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Non-negative matrix factorization with sparseness constraints
Non-negative matrix factorization (NMF) is a recently developed technique for
finding parts-based, linear representations of non-negative data. Although it
has successfully been applied in several applications, it does not always
result in parts-based representations. In this paper, we show how explicitly
incorporating the notion of `sparseness' improves the found decompositions.
Additionally, we provide complete MATLAB code both for standard NMF and for our
extension. Our hope is that this will further the application of these methods
to solving novel data-analysis problems
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
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