$k$-Subspace Method

We propose the k-subspace method, a clustering method based on the subspace method, and the k-subspace classification method, a pattern recognition method that utilizes multiple subspaces for each class. Conventional clustering algorithms, such as the k-means method, operate based on centroids. However, in image recognition, subspaces provide a more essential representation. Existing techniques, such as CLAFIC, define a single subspace per class. However, real-world data often exhibit significant intra-class variations, such as diverse character styles within the same class. We hypothesize that partitioning subspaces into subsets, which account for intra-class variations, will enhance classification accuracy. In this study, we examine the feasibility of partitioning a sub-space into <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$k$</tex> subclasses. We apply the proposed method to image recognition and experimentally demonstrate its effectiveness.