The paper tackles subspace-preserving recovery of sparse signals from overcomplete dictionaries.
problem Recovering sparse signals from overcomplete dictionaries when the signal lies in a subspace of the dictionary.
method Geometric conditions and covering radius/angular distance to ensure subspace-preserving recovery.
result Theoretical analysis shows that subspace-preserving recovery is possible without requiring incoherence or restricted isometry of the dictionary.
State-of-the-art subspace clustering methods are based on expressing each data point as a linear combination of other data points while regularizing the matrix of coefficients with ℓ1, ℓ2 or nuclear norms. ℓ1 regularization is guaranteed to give a subspace-preserving affinity (i.e., there are no conne…
Subspace clustering methods based on ℓ1, ℓ2 or nuclear norm regularization have become very popular due to their simplicity, theoretical guarantees and empirical success. However, the choice of the regularizer can greatly impact both theory and practice. For instance, ℓ1 regularization is guaranteed t…
State-of-the-art algorithms for sparse subspace clustering perform spectral clustering on a similarity matrix typically obtained by representing each data point as a sparse combination of other points using either basis pursuit (BP) or orthogonal matching pursuit (OMP). BP-based methods are often prohibitive in practic…
Quantile regression is a method to estimate the quantiles of the conditional distribution of a response variable, and as such it permits a much more accurate portrayal of the relationship between the response variable and observed covariates than methods such as Least-squares or Least Absolute Deviations regression. It…
Stochastic Sparse Subspace Clustering improves subspace clustering by reducing over-segmentation through dropout.
problem Over-segmentation in subspace clustering.
method Introducing dropout regularization to enforce denser connections between points from the same subspace.
result Stochastic Sparse Subspace Clustering effectively handles large datasets and reduces over-segmentation.
We develop embeddings for nonlinear subspaces preserving vector norms.
problem Preserving vector norms in nonlinear subspaces.
method Low-distortion embeddings for subspaces under nonlinear transformations.
result First low-distortion embeddings for a wide class of nonlinear functions.