Fast Anchor Graph Optimized Projections with Principal Component Analysis and Entropy Regularization

Abstract

Traditional machine learning algorithms often fail when dealing with high-dimensional data, called ``dimensional disaster". In order tosolve this problem, many dimensionality reduction algorithms have been proposed. Graph-based dimensionality reduction algorithms, which are currently a focus of research, have high time complexity of $O(n^2d)$, where $n$ represents the number of samples, and $d$ represents the number of features. On the other hand, these methods do not consider the global data information. To solve the above two problems, we propose a novel method named Fast Anchor Graph Optimized Projections with Principal Component Analysis and Entropy Regularization (FAGPE), which integrates anchor graph, entropy regularization term, and Principal Component Analysis (PCA). In the proposed model, the anchor graph with sparse constraint captures the cluster information of the data, while the embedded Principal Component Analysis takes into account the global data information. This paper introduces a novel iterative optimization approach to address the proposed model. In general, the time complexity of our proposed algorithm is $O(nmd)$, with $m$ representing the number of anchors. Finally, the experiment results on many benchmark datasets show that the proposed algorithm calculates quickly compared with the comparison algorithms, and a better classifier is obtained on the reduced dimension data.

Keywords: Dimensionality reduction, principal component analysis, entropy regularization, unsupervised learning