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Principal Component Analysis (PCA) has been widely used for manifold description and dimensionality reduction. Performance of PCA is however hampered when data exhibits nonlinear feature relations. In this work, we propose a new framework for manifold lear ...
We study the problem of learning ridge functions of the form f(x) = g(aT x), x ∈ ℝd, from random samples. Assuming g to be a twice continuously differentiable function, we leverage techniques from low rank matrix recovery literature to derive a uniform app ...
The matrix completion problem consists of finding or approximating a low-rank matrix based on a few samples of this matrix. We propose a new algorithm for matrix completion that minimizes the least-square distance on the sampling set over the Riemannian ma ...
The network traffic matrix is widely used in network operation and management. It is of crucial importance to analyze the composition and the structure of the network traffic matrix, for which some mathematical approaches such as Principal Component Analys ...
Assume a multichannel data matrix, which due to the column-wise dependencies, has low-rank and joint-sparse representation. This matrix wont have many degrees of freedom. Enormous developments over the last decade in areas of compressed sensing and low-ran ...
Acquisition of three-dimensional (3D) spectral data is nowadays common using many different microanalytical techniques. In order to proceed to the 3D reconstruction, data processing is necessary not only to deal with noisy acquisitions but also to segment ...
We study the spatiotemporal sampling of a diffusion field generated by K point sources, aiming to fully reconstruct the unknown initial field distribution from the sample measurements. The sampling operator in our problem can be described by a matrix deriv ...
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2011
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
In this paper we consider the problem of recovering a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model that can efficiently restrict the degrees of freedom of the problem and is generic enough to ...
Institute of Electrical and Electronics Engineers2012
In this paper we consider recovery of a high dimensional data matrix from a set of incomplete and noisy linear measurements. We introduce a new model which can efficiently restricts the degrees of freedom of data and, at the same time, is generic so that f ...
