A Review on Dimensionality Reduction Techniques

High-dimensional data is ubiquitous in scientific research and industrial production fields. It brings a lot of information to people, at the same time, because of its sparse and redundancy, it also brings great challenges to data mining and pattern recognition. Dimensionality reduction can reduce redundancy and noise, reduce the complexity of learning algorithms, and improve the accuracy of classification, it is an important and key step in pattern recognition system. In this paper, we overview the classical techniques for dimensionality reduction and review their properties, and categorize these techniques according to their implementation process. We deduce each algorithm in detail and intuitively show their underlying mathematical principles. Thereby, the focus is to uncover the optimization process for each technique. We compare the characteristics and limitations of each technique and summarize the scope of application, discussing a number of open problems and a perspective of research trend in future.