Pattern vectors from algebraic graph theory

Graphstructures have proven computationally cumbersome for pattern analysis. The reason for this is that, before graphs can be converted to pattern vectors, correspondences must be established between the nodes of structures which are potentially of different size. To overcome this problem, in this paper, we turn to the spectral decomposition of the Laplacian matrix. We show how the elements of the spectral matrix for the Laplacian can be used to construct symmetric polynomials that are permutation invariants. The coefficients of these polynomials can be used as graph features which can be encoded in a vectorial manner. We extend this representation to graphs in which there are unary attributes on the nodes and binary attributes on the edges by using the spectral decomposition of a Hermitian property matrix that can be viewed as a complex analogue of the Laplacian. To embed the graphs in a pattern space, we explore whether the vectors of invariants can be embedded in a low- dimensional space using a number of alternative strategies, including principal components analysis ( PCA), multidimensional scaling ( MDS), and locality preserving projection ( LPP). Experimentally, we demonstrate that the embeddings result in well- defined graph clusters. Our experiments with the spectral representation involve both synthetic and real- world data. The experiments with synthetic data demonstrate that the distances between spectral feature vectors can be used to discriminate between graphs on the basis of their structure. The real- world experiments show that the method can be used to locate clusters of graphs

Scripting Language for Java Source Code Recognition

AbstractThis paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and subgraph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm

Kernel Manifold Alignment

We introduce a kernel method for manifold alignment (KEMA) and domain adaptation that can match an arbitrary number of data sources without needing corresponding pairs, just few labeled examples in all domains. KEMA has interesting properties: 1) it generalizes other manifold alignment methods, 2) it can align manifolds of very different complexities, performing a sort of manifold unfolding plus alignment, 3) it can define a domain-specific metric to cope with multimodal specificities, 4) it can align data spaces of different dimensionality, 5) it is robust to strong nonlinear feature deformations, and 6) it is closed-form invertible which allows transfer across-domains and data synthesis. We also present a reduced-rank version for computational efficiency and discuss the generalization performance of KEMA under Rademacher principles of stability. KEMA exhibits very good performance over competing methods in synthetic examples, visual object recognition and recognition of facial expressions tasks

Multiple structure recovery via robust preference analysis

2noThis paper address the extraction of multiple models from outlier-contaminated data by exploiting preference analysis and low rank approximation. First points are represented in the preference space, then Robust PCA (Principal Component Analysis) and Symmetric NMF (Non negative Matrix Factorization) are used to break the multi-model fitting problem into many single-model problems, which in turn are tackled with an approach inspired to MSAC (M-estimator SAmple Consensus) coupled with a model-specific scale estimate. Experimental validation on public, real data-sets demonstrates that our method compares favorably with the state of the art.openopenMagri, Luca; Fusiello, AndreaMagri, Luca; Fusiello, Andre

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

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