Clustering of Learnable Subspaces

PROJECT TITLE :

Learnable Subspace Clustering

ABSTRACT:

The large-scale subspace clustering problem, also known as LS 2 C, is investigated in this article using millions of data points. Although many subspace clustering methods are considered to be state-of-the-art for handling small-scale data points, these methods are unable to directly handle the LS 2 C problem. This is despite the fact that these methods are widely used. A straightforward explanation for this is that these methods frequently select all data points as a large dictionary to construct enormous coding models, which results in high complexity in both terms of time and space. For the purpose of solving the LS 2 C problem in an effective manner, we develop a learnable subspace clustering paradigm here in this article. The fundamental idea is to avoid the computationally intensive traditional coding models in favor of the learning of a parametric function that can partition high-dimensional subspaces into the low-dimensional subspaces that lie underneath them. In addition, we suggest using a unified, robust, predictive coding machine (RPCM) to learn the parametric function, which is a problem that can be solved using an alternating minimization algorithm. Additionally, a bounded contraction analysis of the parametric function is presented here by us. This article, to the best of our knowledge, is the first work to cluster millions of data points efficiently using any of the subspace clustering methods. Experiments conducted on million-scale data sets have shown that our paradigm is superior to the related state-of-the-art methods in terms of both its effectiveness and its efficiency.

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