141 research outputs found
Enhanced Lasso Recovery on Graph
This work aims at recovering signals that are sparse on graphs. Compressed
sensing offers techniques for signal recovery from a few linear measurements
and graph Fourier analysis provides a signal representation on graph. In this
paper, we leverage these two frameworks to introduce a new Lasso recovery
algorithm on graphs. More precisely, we present a non-convex, non-smooth
algorithm that outperforms the standard convex Lasso technique. We carry out
numerical experiments on three benchmark graph datasets
Structured Sequence Modeling with Graph Convolutional Recurrent Networks
This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep
learning model able to predict structured sequences of data. Precisely, GCRN is
a generalization of classical recurrent neural networks (RNN) to data
structured by an arbitrary graph. Such structured sequences can represent
series of frames in videos, spatio-temporal measurements on a network of
sensors, or random walks on a vocabulary graph for natural language modeling.
The proposed model combines convolutional neural networks (CNN) on graphs to
identify spatial structures and RNN to find dynamic patterns. We study two
possible architectures of GCRN, and apply the models to two practical problems:
predicting moving MNIST data, and modeling natural language with the Penn
Treebank dataset. Experiments show that exploiting simultaneously graph spatial
and dynamic information about data can improve both precision and learning
speed
Matrix Completion on Graphs
The problem of finding the missing values of a matrix given a few of its
entries, called matrix completion, has gathered a lot of attention in the
recent years. Although the problem under the standard low rank assumption is
NP-hard, Cand\`es and Recht showed that it can be exactly relaxed if the number
of observed entries is sufficiently large. In this work, we introduce a novel
matrix completion model that makes use of proximity information about rows and
columns by assuming they form communities. This assumption makes sense in
several real-world problems like in recommender systems, where there are
communities of people sharing preferences, while products form clusters that
receive similar ratings. Our main goal is thus to find a low-rank solution that
is structured by the proximities of rows and columns encoded by graphs. We
borrow ideas from manifold learning to constrain our solution to be smooth on
these graphs, in order to implicitly force row and column proximities. Our
matrix recovery model is formulated as a convex non-smooth optimization
problem, for which a well-posed iterative scheme is provided. We study and
evaluate the proposed matrix completion on synthetic and real data, showing
that the proposed structured low-rank recovery model outperforms the standard
matrix completion model in many situations.Comment: Version of NIPS 2014 workshop "Out of the Box: Robustness in High
Dimension
FMA: A Dataset For Music Analysis
We introduce the Free Music Archive (FMA), an open and easily accessible
dataset suitable for evaluating several tasks in MIR, a field concerned with
browsing, searching, and organizing large music collections. The community's
growing interest in feature and end-to-end learning is however restrained by
the limited availability of large audio datasets. The FMA aims to overcome this
hurdle by providing 917 GiB and 343 days of Creative Commons-licensed audio
from 106,574 tracks from 16,341 artists and 14,854 albums, arranged in a
hierarchical taxonomy of 161 genres. It provides full-length and high-quality
audio, pre-computed features, together with track- and user-level metadata,
tags, and free-form text such as biographies. We here describe the dataset and
how it was created, propose a train/validation/test split and three subsets,
discuss some suitable MIR tasks, and evaluate some baselines for genre
recognition. Code, data, and usage examples are available at
https://github.com/mdeff/fmaComment: ISMIR 2017 camera-read
CayleyNets: Graph Convolutional Neural Networks with Complex Rational Spectral Filters
The rise of graph-structured data such as social networks, regulatory
networks, citation graphs, and functional brain networks, in combination with
resounding success of deep learning in various applications, has brought the
interest in generalizing deep learning models to non-Euclidean domains. In this
paper, we introduce a new spectral domain convolutional architecture for deep
learning on graphs. The core ingredient of our model is a new class of
parametric rational complex functions (Cayley polynomials) allowing to
efficiently compute spectral filters on graphs that specialize on frequency
bands of interest. Our model generates rich spectral filters that are localized
in space, scales linearly with the size of the input data for
sparsely-connected graphs, and can handle different constructions of Laplacian
operators. Extensive experimental results show the superior performance of our
approach, in comparison to other spectral domain convolutional architectures,
on spectral image classification, community detection, vertex classification
and matrix completion tasks
Robust Principal Component Analysis on Graphs
Principal Component Analysis (PCA) is the most widely used tool for linear
dimensionality reduction and clustering. Still it is highly sensitive to
outliers and does not scale well with respect to the number of data samples.
Robust PCA solves the first issue with a sparse penalty term. The second issue
can be handled with the matrix factorization model, which is however
non-convex. Besides, PCA based clustering can also be enhanced by using a graph
of data similarity. In this article, we introduce a new model called "Robust
PCA on Graphs" which incorporates spectral graph regularization into the Robust
PCA framework. Our proposed model benefits from 1) the robustness of principal
components to occlusions and missing values, 2) enhanced low-rank recovery, 3)
improved clustering property due to the graph smoothness assumption on the
low-rank matrix, and 4) convexity of the resulting optimization problem.
Extensive experiments on 8 benchmark, 3 video and 2 artificial datasets with
corruptions clearly reveal that our model outperforms 10 other state-of-the-art
models in its clustering and low-rank recovery tasks
- …