Mathematics Colloquia and Seminars

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As the size and complexity of data continues to grow, extracting knowledge becomes exponentially more challenging. Active areas of research for mining this high dimensional data can be found across a broad range of scientific fields including pure and applied mathematics, statistics, computer science and engineering. Spectral embedding is one of the most powerful and widely used techniques for extracting the underlying global structure of a data set. Compressed sensing and matrix completion have emerged as prevailing methods for efficiently recovering sparse and partially observed signals. In this talk, we combine the distance preserving measurements of compressed sensing and matrix completion with the robust power of spectral embedding. Our analysis provides rigorous bounds on how small perturbations from using compressed sensing and matrix completion affect the affinity matrix and in succession the spectral coordinates. Theoretical guarantees are complemented with numerical results. A number of examples of the unsupervised organization and clustering of synthetic and real world image data are also shown.