This document provides the foundations behind the functionality provided by the @math G library (this https URL), focusing on the basic operations the library provides: subsumption, refinement of directed labeled graphs, and distance similarity assessment between directed labeled graphs. @math G development was initially supported by the National Science Foundation, by the EAGER grant IIS-1551338.
Similarity measures for specific application domains, such as molecular structures in domains of biology or chemistry have also been studied @cite_30 , and they are typically grouped into three classes @cite_43 : sequence similarities (e.g., for DNA fragments), fingerprint-based (transform each molecule into a sequence of binary features representing whether a particular molecule exhibits particular properties or contains certain substructures) and graph-based (based on maximum common sub-graphs). The latter is a computationally expensive process, and thus there are a number of strategies to simplify the computations (e.g., @cite_17 ).
@cite_30 @cite_43 @cite_17
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Measures of sequence similarity and distance based more or less explicitly on subword composition are attracting an increasing interest driven by intensive applications such as massive document classification and genome-wide molecular taxonomy. A uniform character of such measures is in some underlying notion of relative compressibility, whereby two similar sequences are expected to share a larger number of common substrings than two distant ones. This paper reviews some of the approaches to sequence comparison based on subword composition and suggests that their common denominator may ultimately reside in special classes of subwords, the nature of which resonates in interesting ways with the structure of popular subword trees and graphs. Preface Introduction Molecular Biology Mathematics, Statistics, and Computer Science Some Molecular Biology DNA and Proteins The Central Dogma The Genetic Code Transfer RNA and Protein Sequences Genes Are Not Simple Biological Chemistry Restriction Maps Introduction Graphs Interval Graphs Measuring Fragment Sizes Multiple Maps Double Digest Problem Classifying Multiple Solutions Algorithms for DDP Algorithms and Complexity DDP is N P-Complete Approaches to DDP Simulated Annealing: TSP and DDP Mapping with Real Data Cloning and Clone Libraries A Finite Number of Random Clones Libraries by Complete Digestion Libraries by Partial Digestion Genomes per Microgram Physical Genome Maps: Oceans, Islands, and Anchors Mapping by Fingerprinting Mapping by Anchoring An Overview of Clone Overlap Putting It Together Sequence Assembly Shotgun Sequencing Sequencing by Hybridization Shotgun Sequencing Revisited Databases and Rapid Sequence Analysis DNA and Protein Sequence Databases A Tree Representation of a Sequence Hashing a Sequence Repeats in a Sequence Sequence Comparison by Hashing Sequence Comparison with at most l Mismatches Sequence Comparison by Statistical Content Dynamic Programming Alignment of Two Sequences The Number of Alignments Shortest and Longest Paths in a Network Global Distance Alignment Global Similarity Alignment Fitting One Sequence into Another Local Alignment and Clumps Linear Space Algorithms Tracebacks Inversions Map Alignment Parametric Sequence Comparisons Multiple Sequence Alignment The Cystic Fibrosis Gene Dynamic Programming in r-Dimensions Weighted-Average Sequences Profile Analysis Alignment by Hidden Markov Models Consensus Word Analysis Probability and Statistics for Sequence Alignment Global Alignment Local Alignment Extreme Value Distributions The Chein-Stein Method Poisson Approximation and Long Matches Sequence Alignment with Scores Probability and Statistics for Sequence Patterns A Central Limit Theorem Nonoverlapping Pattern Counts Poisson Approximation Site Distributions RNA Secondary Structure Combinatorics Minimum Free-energy Structures Consensus folding Trees and Sequences Trees Distance Parsimony Maximum Likelihood Trees Sources and Perspectives Molecular Biology Physical Maps and Clone Libraries Sequence Assembly Sequence Comparisons Probability and Statistics RNA Secondary Structure Trees and Sequences References Problem Solutions and Hints Mathematical Notation Algorithm Index Author Index Subject Index This paper reviews the use of similarity searching in chemical databases. It begins by introducing the concept of similarity searching, differentiating it from the more common substructure searching, and then discusses the current generation of fragment-based measures that are used for searching chemical structure databases. The next sections focus upon two of the principal characteristics of a similarity measure: the coefficient that is used to quantify the degree of structural resemblance between pairs of molecules and the structural representations that are used to characterize molecules that are being compared in a similarity calculation. New types of similarity