Matrixized Learning Machine with Feature-Clustering Interpolation

The existing matrixized learning machines (MLMs) use bilateral weight vectors on both side of one pattern as the constraints to manipulate matrix-based datasets directly. However, MLM might be challenged while the input pattern is a vector whose features are independent from each others. The traditional solution is to transform the vector into its all corresponding matrix forms, which is not only irrational, but also requiring extra computation in preprocessing. To overcome the problem, this paper proposes a novel matrixized learning model that utilizes an efficient clustering-based interpolation strategy to mapping the original vector-based pattern to an unique matrix. The proposed method first selects the most typical features defined as $$candidate\hbox {s}$$candidates from each dimension of all patterns in the same class through a fast clustering method, and then measures the relationship between the features of each training pattern and the $$candidate\hbox {s}$$candidates to generate a new matrix named the candidate-matrix in turn. Afterwards, the candidate-matrix is combined with the pattern to form the corresponding final matrix. At last, all final matrices are collected to form the new training set for the subsequent matrixized classifier. Named FCIMLM for short, the proposed matrixized method is proved more effective and efficient than the traditional MLM under the same structural risk minimum framework through the designed experiments on 21 vector-based benchmark datasets from UCI repository. The main contributions of this paper are: (1) proposing a new matrixized learning model with a more efficient matrixization process using a feature-based fast clustering strategy; (2) combining the feature-clustering-based interpolation to the matrix-pattern-oriented classifier for the first time; (3) extending the existing MLM design techniques.