33 research outputs found
Expectile Matrix Factorization for Skewed Data Analysis
Matrix factorization is a popular approach to solving matrix estimation
problems based on partial observations. Existing matrix factorization is based
on least squares and aims to yield a low-rank matrix to interpret the
conditional sample means given the observations. However, in many real
applications with skewed and extreme data, least squares cannot explain their
central tendency or tail distributions, yielding undesired estimates. In this
paper, we propose \emph{expectile matrix factorization} by introducing
asymmetric least squares, a key concept in expectile regression analysis, into
the matrix factorization framework. We propose an efficient algorithm to solve
the new problem based on alternating minimization and quadratic programming. We
prove that our algorithm converges to a global optimum and exactly recovers the
true underlying low-rank matrices when noise is zero. For synthetic data with
skewed noise and a real-world dataset containing web service response times,
the proposed scheme achieves lower recovery errors than the existing matrix
factorization method based on least squares in a wide range of settings.Comment: 8 page main text with 5 page supplementary documents, published in
AAAI 201
Poisson noise reduction with non-local PCA
Photon-limited imaging arises when the number of photons collected by a
sensor array is small relative to the number of detector elements. Photon
limitations are an important concern for many applications such as spectral
imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson
distribution is used to model these observations, and the inherent
heteroscedasticity of the data combined with standard noise removal methods
yields significant artifacts. This paper introduces a novel denoising algorithm
for photon-limited images which combines elements of dictionary learning and
sparse patch-based representations of images. The method employs both an
adaptation of Principal Component Analysis (PCA) for Poisson noise and recently
developed sparsity-regularized convex optimization algorithms for
photon-limited images. A comprehensive empirical evaluation of the proposed
method helps characterize the performance of this approach relative to other
state-of-the-art denoising methods. The results reveal that, despite its
conceptual simplicity, Poisson PCA-based denoising appears to be highly
competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio
Structured Sparse Principal Component Analysis
We present an extension of sparse PCA, or sparse dictionary learning, where
the sparsity patterns of all dictionary elements are structured and constrained
to belong to a prespecified set of shapes. This \emph{structured sparse PCA} is
based on a structured regularization recently introduced by [1]. While
classical sparse priors only deal with \textit{cardinality}, the regularization
we use encodes higher-order information about the data. We propose an efficient
and simple optimization procedure to solve this problem. Experiments with two
practical tasks, face recognition and the study of the dynamics of a protein
complex, demonstrate the benefits of the proposed structured approach over
unstructured approaches