18,042 research outputs found
Constrained Optimization for a Subset of the Gaussian Parsimonious Clustering Models
The expectation-maximization (EM) algorithm is an iterative method for
finding maximum likelihood estimates when data are incomplete or are treated as
being incomplete. The EM algorithm and its variants are commonly used for
parameter estimation in applications of mixture models for clustering and
classification. This despite the fact that even the Gaussian mixture model
likelihood surface contains many local maxima and is singularity riddled.
Previous work has focused on circumventing this problem by constraining the
smallest eigenvalue of the component covariance matrices. In this paper, we
consider constraining the smallest eigenvalue, the largest eigenvalue, and both
the smallest and largest within the family setting. Specifically, a subset of
the GPCM family is considered for model-based clustering, where we use a
re-parameterized version of the famous eigenvalue decomposition of the
component covariance matrices. Our approach is illustrated using various
experiments with simulated and real data
Extension of SBL Algorithms for the Recovery of Block Sparse Signals with Intra-Block Correlation
We examine the recovery of block sparse signals and extend the framework in
two important directions; one by exploiting signals' intra-block correlation
and the other by generalizing signals' block structure. We propose two families
of algorithms based on the framework of block sparse Bayesian learning (BSBL).
One family, directly derived from the BSBL framework, requires knowledge of the
block structure. Another family, derived from an expanded BSBL framework, is
based on a weaker assumption on the block structure, and can be used when the
block structure is completely unknown. Using these algorithms we show that
exploiting intra-block correlation is very helpful in improving recovery
performance. These algorithms also shed light on how to modify existing
algorithms or design new ones to exploit such correlation and improve
performance.Comment: Matlab codes can be downloaded at:
https://sites.google.com/site/researchbyzhang/bsbl, or
http://dsp.ucsd.edu/~zhilin/BSBL.htm
Image Restoration using Total Variation Regularized Deep Image Prior
In the past decade, sparsity-driven regularization has led to significant
improvements in image reconstruction. Traditional regularizers, such as total
variation (TV), rely on analytical models of sparsity. However, increasingly
the field is moving towards trainable models, inspired from deep learning. Deep
image prior (DIP) is a recent regularization framework that uses a
convolutional neural network (CNN) architecture without data-driven training.
This paper extends the DIP framework by combining it with the traditional TV
regularization. We show that the inclusion of TV leads to considerable
performance gains when tested on several traditional restoration tasks such as
image denoising and deblurring
- …