measure are then compared with current approaches, and examples are given of several applications that are related to similarity searching. A new class of distances appropriate for measuring similarity relations between sequences, say one type of similarity per distance, is studied. We propose a new "normalized information distance," based on the noncomputable notion of Kolmogorov complexity, and show that it is in this class and it minorizes every computable distance in the class (that is, it is universal in that it discovers all computable similarities). We demonstrate that it is a metric and call it the similarity metric . This theory forms the foundation for a new practical tool. To evidence generality and robustness, we give two distinctive applications in widely divergent areas using standard compression programs like gzip and GenCompress. First, we compare whole mitochondrial genomes and infer their evolutionary history. This results in a first completely automatic computed whole mitochondrial phylogeny tree. Secondly, we fully automatically compute the language tree of 52 different languages. From bacteria following simple chemical gradients to the brain distinguishing complex odour information, the ability to recognize molecular patterns is essential for biological organisms. This type of information-processing function has been implemented using DNA-based neural networks, but has been limited to the recognition of a set of no more than four patterns, each composed of four distinct DNA molecules. Winner-take-all computation has been suggested as a potential strategy for enhancing the capability of DNA-based neural networks. Compared to the linear-threshold circuits and Hopfield networks used previously, winner-take-all circuits are computationally more powerful, allow simpler molecular implementation and are not constrained by the number of patterns and their complexity, so both a large number of simple patterns and a small number of complex patterns can be recognized. Here we report a systematic implementation of winner-take-all neural networks based on DNA-strand-displacement reactions. We use a previously developed seesaw DNA gate motif, extended to include a simple and robust component that facilitates the cooperative hybridization that is involved in the process of selecting a ‘winner’. We show that with this extended seesaw motif DNA-based neural networks can classify patterns into up to nine categories. Each of these patterns consists of 20 distinct DNA molecules chosen from the set of 100 that represents the 100 bits in 10 × 10 patterns, with the 20 DNA molecules selected tracing one of the handwritten digits ‘1’ to ‘9’. The network successfully classified test patterns with up to 30 of the 100 bits flipped relative to the digit patterns ‘remembered’ during training, suggesting that molecular circuits can robustly accomplish the sophisticated task of classifying highly complex and noisy information on the basis of similarity to a memory. A growing number of measures of sequence similarity are being based on some underlying notion of relative compressibility. Within this paradigm, similar sequences are expected to share a large number of common substrings, or subsequences, or more complex patterns or motifs, and so on. In this paper, measures of sequence similarity are introduced and studied in which patterns in a pair are considered similar if they coincide up to a preset number of mismatches, that is, within a bounded Hamming distance. It is shown here that for some such measures bounds are achievable that are slightly better than O ( n 2 ) . Preliminary experiments demonstrate the potential applicability to phylogeny and classification of these similarity measures. The nearestor near-neighbor query problems arise in a large variety of database applications, usually in the context of similarity searching. Of late, there has been increasing interest in building search index structures for performing similarity search over high-dimensional data, e.g., image databases, document collections, time-series databases, and genome databases. Unfortunately, all known techniques for solving this problem fall prey to the of dimensionality." That is, the data structures scale poorly with data dimensionality; in fact, if the number of dimensions exceeds 10 to 20, searching in k-d trees and related structures involves the inspection of a large fraction of the database, thereby doing no better than brute-force linear search. It has been suggested that since the selection of features and the choice of a distance metric in typical applications is rather heuristic, determining an approximate nearest neighbor should su ce for most practical purposes. In this paper, we examine a novel scheme for approximate similarity search based on hashing. The basic idea is to hash the points Supported by NAVY N00014-96-1-1221 grant and NSF Grant IIS-9811904. Supported by Stanford Graduate Fellowship and NSF NYI Award CCR-9357849. Supported by ARO MURI Grant DAAH04-96-1-0007, NSF Grant IIS-9811904, and NSF Young Investigator Award CCR9357849, with matching funds from IBM, Mitsubishi, Schlumberger Foundation, Shell Foundation, and Xerox Corporation. