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

GASP : Geometric Association with Surface Patches

A fundamental challenge to sensory processing tasks in perception and robotics is the problem of obtaining data associations across views. We present a robust solution for ascertaining potentially dense surface patch (superpixel) associations, requiring just range information. Our approach involves decomposition of a view into regularized surface patches. We represent them as sequences expressing geometry invariantly over their superpixel neighborhoods, as uniquely consistent partial orderings. We match these representations through an optimal sequence comparison metric based on the Damerau-Levenshtein distance - enabling robust association with quadratic complexity (in contrast to hitherto employed joint matching formulations which are NP-complete). The approach is able to perform under wide baselines, heavy rotations, partial overlaps, significant occlusions and sensor noise. The technique does not require any priors -- motion or otherwise, and does not make restrictive assumptions on scene structure and sensor movement. It does not require appearance -- is hence more widely applicable than appearance reliant methods, and invulnerable to related ambiguities such as textureless or aliased content. We present promising qualitative and quantitative results under diverse settings, along with comparatives with popular approaches based on range as well as RGB-D data.Comment: International Conference on 3D Vision, 201

Improved Algorithms for Approximate String Matching (Extended Abstract)

The problem of approximate string matching is important in many different areas such as computational biology, text processing and pattern recognition. A great effort has been made to design efficient algorithms addressing several variants of the problem, including comparison of two strings, approximate pattern identification in a string or calculation of the longest common subsequence that two strings share. We designed an output sensitive algorithm solving the edit distance problem between two strings of lengths n and m respectively in time O((s-|n-m|)min(m,n,s)+m+n) and linear space, where s is the edit distance between the two strings. This worst-case time bound sets the quadratic factor of the algorithm independent of the longest string length and improves existing theoretical bounds for this problem. The implementation of our algorithm excels also in practice, especially in cases where the two strings compared differ significantly in length. Source code of our algorithm is available at http://www.cs.miami.edu/\~dimitris/edit_distanceComment: 10 page

Statistical interaction modeling of bovine herd behaviors

While there has been interest in modeling the group behavior of herds or flocks, much of this work has focused on simulating their collective spatial motion patterns which have not accounted for individuality in the herd and instead assume a homogenized role for all members or sub-groups of the herd. Animal behavior experts have noted that domestic animals exhibit behaviors that are indicative of social hierarchy: leader/follower type behaviors are present as well as dominance and subordination, aggression and rank order, and specific social affiliations may also exist. Both wild and domestic cattle are social species, and group behaviors are likely to be influenced by the expression of specific social interactions. In this paper, Global Positioning System coordinate fixes gathered from a herd of beef cows tracked in open fields over several days at a time are utilized to learn a model that focuses on the interactions within the herd as well as its overall movement. Using these data in this way explores the validity of existing group behavior models against actual herding behaviors. Domain knowledge, location geography and human observations, are utilized to explain the causes of these deviations from this idealized behavior

Topology Discovery of Sparse Random Graphs With Few Participants

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is scheduled to appear in J. on Random Structures and Algorithm

Multiple graph matching and applications

En aplicaciones de reconocimiento de patrones, los grafos con atributos son en gran medida apropiados. Normalmente, los vértices de los grafos representan partes locales de los objetos i las aristas relaciones entre estas partes locales. No obstante, estas ventajas vienen juntas con un severo inconveniente, la distancia entre dos grafos no puede ser calculada en un tiempo polinómico. Considerando estas características especiales el uso de los prototipos de grafos es necesariamente omnipresente. Las aplicaciones de los prototipos de grafos son extensas, siendo las más habituales clustering, clasificación, reconocimiento de objetos, caracterización de objetos i bases de datos de grafos entre otras. A pesar de la diversidad de aplicaciones de los prototipos de grafos, el objetivo del mismo es equivalente en todas ellas, la representación de un conjunto de grafos. Para construir un prototipo de un grafo todos los elementos del conjunto de enteramiento tienen que ser etiquetados comúnmente. Este etiquetado común consiste en identificar que nodos de que grafos representan el mismo tipo de información en el conjunto de entrenamiento. Una vez este etiquetaje común esta hecho, los atributos locales pueden ser combinados i el prototipo construido. Hasta ahora los algoritmos del estado del arte para calcular este etiquetaje común mancan de efectividad o bases teóricas. En esta tesis, describimos formalmente el problema del etiquetaje global i mostramos una taxonomía de los tipos de algoritmos existentes. Además, proponemos seis nuevos algoritmos para calcular soluciones aproximadas al problema del etiquetaje común. La eficiencia de los algoritmos propuestos es evaluada en diversas bases de datos reales i sintéticas. En la mayoría de experimentos realizados los algoritmos propuestos dan mejores resultados que los existentes en el estado del arte.In pattern recognition, the use of graphs is, to a great extend, appropriate and advantageous. Usually, vertices of the graph represent local parts of an object while edges represent relations between these local parts. However, its advantages come together with a sever drawback, the distance between two graph cannot be optimally computed in polynomial time. Taking into account this special characteristic the use of graph prototypes becomes ubiquitous. The applicability of graphs prototypes is extensive, being the most common applications clustering, classification, object characterization and graph databases to name some. However, the objective of a graph prototype is equivalent to all applications, the representation of a set of graph. To synthesize a prototype all elements of the set must be mutually labeled. This mutual labeling consists in identifying which nodes of which graphs represent the same information in the training set. Once this mutual labeling is done the set can be characterized and combined to create a graph prototype. We call this initial labeling a common labeling. Up to now, all state of the art algorithms to compute a common labeling lack on either performance or theoretical basis. In this thesis, we formally describe the common labeling problem and we give a clear taxonomy of the types of algorithms. Six new algorithms that rely on different techniques are described to compute a suboptimal solution to the common labeling problem. The performance of the proposed algorithms is evaluated using an artificial and several real datasets. In addition, the algorithms have been evaluated on several real applications. These applications include graph databases and group-wise image registration. In most of the tests and applications evaluated the presented algorithms have showed a great improvement in comparison to state of the art applications