Non-Negative Local Sparse Coding for Subspace Clustering

Subspace sparse coding (SSC) algorithms have proven to be beneficial to clustering problems. They provide an alternative data representation in which the underlying structure of the clusters can be better captured. However, most of the research in this area is mainly focused on enhancing the sparse coding part of the problem. In contrast, we introduce a novel objective term in our proposed SSC framework which focuses on the separability of data points in the coding space. We also provide mathematical insights into how this local-separability term improves the clustering result of the SSC framework. Our proposed non-linear local SSC algorithm (NLSSC) also benefits from the efficient choice of its sparsity terms and constraints. The NLSSC algorithm is also formulated in the kernel-based framework (NLKSSC) which can represent the nonlinear structure of data. In addition, we address the possibility of having redundancies in sparse coding results and its negative effect on graph-based clustering problems. We introduce the link-restore post-processing step to improve the representation graph of non-negative SSC algorithms such as ours. Empirical evaluations on well-known clustering benchmarks show that our proposed NLSSC framework results in better clusterings compared to the state-of-the-art baselines and demonstrate the effectiveness of the link-restore post-processing in improving the clustering accuracy via correcting the broken links of the representation graph.Comment: 15 pages, IDA 2018 conferenc

Affine Modeling of Program Traces

This is a post-peer-review, pre-copyedit version of an article published in IEEE Transactions on Computers. The final authenticated version is available online at: http://dx.doi.org/10.1109/TC.2018.2853747[Abstract] A formal, high-level representation of programs is typically needed for static and dynamic analyses performed by compilers. However, the source code of target applications is not always available in an analyzable form, e.g., to protect intellectual property. To reason on such applications it becomes necessary to build models from observations of its execution. This paper presents an algebraic approach which, taking as input the trace of memory addresses accessed by a single memory reference, synthesizes an affine loop with a single perfectly nested statement that generates the original trace. This approach is extended to support the synthesis of unions of affine loops, useful for minimally modeling traces generated by automatic transformations of polyhedral programs, such as tiling. The resulting system is capable of processing hundreds of gigabytes of trace data in minutes, minimally reconstructing 100 percent of the static control parts in PolyBench/C applications and 99.9 percent in the Pluto-tiled versions of these benchmarks.Ministerio de Economía y Competitividad; TIN2016-75845-PNational Science Foundation (Estados Unidos); 1626251National Science Foundation (Estados Unidos); 1409095National Science Foundation (Estados Unidos); 1439057National Science Foundation (Estados Unidos); 1213052National Science Foundation (Estados Unidos); 1439021National Science Foundation (Estados Unidos); 162912

Multi-aperture foveated imaging

Foveated imaging, such as that evolved by biological systems to provide high angular resolution with a reduced space–bandwidth product, also offers advantages for man-made task-specific imaging. Foveated imaging systems using exclusively optical distortion are complex, bulky, and high cost, however. We demonstrate foveated imaging using a planar array of identical cameras combined with a prism array and superresolution reconstruction of a mosaicked image with a foveal variation in angular resolution of 5.9:1 and a quadrupling of the field of view. The combination of low-cost, mass-produced cameras and optics with computational image recovery offers enhanced capability of achieving large foveal ratios from compact, low-cost imaging systems

Signal reconstruction from the magnitude of subspace components

We consider signal reconstruction from the norms of subspace components generalizing standard phase retrieval problems. In the deterministic setting, a closed reconstruction formula is derived when the subspaces satisfy certain cubature conditions, that require at least a quadratic number of subspaces. Moreover, we address reconstruction under the erasure of a subset of the norms; using the concepts of $p$-fusion frames and list decoding, we propose an algorithm that outputs a finite list of candidate signals, one of which is the correct one. In the random setting, we show that a set of subspaces chosen at random and of cardinality scaling linearly in the ambient dimension allows for exact reconstruction with high probability by solving the feasibility problem of a semidefinite program

Extrinsic Methods for Coding and Dictionary Learning on Grassmann Manifolds

Sparsity-based representations have recently led to notable results in various visual recognition tasks. In a separate line of research, Riemannian manifolds have been shown useful for dealing with features and models that do not lie in Euclidean spaces. With the aim of building a bridge between the two realms, we address the problem of sparse coding and dictionary learning over the space of linear subspaces, which form Riemannian structures known as Grassmann manifolds. To this end, we propose to embed Grassmann manifolds into the space of symmetric matrices by an isometric mapping. This in turn enables us to extend two sparse coding schemes to Grassmann manifolds. Furthermore, we propose closed-form solutions for learning a Grassmann dictionary, atom by atom. Lastly, to handle non-linearity in data, we extend the proposed Grassmann sparse coding and dictionary learning algorithms through embedding into Hilbert spaces. Experiments on several classification tasks (gender recognition, gesture classification, scene analysis, face recognition, action recognition and dynamic texture classification) show that the proposed approaches achieve considerable improvements in discrimination accuracy, in comparison to state-of-the-art methods such as kernelized Affine Hull Method and graph-embedding Grassmann discriminant analysis.Comment: Appearing in International Journal of Computer Visio