The Effectiveness of Johnson-Lindenstrauss Transform for High Dimensional Optimization with Outliers
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Johnson-Lindenstrauss (JL) Transform is one of the most popular methods for dimension reduction. In this paper, we study the effectiveness of JL transform for solving the high dimensional optimization problems with outliers. We focus on two fundamental optimization problems: k-center clustering with outliers and SVM with outliers. In general, the time complexity for dealing with outliers in high dimensional space could be very large. Based on some novel insights in geometry, we prove that the complexities of these two problems can be significantly reduced through JL transform. In the experiments, we compare JL transform with several other well known dimension reduction methods, and study their performances on synthetic and real datasets.
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