Nonnegative matrix factorization-based dimensionality reducing method used for clustering

Abstract

The invention belongs to the technical field of statistical model identification and machine learning, and in particular discloses a nonnegative matrix factorization-based dimensionality reducing method used for clustering. The method comprises the following steps of: adopting a KL distance; adding a data normalization constraint; directly discovering the internal relation among data dimensionalities by minimizing an object error function between data compression and reconstruction; obtaining a mapping matrix; and projecting high-dimensional data to a low-dimensional subspace by using the mapping matrix so as to perform effective data analysis such as clustering and the like. A simpler iterative formula compared with an original factorization method is obtained by the method; and normalization can be maintained naturally in each iterative updating. The normalization makes a final mapping matrix have higher sparsity compared with the original factorization method. In the obtained low-dimensional space, a clustering result shows that a more effective low-dimensional data characteristic can be obtained by the method; and an algorithm is simple and effective.

Description

technical field [0001] The invention belongs to the technical field of statistical pattern recognition and machine learning, and in particular relates to a dimensionality reduction method for clustering based on non-negative matrix decomposition. Background technique [0002] Clustering is one of the most fundamental research tasks in the field of machine learning. In practical applications, each dimension of the data represents a related feature. Usually, it is difficult to simply judge which features are conducive to clustering. A common method is to collect as many data features as possible and then perform clustering. Therefore, data features are generally high-dimensional, and high-dimensional data features usually bring two problems: 1) high storage and calculation costs, and 2) the curse of dimensionality. In practical applications, the curse of dimensionality problem is one of the main problems faced by many pattern recognition methods, such as gait recognition, im...

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Problems solved by technology

Therefore, data features are generally high-dimensional, and high-dimensional data features usually bring two problems: 1) high storage and calculation costs, 2) dimensionality disaster problem

First, they complicate the original NNMF method to varying degrees, so the final update rule requires more computation time than the original method

Secondly, the iterative update method shows that both matrices C and M are functions of themselves, so C and M need to be initialized at the same time, too many initials may not produce more effective matrix decomposition

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