8,932 research outputs found
Proximal Methods for Hierarchical Sparse Coding
Sparse coding consists in representing signals as sparse linear combinations
of atoms selected from a dictionary. We consider an extension of this framework
where the atoms are further assumed to be embedded in a tree. This is achieved
using a recently introduced tree-structured sparse regularization norm, which
has proven useful in several applications. This norm leads to regularized
problems that are difficult to optimize, and we propose in this paper efficient
algorithms for solving them. More precisely, we show that the proximal operator
associated with this norm is computable exactly via a dual approach that can be
viewed as the composition of elementary proximal operators. Our procedure has a
complexity linear, or close to linear, in the number of atoms, and allows the
use of accelerated gradient techniques to solve the tree-structured sparse
approximation problem at the same computational cost as traditional ones using
the L1-norm. Our method is efficient and scales gracefully to millions of
variables, which we illustrate in two types of applications: first, we consider
fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we
apply our optimization tools in the context of dictionary learning, where
learned dictionary elements naturally organize in a prespecified arborescent
structure, leading to a better performance in reconstruction of natural image
patches. When applied to text documents, our method learns hierarchies of
topics, thus providing a competitive alternative to probabilistic topic models
Collaborative Filtering via Group-Structured Dictionary Learning
Structured sparse coding and the related structured dictionary learning
problems are novel research areas in machine learning. In this paper we present
a new application of structured dictionary learning for collaborative filtering
based recommender systems. Our extensive numerical experiments demonstrate that
the presented technique outperforms its state-of-the-art competitors and has
several advantages over approaches that do not put structured constraints on
the dictionary elements.Comment: A compressed version of the paper has been accepted for publication
at the 10th International Conference on Latent Variable Analysis and Source
Separation (LVA/ICA 2012
Compressed k2-Triples for Full-In-Memory RDF Engines
Current "data deluge" has flooded the Web of Data with very large RDF
datasets. They are hosted and queried through SPARQL endpoints which act as
nodes of a semantic net built on the principles of the Linked Data project.
Although this is a realistic philosophy for global data publishing, its query
performance is diminished when the RDF engines (behind the endpoints) manage
these huge datasets. Their indexes cannot be fully loaded in main memory, hence
these systems need to perform slow disk accesses to solve SPARQL queries. This
paper addresses this problem by a compact indexed RDF structure (called
k2-triples) applying compact k2-tree structures to the well-known
vertical-partitioning technique. It obtains an ultra-compressed representation
of large RDF graphs and allows SPARQL queries to be full-in-memory performed
without decompression. We show that k2-triples clearly outperforms
state-of-the-art compressibility and traditional vertical-partitioning query
resolution, remaining very competitive with multi-index solutions.Comment: In Proc. of AMCIS'201
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
Top-Down Skiplists
We describe todolists (top-down skiplists), a variant of skiplists (Pugh
1990) that can execute searches using at most
binary comparisons per search and that have amortized update time
. A variant of todolists, called working-todolists,
can execute a search for any element using binary comparisons and have amortized search time
. Here, is the "working-set number" of
. No previous data structure is known to achieve a bound better than
comparisons. We show through experiments that, if implemented
carefully, todolists are comparable to other common dictionary implementations
in terms of insertion times and outperform them in terms of search times.Comment: 18 pages, 5 figure
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