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Low-Rank Matrices on Graphs: Generalized Recovery & Applications

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Enumeration of reversible functions and its application to circuit complexity

Giovanni De Micheli, Mathias Soeken, Nabila Abdessaied

We review combinational results to enumerate and classify reversible functions and investigate the application to circuit complexity. In particularly, we consider the effect of negating and permuting input and output variables and the effect of applying li ...

Springer2016

Compressive PCA for Low-Rank Matrices on Graphs

Pierre Vandergheynst, Gilles Puy, Nathanaël Perraudin, Nauman Shahid

We introduce a novel framework for an approxi- mate recovery of data matrices which are low-rank on graphs, from sampled measurements. The rows and columns of such matrices belong to the span of the first few eigenvectors of the graphs constructed between ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Robust Principal Component Analysis on Graphs

Pierre Vandergheynst, Michael Bronstein, Xavier Bresson, Nauman Shahid, Vasilis Kalofolias

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 iss ...

2015

Signal structure: from manifolds to molecules and structured sparsity

Sofia Karygianni

Effective representation methods and proper signal priors are crucial in most signal processing applications. In this thesis we focus on different structured models and we design appropriate schemes that allow the discovery of low dimensional latent struct ...

EPFL2015

Energy-aware adaptive bi-Lipschitz embeddings

Volkan Cevher, Bubacarr Bah, Ali Sadeghian

We propose a dimensionality reducing matrix design based on training data with constraints on its Frobenius norm and number of rows. Our design criteria is aimed at preserving the distances between the data points in the dimensionality reduced space as muc ...

2013

Low-rank Matrix Approximation Using Point-wise Operators

Arash Amini, Amin Karbasi

Extracting low dimensional structure from high dimensional data arises in many applications such as machine learning, statistical pattern recognition, wireless sensor networks, and data compression. If the data is restricted to a lower dimensional subspace ...

Institute of Electrical and Electronics Engineers2012

Subspaces Indexing Model on Grassmann Manifold for Image Search

Xinchao Wang

Conventional linear subspace learning methods like principal component analysis (PCA), linear discriminant analysis (LDA) derive subspaces from the whole data set. These approaches have limitations in the sense that they are linear while the data distribut ...

Institute of Electrical and Electronics Engineers2011

Information Processing and Structure of Dynamical Networks

Ali Ajdari Rad

Networks are everywhere and we are confronted with many networks in our daily life. Networks such as Internet, World Wide Web, social, biological and economical networks have been subject to extensive studies in the last decade. The volume of publications ...

EPFL2011

An output-sensitive algorithm for multi-parametric LCPs with sufficient matrices

Colin Neil Jones

This paper considers the multi-parametric linear complementarity problem (pLCP) with sufficient matrices. The main result is an algorithm to find a polyhedral decomposition of the set of feasible parameters and to construct a piecewise affine function that ...

2009

Distributed target localization via spatial sparsity

Volkan Cevher

We propose an approximation framework for distributed target localization in sensor networks. We represent the unknown target positions on a location grid as a sparse vector, whose support encodes the multiple target locations. The location vector is linea ...

2008