Clustering joint Locality Preserving Projections
Yuanhao Li · 2023
When clustering high-dimensional data, dimensionality reduction techniques are usually employed to project the data into a low-dimensional subspace. However, the existing graph-based dimensionality reduction algorithms only consider the weights among samples and don't consider the cluster structure of the raw data, which leads to the weakening or even disappearance of the cluster structure after dimensionality reduction. On the one hand, we hope to obtain well-formed clusters in the projected data, on the other hand, the local structure of data is also maintained. Therefore, we integrate the dimensionality reduction model and clustering model into one model, especially, the proposed model also considers the relationship between the cluster information in the original space and the cluster information in the subspace. The proposed model learns the optimal projection matrix while preserving the local information. Because the clustering model is embedded, the projected data can obtain well-formed clusters. The proposed model is solved by an iterative algorithm and the convergence is proved. We conducted a lot of experiments on six high-dimensional image data sets and the experimental results show the effectiveness of our algorithm.