Fast anchor graph optimized projections with principal component analysis and entropy regularization

Traditional machine learning algorithms often fail when dealing with high-dimensional data, which is called “curse of dimensionality”. In order to solve this problem, many dimensionality reduction algorithms have been proposed. Graph-based dimensionality reduction technology is a research hotspot. Traditional graph-based dimensionality reduction algorithms are based on similarity graphs and have a high time complexity of O(n²d), 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 structure 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 experimental results on many benchmark data sets show that the proposed algorithm achieves better classification performance on the reduced dimension data.