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Learning from high-dimensional noisy data via projections onto multi-dimensional ellipsoids

In this paper, we examine the problem of learning from noise-contaminated data in high-dimensional space. A new learning approach based on projections onto multi-dimensional ellipsoids (POME) is introduced, which is applicable to unsupervised clustering, semi-supervised clustering and classification in high-dimensional noisy data. Unlike the traditional learning techniques, where local information is used for data analysis, the proposed POME-based scheme incorporates a priori information of the data distribution. Experimental results in unsupervised clustering demonstrate the superiority of the proposed POME-based scheme to some well-known clustering algorithms, including the k-means and the hierarchical agglomerative clustering. We also illustrate the effectiveness of our proposed POME-based scheme in semi-supervised learning by simulation.