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the VLDB copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Very Large Data Base Endowment. To copy otherwise, or to republish, requires a fee and or special permission from the Endowment. Proceedings of the 25th VLDB Conference, Edinburgh, Scotland, 1999. from the database so as to ensure that the probability of collision is much higher for objects that are close to each other than for those that are far apart. We provide experimental evidence that our method gives signi cant improvement in running time over other methods for searching in highdimensional spaces based on hierarchical tree decomposition. Experimental results also indicate that our scheme scales well even for a relatively large number of dimensions (more than 50). Domain specific (dis-)similarity or proximity measures used e.g. in alignment algorithms of sequence data are popular to analyze complicated data objects and to cover domain specific data properties. Without an underlying vector space these data are given as pairwise (dis-)similarities only. The few available methods for such data focus widely on similarities and do not scale to large datasets. Kernel methods are very effective for metric similarity matrices, also at large scale, but costly transformations are necessary starting with non-metric (dis-) similarities. We propose an integrative combination of Nystrom approximation, potential double centering and eigenvalue correction to obtain valid kernel matrices at linear costs in the number of samples. By the proposed approach effective kernel approaches become accessible. Experiments with several larger (dis-)similarity datasets show that the proposed method achieves much better runtime performance than the standard strategy while keeping competitive model accuracy. The main contribution is an efficient and accurate technique, to convert (potentially non-metric) large scale dissimilarity matrices into approximated positive semi-definite kernel matrices at linear costs. HighlightsWe propose a linear time and memory efficient approach for converting low rank dissimilarity matrices to similarity matrices and vice versa.Our approach is applicable for proximities obtained from non-metric proximity measures (indefinite kernels, non-standard dissimilarity measures).The presented approach also comprises a generalization of Landmark MDS - the presented approach is in general more accurate and flexible than Landmark MDS.We provide an alternative derivation of the Nystrom approximation together with a convergence proof, also for indefinite kernels not given in the workshop paper as a core element of the approach. Structured data including sets, sequences, trees and graphs, pose significant challenges to fundamental aspects of data management such as efficient storage, indexing, and similarity search. With the fast accumulation of graph databases, similarity search in graph databases has emerged as an important research topic. Graph similarity search has applications in a wide range of domains including cheminformatics, bioinformatics, sensor network management, social network management, and XML documents, among others. Most of the current graph indexing methods focus on subgraph query processing, i.e. determining the set of database graphs that contains the query graph and hence do not directly support similarity search. In data mining and machine learning, various graph kernel functions have been designed to capture the intrinsic similarity of graphs. Though successful in constructing accurate predictive and classification models for supervised learning, graph kernel functions have (i) high computational complexity and (ii) non-trivial difficulty to be indexed in a graph database. Our objective is to bridge graph kernel function and similarity search in graph databases by proposing (i) a novel kernel-based similarity measurement and (ii) an efficient indexing structure for graph data management. Our method of similarity measurement builds upon local features extracted from each node and their neighboring nodes in graphs. A hash table is utilized to support efficient storage and fast search of the extracted local features. Using the hash table, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing. We have implemented our method, which we have named G-hash, and have demonstrated its utility on large chemical graph databases. Our results show that the G-hash method achieves state-of-the-art performance for k-nearest neighbor (k-NN) classification. Most importantly, the new similarity measurement and the index structure is scalable to large database with smaller indexing size, faster indexing construction time, and faster query processing time as compared to state-of-the-art indexing methods such as C-tree, gIndex, and GraphGrep. Abstract