PPT-Noisy Sparse Subspace Clustering with dimension reduction

Yining Wang YuXiang Wang Aarti Singh Machine Learning Department Carnegie mellon university 1 Subspace Clustering 2 Subspace Clustering Applications Motion Trajectories tracking 1. edusg Department of Mechanical Engineering National University of Singapore Singapore 117576 Huan Xu mpexuhnusedusg Department of Mechanical Engineering National University of Singapore Singapore 117576 Abstract This paper considers the problem of su Chun Lam Chan. , Pak . Hou. . Che. and . Sidharth. . Jaggi. The Chinese University of Hong Kong. Venkatesh. . Saligrama. Boston University. Non-adaptive probabilistic group testing with noisy measurements: Near-optimal bounds with efficient algorithms. Asymptotics. Yining Wang. , Jun . zhu. Carnegie Mellon University. Tsinghua University. 1. Subspace Clustering. 2. Subspace Clustering Applications. Motion Trajectories tracking. 1. 1 . (. Elhamifar. Lecture outline. Distance/Similarity between data objects. Data objects as geometric data points. Clustering problems and algorithms . K-means. K-median. K-center. What is clustering?. A . grouping. of data objects such that the objects . Tianzhu . Zhang. 1,2. , . Adel Bibi. 1. , . Bernard Ghanem. 1. 1. 2. Circulant. Primal . Formulation. 3. Dual Formulation. Fourier Domain. Time . Domain. Here, the inverse Fourier transform is for each . Iterative Methods. Erin Carson. UC Berkeley Parallel Computing Lab. BeBop. Group. Discovery 2015: HPC and Cloud Computing. Workshop, June 2011. President . Obama. cites Communication Avoiding algorithms in the FY 2012 Department of Energy Budget Request to Congress:. Moritz . Hardt. , David P. Woodruff. IBM Research . Almaden. Two Aspects of Coping with Big Data. Efficiency. Handle. enormous inputs. Robustness. Handle . adverse conditions. Big Question: Can we have both?. Author: . Vikas. . Sindhwani. and . Amol. . Ghoting. Presenter: . Jinze. Li. Problem Introduction. we are given a collection of N data points or signals in a high-dimensional space R. D. : xi ∈ . René Vidal. Center for Imaging Science. Institute for Computational Medicine. Johns Hopkins University. Manifold Clustering with Applications to Computer Vision and Diffusion Imaging. René Vidal. Center for Imaging Science. Contents. Motivation. Data. Dimension. ality. . Reduction-MDS, Isomap. Clustering-Kmeans, Ncut, Ratio Cut, SCC. Conclustion. Reference. Motivation. Clustering is a main task of exploratory data mining. issue in . computing a representative simplicial complex. . Mapper does . not place any conditions on the clustering . algorithm. Thus . any domain-specific clustering algorithm can . be used.. We . Venkat. . Guruswami. , Nicolas Resch and . Chaoping. Xing. Algebraic . Pseudorandomness. Traditional pseudorandom objects (e.g., . expander graphs. , . randomness extractors. , . pseudorandom generators. What is clustering?. Why would we want to cluster?. How would you determine clusters?. How can you do this efficiently?. K-means Clustering. Strengths. Simple iterative method. User provides “K”. Metric . Embeddings. COMS E6998-9. . F15. Administrivia. , Plan. PS2:. Pick up after class. 120->144 auto extension. Plan:. Least Squares Regression (finish). Metric . Embeddings. “reductions for distances”.