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

Secure Similar Sequence Query on Outsourced Genomic Data

The growing availability of genomic data is unlocking research potentials on genomic-data analysis. It is of great importance to outsource the genomic-analysis tasks onto clouds to leverage their powerful computational resources over the large-scale genomic sequences. However, the remote placement of the data raises personal-privacy concerns, and it is challenging to evaluate data-analysis functions on outsourced genomic data securely and efficiently. In this work, we study the secure similar-sequence-query (SSQ) problem over outsourced genomic data, which has not been fully investigated. To address the challenges of security and efficiency, we propose two protocols in the mixed form, which combine two-party secure secret sharing, garbled circuit, and partial homomorphic encryptions together and use them to jointly fulfill the secure SSQ function. In addition, our protocols support multi-user queries over a joint genomic data set collected from multiple data owners, making our solution scalable. We formally prove the security of protocols under the semi-honest adversary model, and theoretically analyze the performance. We use extensive experiments over real-world dataset on a commercial cloud platform to validate the efficacy of our proposed solution, and demonstrate the performance improvements compared with state-of-the-art works

CSM-467: Quotient Geometric Crossovers

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In previous work we have started studying how metric transformations of the distance associated with geometric crossover affect the original geometric crossover. In particular, we focused on the product of metric spaces. This metric transformation gives rise to the notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way. In this paper, we study another metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many examples of application of the quotient geometric crossover

Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover

Parameterized Strings: Algorithms and Applications

The parameterized string (p-string), a generalization of the traditional string, is composed of constant and parameter symbols. A parameterized match (p-match) exists between two p-strings if the constants match exactly and there exists a bijection between the parameter symbols. Historically, p-strings have been employed in source code cloning, plagiarism detection, and structural similarity between biological sequences. By handling the intricacies of the parameterized suffix, we can efficiently address complex applications with data structures also reusable in traditional matching scenarios. In this dissertation, we extend data structures for p-strings (and variants) to address sophisticated string computations.;We introduce a taxonomy of classes for longest factor problems. Using this taxonomy, we show an interesting connection between the parameterized longest previous factor (pLPF) and familiar data structures in string theory, including the border array, prefix array, longest common prefix array, and analogous p-string data structures. Exploiting this connection, we construct a multitude of data structures using the same general pLPF framework.;Before this dissertation, the p-match was defined predominately by the matching between uncompressed p-strings. Here, we introduce the compressed parameterized pattern match to find all p-matches between a pattern and a text, using only the pattern and a compressed form of the text. We present parameterized compression (p-compression) as a new way to losslessly compress data to support p-matching. Experimentally, it is shown that p-compression is competitive with standard compression schemes. Using p-compression, we address the compressed p-match independent of the underlying compression routine.;Currently, p-string theory lacks the capability to support indeterminate symbols, a staple essential for applications involving inexact matching such as in music analysis. In this work, we propose and efficiently address two new types of p-matching with indeterminate symbols. (1) We introduce the indeterminate parameterized match (ip-match) to permit matching with indeterminate holes in a p-string. We support the ip-match by introducing data structures that extend the prefix array. (2) From a different perspective, the equivalence parameterized match (e-match) evolves the p-match to consider intra-alphabet symbol classes as equivalence classes. We propose a method to perform the e-match using the p-string suffix array framework, i.e. the parameterized suffix array (pSA) and parameterized longest common prefix array (pLCP). Historically, direct constructions of the pSA and pLCP have suffered from quadratic time bounds in the worst-case. Here, we introduce new p-string theory to efficiently construct the pSA/pLCP and break the theoretical worst-case time barrier.;Biological applications have become a classical use of p-string theory. Here, we introduce the structural border array to provide a lightweight solution to the biologically-oriented variant of the p-match, i.e. the structural match (s-match) on structural strings (s-strings). Following the s-match, we show how to use s-string suffix structures to support various pattern matching problems involving RNA secondary structures. Finally, we propose/construct the forward stem matrix (FSM), a data structure to access RNA stem structures, and we apply the FSM to the detection of hairpins and pseudoknots in an RNA sequence.;This dissertation advances the state-of-the-art in p-string theory by developing data structures for p-strings/s-strings and using p-string/s-string theory in new and old contexts to address various applications. Due to the flexibility of the p-string/s-string, the data structures and algorithms in this work are also applicable to the myriad of problems in the string community that involve traditional strings

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a hierarchical low-rank approximation, "compression," of an arbitrary dense symmetric positive definite (SPD) matrix. For many applications, GOFMM enables an approximate matrix-vector multiplication in $N \log N$ or even $N$ time, where $N$ is the matrix size. Compression requires $N \log N$ storage and work. In general, our scheme belongs to the family of hierarchical matrix approximation methods. In particular, it generalizes the fast multipole method (FMM) to a purely algebraic setting by only requiring the ability to sample matrix entries. Neither geometric information (i.e., point coordinates) nor knowledge of how the matrix entries have been generated is required, thus the term "geometry-oblivious." Also, we introduce a shared-memory parallel scheme for hierarchical matrix computations that reduces synchronization barriers. We present results on the Intel Knights Landing and Haswell architectures, and on the NVIDIA Pascal architecture for a variety of matrices.Comment: 13 pages, accepted by SC'1

A Robust Parsing Algorithm For Link Grammars

In this paper we present a robust parsing algorithm based on the link grammar formalism for parsing natural languages. Our algorithm is a natural extension of the original dynamic programming recognition algorithm which recursively counts the number of linkages between two words in the input sentence. The modified algorithm uses the notion of a null link in order to allow a connection between any pair of adjacent words, regardless of their dictionary definitions. The algorithm proceeds by making three dynamic programming passes. In the first pass, the input is parsed using the original algorithm which enforces the constraints on links to ensure grammaticality. In the second pass, the total cost of each substring of words is computed, where cost is determined by the number of null links necessary to parse the substring. The final pass counts the total number of parses with minimal cost. All of the original pruning techniques have natural counterparts in the robust algorithm. When used together with memoization, these techniques enable the algorithm to run efficiently with cubic worst-case complexity. We have implemented these ideas and tested them by parsing the Switchboard corpus of conversational English. This corpus is comprised of approximately three million words of text, corresponding to more than 150 hours of transcribed speech collected from telephone conversations restricted to 70 different topics. Although only a small fraction of the sentences in this corpus are "grammatical" by standard criteria, the robust link grammar parser is able to extract relevant structure for a large portion of the sentences. We present the results of our experiments using this system, including the analyses of selected and random sentences from the corpus.Comment: 17 pages, compressed postscrip

A Convolutional Neural Network into graph space

Convolutional neural networks (CNNs), in a few decades, have outperformed the existing state of the art methods in classification context. However, in the way they were formalised, CNNs are bound to operate on euclidean spaces. Indeed, convolution is a signal operation that are defined on euclidean spaces. This has restricted deep learning main use to euclidean-defined data such as sound or image. And yet, numerous computer application fields (among which network analysis, computational social science, chemo-informatics or computer graphics) induce non-euclideanly defined data such as graphs, networks or manifolds. In this paper we propose a new convolution neural network architecture, defined directly into graph space. Convolution and pooling operators are defined in graph domain. We show its usability in a back-propagation context. Experimental results show that our model performance is at state of the art level on simple tasks. It shows robustness with respect to graph domain changes and improvement with respect to other euclidean and non-euclidean convolutional architectures.Comment: arXiv admin note: text overlap with arXiv:1611.08402 by other author