When dealing with the registration of information from different image sources, the de facto similarity measure used is Mutual Information (MI). Although MI gives good performance in many image registration applications, recent works in thermal–visible registration have shown that other similarity measures can give results that are as accurate, if not more than MI. Furthermore, some of these measures also have the advantage of being calculated independently from each image to register, which allows them to be integrated more easily in energy minimization frameworks. In this article, we investigate the accuracy of similarity measures for thermal–visible image registration of human silhouettes, including MI, Sum of Squared Differences (SSD), Normalized Cross-Correlation (NCC), Histograms of Oriented Gradients (HOG), Local Self-Similarity (LSS), Scale-Invariant Feature Transform (SIFT), Speeded-Up Robust Features (SURF), Census, Fast Retina Keypoint (FREAK), and Binary Robust Independent Elementary Feature (BRIEF). We tested the various similarity measures in dense stereo matching tasks over 25,000 windows to have statistically significant results. To do so, we created a new dataset in which one to five humans are walking in a scene in various depth planes. Results show that even if MI is a very strong performer, particularly for large regions of interest (ROI), LSS gives better accuracies when ROI are small or segmented into small fragments because of its ability to capture shape. The other tested similarity measures did not give consistently accurate results. Theproteinsequencedatabasewas analyzed for evidence that some distinct sequence families might be distantly related in evolution by changes in frame of translation. Sequences were compared using special amino acid substitution matrices for the alternate frames of translation. The statistical significance of alignment scores were computed in the true database and shuffled versions of the database that preserve any potential codon bias. The comparison of results from these two databases provides a very sensitive method for de- tecting remote relationships. We find a weak but measurable relatedness within the database as a whole, supporting the notion that some proteins may have evolved from others through changes in frame of translation. We also quantify residual ho- mology in the ordinary sense within a database of generally unrelated sequences. Proteins 1999;37: Abstract Similarity networks contain important topological features and patterns critical to understanding interactions among samples in a large dataset. To create a comprehensive view of the interactions within a dataset, the Similarity Network Fusion (SNF) technique has been proposed to fuse the similarity networks based on different data types into one similarity network that represents the full spectrum of underlying data. In this paper, a modified version of SNF, which is named as Contextual Information based SNF (CI-SNF), is proposed. In CI-SNF, first, modified Jaccard distance is performed on the SNF fused similarity to utilize the contextual information contained in the fused similarity network. Second, the local consistency of samples from the same category is enhanced by speculating that the samples which are located high in the Jaccard distance based ranking list of a specific query are from the same category as the query. Third, the inverted index technique is introduced to utilize the sparsity property of the locally consistent similarity network to enhance the computational efficiency. To verify the effectiveness and efficiency of CI-SNF model, it is applied in four different tasks, Cover Song Identification (CSI), image classification, cancer subtype identification, and drug taxonomy, respectively. Extensive experiments on thirteen challenging datasets demonstrate that CI-SNF scheme outperforms state-of-the-art similarity fusion algorithms including SNF in all four tasks. It is also verified that utilizing the contextual information contained in the SNF-based similarity network helps to enhance the performance of the SNF-based scheme, further. In recent years the development of computational techniques that build models to correctly assign chemical compounds to various classes or to retrieve potential drug-like compounds has been an active area of research. Many of the best-performing techniques for these tasks utilize a descriptor-based representation of the compound that captures various aspects of the underlying molecular graph?s topology. In this paper we compare different set of descriptors that are currently used for chemical compound classification. In this process, we also introduce four different descriptors derived from all connected fragments present in the molecular graphs. In addition, we introduce an extension to existing vector-based kernel functions to take into account the length of the fragments present in the descriptors. We experimentally evaluate the performance of the previously introduced and