2 research outputs found
Evolutionary Self-Expressive Models for Subspace Clustering
The problem of organizing data that evolves over time into clusters is
encountered in a number of practical settings. We introduce evolutionary
subspace clustering, a method whose objective is to cluster a collection of
evolving data points that lie on a union of low-dimensional evolving subspaces.
To learn the parsimonious representation of the data points at each time step,
we propose a non-convex optimization framework that exploits the
self-expressiveness property of the evolving data while taking into account
representation from the preceding time step. To find an approximate solution to
the aforementioned non-convex optimization problem, we develop a scheme based
on alternating minimization that both learns the parsimonious representation as
well as adaptively tunes and infers a smoothing parameter reflective of the
rate of data evolution. The latter addresses a fundamental challenge in
evolutionary clustering -- determining if and to what extent one should
consider previous clustering solutions when analyzing an evolving data
collection. Our experiments on both synthetic and real-world datasets
demonstrate that the proposed framework outperforms state-of-the-art static
subspace clustering algorithms and existing evolutionary clustering schemes in
terms of both accuracy and running time, in a range of scenarios
Efficient Least Residual Greedy Algorithms for Sparse Recovery
We present a novel stagewise strategy for improving greedy algorithms for
sparse recovery. We demonstrate its efficiency both for synthesis and analysis
sparse priors, where in both cases we demonstrate its computational efficiency
and competitive reconstruction accuracy. In the synthesis case, we also provide
theoretical guarantees for the signal recovery that are on par with the
existing perfect reconstruction bounds for the relaxation-based solvers and
other sophisticated greedy algorithms.Comment: accepted to IEEE Transactions on Signal Processin