IMAT: matrix learning machine with interpolation mapping

Abstract

In matrix learning, vector patterns are simply transformed into matrix ones by some reshaping techniques such as from 100 × 1 to 20 × 5. Unfortunately, the techniques are random and fail in some cases. To this end, a matrix learning machine with interpolation mapping named IMAT for short is proposed. IMAT interpolates each feature of the original vector pattern into its corresponding k-means slots so as to generate a matrix pattern with more structural information. Furthermore, the pairwise information of every two features can be introduced into the IMAT. After that, the IMAT can be applied into matrix-based classifiers. The contributions of the proposed IMAT are listed as follows. (i) the IMAT can extract more intrinsic structural information compared with those random techniques reshaping the vector into a matrix. (ii) The IMAT is supposed to be reasonably and naturally embedded into matrix-based classifiers. In the experiments, the authors' previous work is adopted, a matrix-based classifier named MatMHKS, to examine the IMAT on some UCI datasets. The results verify the superior classification performance of IMAT.

Matrixized Learning Machine with Feature-Clustering Interpolation

“…The traditional strategy to help MLM deal with vector-based datasets is to reshape the vector into different kinds of matrix forms by rearranging different features of the pattern in row or column order [3]. Nevertheless, the first strategy is arbitrary and might fail in some special cases [23]. Furthermore, if the dimensionality of the pattern is high, the complexity of the reshaping and the subsequent training process would become very high [23].…”

“…Nevertheless, the first strategy is arbitrary and might fail in some special cases [23]. Furthermore, if the dimensionality of the pattern is high, the complexity of the reshaping and the subsequent training process would become very high [23]. In this paper, the proposed algorithm is expected to transform the vector into only one matrix form and capture more prior global knowledge.…”

“…Finally, the form should include more informative global knowledge if possible. Inspired by a novel interpolation idea focusing on non-linear feature mapping from the discretization of each individual [19], the previous work [23] proposes a new interpolation mapping strategy for MLM to solve the origianl re-shaping problem by concatenating the newly-generated featrues into a matrix side by side. However, such mapping method needs to calculate all pairs between one feature and its neighbors [23], leading to a high computational complexity.…”

“…Inspired by a novel interpolation idea focusing on non-linear feature mapping from the discretization of each individual [19], the previous work [23] proposes a new interpolation mapping strategy for MLM to solve the origianl re-shaping problem by concatenating the newly-generated featrues into a matrix side by side. However, such mapping method needs to calculate all pairs between one feature and its neighbors [23], leading to a high computational complexity. In this paper, we try to build a relatively faster learning model to mapping the vector to the matrix and operate the subsequent training with the following four main steps: Initially, the γ most typical features rather than patterns, defined as the candidate of each dimension from each training class, are selected through a fast clustering method.…”

Matrixized learning machine with modified pairwise constraints

“…It implies that the matrixized method could deal with the vector-based patterns too. Moreover, the matrixized method could provide a new perspective for operating the original vector-based patterns, such as the multi-view learning using different matrices transformed from the same vector [48] and the interpolation mapping expanding a vector to a matrix with extra information [47]. The detailed comparison between the matrixized model and the vectorized model is demonstrated in Section 2.…”