the new descriptors in the context of SVM-based classification and ranked-retrieval on 28 classification and retrieval problems derived from 18 datasets. Our experiments show that for both these tasks, the new descriptors consistently and statistically outperform previously developed schemes based on the widely used fingerprint- and Maccs keys-based descriptors, as well as recently introduced descriptors obtained by mining and analyzing the structure of the molecular graphs. Motivation: Analogous to biological sequence comparison, comparing cellular networks is an important problem that could provide insight into biological understanding and therapeutics. For technical reasons, comparing large networks is computationally infeasible, and thus heuristics, such as the degree distribution, clustering coefficient, diameter, and relative graphlet frequency distribution have been sought. It is easy to demonstrate that two networks are different by simply showing a short list of properties in which they differ. It is much harder to show that two networks are similar, as it requires demonstrating their similarity in all of their exponentially many properties. Clearly, it is computationally prohibitive to analyze all network properties, but the larger the number of constraints we impose in determining network similarity, the more likely it is that the networks will truly be similar. Results: We introduce a new systematic measure of a network's local structure that imposes a large number of similarity constraints on networks being compared. In particular, we generalize the degree distribution, which measures the number of nodes 'touching' k edges, into distributions measuring the number of nodes 'touching' k graphlets, where graphlets are small connected non-isomorphic subgraphs of a large network. Our new measure of network local structure consists of 73 graphlet degree distributions of graphlets with 2--5 nodes, but it is easily extendible to a greater number of constraints (i.e. graphlets), if necessary, and the extensions are limited only by the available CPU. Furthermore, we show a way to combine the 73 graphlet degree distributions into a network 'agreement' measure which is a number between 0 and 1, where 1 means that networks have identical distributions and 0 means that they are far apart. Based on this new network agreement measure, we show that almost all of the 14 eukaryotic PPI networks, including human, resulting from various high-throughput experimental techniques, as well as from curated databases, are better modeled by geometric random graphs than by Erdos--Reny, random scale-free, or Barabasi--Albert scale-free networks. Availability: Software executables are available upon request. Contact: natasha@ics.uci.edu A major challenge in molecular biology is reverse-engineering the cis-regulatory logic that plays a major role in the control of gene expression. This program includes searching through DNA sequences to identify “motifs” that serve as the binding sites for transcription factors or, more generally, are predictive of gene expression across cellular conditions. Several approaches have been proposed for de novo motif discovery–searching sequences without prior knowledge of binding sites or nucleotide patterns. However, unbiased validation is not straightforward. We consider two approaches to unbiased validation of discovered motifs: testing the statistical significance of a motif using a DNA “background” sequence model to represent the null hypothesis and measuring performance in predicting membership in gene clusters. We demonstrate that the background models typically used are “too null,” resulting in overly optimistic assessments of significance, and argue that performance in predicting TF binding or expression patterns from DNA motifs should be assessed by held-out data, as in predictive learning. Applying this criterion to common motif discovery methods resulted in universally poor performance, although there is a marked improvement when motifs are statistically significant against real background sequences. Moreover, on synthetic data where “ground truth” is known, discriminative performance of all algorithms is far below the theoretical upper bound, with pronounced “over-fitting” in training. A key conclusion from this work is that the failure of de novo discovery approaches to accurately identify motifs is basically due to statistical intractability resulting from the fixed size of co-regulated gene clusters, and thus such failures do not necessarily provide evidence that unfound motifs are not active biologically. Consequently, the use of prior knowledge to enhance motif discovery is not just advantageous but necessary. An implementation of the LR and ALR algorithms is available at http: code.google.com p likelihood-ratio-motifs . Alignment free sequence comparison methods are attracting persistent interest, driven by data-intensive applications in genome-wide molecular taxonomy and phylogentic reconstruction. Among the