795 research outputs found
Robust Near-Separable Nonnegative Matrix Factorization Using Linear Optimization
Nonnegative matrix factorization (NMF) has been shown recently to be
tractable under the separability assumption, under which all the columns of the
input data matrix belong to the convex cone generated by only a few of these
columns. Bittorf, Recht, R\'e and Tropp (`Factoring nonnegative matrices with
linear programs', NIPS 2012) proposed a linear programming (LP) model, referred
to as Hottopixx, which is robust under any small perturbation of the input
matrix. However, Hottopixx has two important drawbacks: (i) the input matrix
has to be normalized, and (ii) the factorization rank has to be known in
advance. In this paper, we generalize Hottopixx in order to resolve these two
drawbacks, that is, we propose a new LP model which does not require
normalization and detects the factorization rank automatically. Moreover, the
new LP model is more flexible, significantly more tolerant to noise, and can
easily be adapted to handle outliers and other noise models. Finally, we show
on several synthetic datasets that it outperforms Hottopixx while competing
favorably with two state-of-the-art methods.Comment: 27 page; 4 figures. New Example, new experiment on the Swimmer data
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A D.C. Programming Approach to the Sparse Generalized Eigenvalue Problem
In this paper, we consider the sparse eigenvalue problem wherein the goal is
to obtain a sparse solution to the generalized eigenvalue problem. We achieve
this by constraining the cardinality of the solution to the generalized
eigenvalue problem and obtain sparse principal component analysis (PCA), sparse
canonical correlation analysis (CCA) and sparse Fisher discriminant analysis
(FDA) as special cases. Unlike the -norm approximation to the
cardinality constraint, which previous methods have used in the context of
sparse PCA, we propose a tighter approximation that is related to the negative
log-likelihood of a Student's t-distribution. The problem is then framed as a
d.c. (difference of convex functions) program and is solved as a sequence of
convex programs by invoking the majorization-minimization method. The resulting
algorithm is proved to exhibit \emph{global convergence} behavior, i.e., for
any random initialization, the sequence (subsequence) of iterates generated by
the algorithm converges to a stationary point of the d.c. program. The
performance of the algorithm is empirically demonstrated on both sparse PCA
(finding few relevant genes that explain as much variance as possible in a
high-dimensional gene dataset) and sparse CCA (cross-language document
retrieval and vocabulary selection for music retrieval) applications.Comment: 40 page
Facts and Fabrications about Ebola: A Twitter Based Study
Microblogging websites like Twitter have been shown to be immensely useful
for spreading information on a global scale within seconds. The detrimental
effect, however, of such platforms is that misinformation and rumors are also
as likely to spread on the network as credible, verified information. From a
public health standpoint, the spread of misinformation creates unnecessary
panic for the public. We recently witnessed several such scenarios during the
outbreak of Ebola in 2014 [14, 1]. In order to effectively counter the medical
misinformation in a timely manner, our goal here is to study the nature of such
misinformation and rumors in the United States during fall 2014 when a handful
of Ebola cases were confirmed in North America. It is a well known convention
on Twitter to use hashtags to give context to a Twitter message (a tweet). In
this study, we collected approximately 47M tweets from the Twitter streaming
API related to Ebola. Based on hashtags, we propose a method to classify the
tweets into two sets: credible and speculative. We analyze these two sets and
study how they differ in terms of a number of features extracted from the
Twitter API. In conclusion, we infer several interesting differences between
the two sets. We outline further potential directions to using this material
for monitoring and separating speculative tweets from credible ones, to enable
improved public health information.Comment: Appears in SIGKDD BigCHat Workshop 201
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