Supervised Hessian Eigenmap for Dimensionality Reduction
Abstract: Hessian Eigenmap is one proposed technique for dimensionality reduction. Many methods, such as ISOMAP, LLE, Laplacian Eigenmap, have been proposed under manifold learning for dimensionality reduction. However, all these ideas have not taken the influence of different class into consideration, which limit the effectiveness of manifold learning. To take account for the influence for multiclass and improve the performance of dimensional reduction, we proposed a new method, supervised Hessian LLE(SHLLE). To evaluate the proposed method, extensive experiments were conducted on the artificial dataset and real dataset(COIL-20). Our result demonstrate that the proposed method outperform HLLE method.
Keywords: Manifold Learning; Locally Linear Embedding; Hessian Eigenmap; Supervised Learning
Density Peak based Co-Spectral Clustering
Abstract: Spectral clustering employs spectral-graph structure of a similarity matrix to partition data into disjoint meaningful groups, because of its well-defined mathematical framework, good performance on arbitrary shaped clusters and simplicity, spectral clustering has gained considerable attentions in the recent past. Despite these virtues, spectral clustering suffers from several drawbacks, such as it is sensitive to initial condition, not robust to outliers and unable to determine a reasonable cluster number and so on. In this paper, we present a new approach named density peak spectral clustering (DPSC) which combines spectral clustering with density peak clustering algorithm (DPCA) into a unified framework to solve these problems. Since multi-view data is common in clustering problem, to further bootstrap the clustering performance by using complementary information from different view, then we propose co-trained density peak spectral clustering (Co-DPSC) which is an extension of DPSC to multi-views based on the co-training idea. Experimental comparisons with a number of baselines on a toy and three real-world datasets show the effectiveness of our proposed DPSC and Co-DPSC algorithm.
Keywords: Spectral clustering; Density peak clustering; Multi-view; Co-training