Topological Gradient-based Competitive Learning
This work addresses the problem of overly complex feature extractors in deep clustering for researchers in unsupervised learning, offering a more integrated approach, though it appears incremental in bridging existing methods.
The paper tackles the gap between competitive learning and gradient-based optimization by introducing a novel theory that bridges the two, enabling the use of deep neural networks for feature extraction combined with competitive learning's flexibility. Preliminary experiments show that the dual approach, trained on the transpose of the input matrix, leads to faster convergence and higher training accuracy in both low and high-dimensional scenarios.
Topological learning is a wide research area aiming at uncovering the mutual spatial relationships between the elements of a set. Some of the most common and oldest approaches involve the use of unsupervised competitive neural networks. However, these methods are not based on gradient optimization which has been proven to provide striking results in feature extraction also in unsupervised learning. Unfortunately, by focusing mostly on algorithmic efficiency and accuracy, deep clustering techniques are composed of overly complex feature extractors, while using trivial algorithms in their top layer. The aim of this work is to present a novel comprehensive theory aspiring at bridging competitive learning with gradient-based learning, thus allowing the use of extremely powerful deep neural networks for feature extraction and projection combined with the remarkable flexibility and expressiveness of competitive learning. In this paper we fully demonstrate the theoretical equivalence of two novel gradient-based competitive layers. Preliminary experiments show how the dual approach, trained on the transpose of the input matrix i.e. $X^T$, lead to faster convergence rate and higher training accuracy both in low and high-dimensional scenarios.