Matrixized learning machine with modified pairwise constraints

• A novel matrix-oriented classification algorithm named MLMMPC is proposed.
• To improve the original matrix learning framework by a new regularization term RpRp.
• To combine pairwise constraints and spatial measure together in RpRp.
• Implementability is demonstrated on both image- and vector-based datasets.

Matrix-pattern-oriented Classifier Design (MatCD) has been demonstrated to be effective in terms of the classification performance since it utilizes two-sided weight vectors to constrain the matrix-based patterns. However, the existing MatCD might not be able to acquire the prior distribution knowledge, such as the relationship between two patterns. Inspired by the Pairwise Constraints (PC) method, i.e., must-links and cannot-links between the patterns, this paper introduces a new regularization term named Rp with a modified PC method into MatCD. The new classifier design strategy is expected to not only learn the structural information of each pattern itself, but also acquire the prior distribution knowledge about each constrained pair with both the discrimination metric from the traditional PC and the spatial distance measure from the heat kernel method. In practice, this paper selects one typical matrixized classifier named MatMHKS as the basic building block and introduces the term Rp into it. The newly-proposed classifier is named MLMMPC and the subsequent experiments validate the effectiveness of it. Two major contributions of this paper can be concluded as (1) improving the existing matrix-pattern-oriented classifier design techniques and (2) modifying the traditional PC method by combining the discrimination metric and the distance measure together.