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Sparse PCA via Bipartite Matchings
Megasthenis Asteris · Dimitris Papailiopoulos · Anastasios Kyrillidis · Alex Dimakis

Wed Dec 09 04:00 PM -- 08:59 PM (PST) @ 210 C #57
We consider the following multi-component sparse PCA problem:given a set of data points, we seek to extract a small number of sparse components with \emph{disjoint} supports that jointly capture the maximum possible variance.Such components can be computed one by one, repeatedly solving the single-component problem and deflating the input data matrix, but this greedy procedure is suboptimal.We present a novel algorithm for sparse PCA that jointly optimizes multiple disjoint components. The extracted features capture variance that lies within a multiplicative factor arbitrarily close to $1$ from the optimal.Our algorithm is combinatorial and computes the desired components by solving multiple instances of the bipartite maximum weight matching problem.Its complexity grows as a low order polynomial in the ambient dimension of the input data, but exponentially in its rank.However, it can be effectively applied on a low-dimensional sketch of the input data.We evaluate our algorithm on real datasets and empirically demonstrate that in many cases it outperforms existing, deflation-based approaches.

Author Information

Megasthenis Asteris (University of Texas at Austin)
Dimitris Papailiopoulos (UC Berkeley)
Anastasios Kyrillidis (University of Texas at Austin)
Alex Dimakis (University of Texas, Austin)

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