Cognitive Gravity Model Based Semi-Supervised Dimension Reduction

Dimension reduction is very important for pattern recognition. Preserving the manifold is a popular way to enhance the effect of the dimension reduction method. However, most of the manifold is designed according to the distribution of the data but not the requirement of the classifier, and then the preserved manifold structure could be not what the classifier need. In this paper, we note that the samples are often with different densities, and it is often ignored by many classifiers, such as support vector machine and k-nearest neighbors. To overcome this problem, a new manifold based on the cognitive gravity model and Laplace matrix is designed, where the weight of the similar matrix of the Laplace matrix is set by the corresponding gravity. As a result, the difference among the densities of samples can be reduced by preserving the manifold. Subsequently, a new semi-supervised dimension reduction based on the above manifold is designed. The conducted experiments validate the proposed approach in term of the performance of classification.