset of features only considering which have a great discriminability for all labels or for a label. Besides, they are built on an assumption that if two labels are correlated, their regression coefficient vectors should be similar. However, it is hard to hold this assumption in real-world applications. Therefore, we propose a novel multi-label classification approach for missing labels via considering common and label-specific features with correlation information. More specifically, we firstly utilize <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{1}$</tex> - norm regularizer over label correlation matrix, and a new sup-plementary label matrix is augmented from the incomplete label matrix by learning label correlations. Then, for a better label recovery, we introduce <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{2,1}$</tex> -norm and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$l_{1}$</tex> -norm regularizers to learn common and label-specific features simultaneously. Thirdly, to make more rational use of label correlation to solve missing labels, we use a regularizer to constrain label correlations on outputs of labels instead of regression coefficient matrix. Finally, an objective function is designed in terms of the above processing. Extensive experiments conducted on eight data sets demonstrate the effectiveness of the proposed approach.