methods based on substring composition, the Average Common Substring ( ( ACS )) measure proposed by (RECOMB 2005) admits a straightforward linear time sequence comparison algorithm, while yielding impressive results in multiple applications. An important direction of research is to extend the approach to permit a bounded edit hamming distance between substrings, so as to reflect more accurately the evolutionary process. To date, however, algorithms designed to incorporate (k 1 ) mismatches have (O(kn^2) ) worst-case complexity, worse than the (O(n^2) ) alignment algorithms they are meant to replace. On the other hand, accounting for mismatches does show to lead to much improved classification, while heuristics can improve practical performance. In this paper, we close the gap by presenting the first provably efficient algorithm for the (k ) -mismatch average common string ( ( ACS _k )) problem that takes (O(n) ) space and (O(n ^ k+1 n) ) time in the worst case for any constant (k ). Our method extends the generalized suffix tree model to incorporate a carefully selected bounded set of perturbed suffixes, and can be applicable to other complex approximate sequence matching problems. In the past several years studies have started to appear comparing the accuracies of various science mapping approaches. These studies primarily compare the cluster solutions resulting from different similarity approaches, and give varying results. In this study we compare the accuracies of cluster solutions of a large corpus of 2,153,769 recent articles from the biomedical literature (2004–2008) using four similarity approaches: co-citation analysis, bibliographic coupling, direct citation, and a bibliographic coupling-based citation-text hybrid approach. Each of the four approaches can be considered a way to represent the research front in biomedicine, and each is able to successfully cluster over 92p of the corpus. Accuracies are compared using two metrics—within-cluster textual coherence as defined by the Jensen-Shannon divergence, and a concentration measure based on the grant-to-article linkages indexed in MEDLINE. Of the three pure citation-based approaches, bibliographic coupling slightly outperforms co-citation analysis using both accuracy measures; direct citation is the least accurate mapping approach by far. The hybrid approach improves upon the bibliographic coupling results in all respects. We consider the results of this study to be robust given the very large size of the corpus, and the specificity of the accuracy measures used. © 2010 Wiley Periodicals, Inc. We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set. Motivation: The sequence specificity of DNA-binding proteins is typically represented as a position weight matrix in which each base position contributes independently to relative affinity. Assessment of the accuracy and broad applicability of this representation has been limited by the lack of extensive DNA-binding data. However, new microarray techniques, in which preferences for all possible K-mers are measured, enable a broad comparison of both motif representation and methods for motif discovery. Here, we consider the problem of accounting for all of the binding data in such experiments, rather than the highest affinity binding data. We introduce the RankMotif++, an algorithm designed for finding motifs whenever sequences are associated with a semi-quantitative measure of protein-DNA-binding affinity. RankMotif++ learns motif models by maximizing the likelihood of a set of binding preferences under a probabilistic model of how sequence binding affinity translates into binding preference observations. Because RankMotif++ makes few assumptions about the relationship between binding affinity and the semi-quantitative readout, it is applicable to a wide variety of experimental assays of DNA-binding preference. Results: By several criteria, RankMotif++ predicts binding affinity better than two widely used motif finding algorithms (MDScan, MatrixREDUCE) or more recently developed algorithms (PREGO, Seed and Wobble), and its performance is comparable to a motif model that separately assigns affinities to 8-mers. Our results validate the PWM model and provide an approximation of the precision and recall that can be expected in a genomic scan. Availability: RankMotif++ is available upon request. Contact: quaid.morris@utoronto.ca Supplementary information: Supplementary data are available at Bioinformatics online. The problem of measuring "similarity" of objects arises in many applications, and many domain-specific measures have been developed, e.g., matching text across documents or computing overlap among item-sets. We propose a complementary approach, applicable in any domain with object-to-object relationships, that measures similarity of the structural context in which objects occur, based on their relationships with other objects. Effectively, we compute a measure that says "two objects are similar if they are related to similar objects:" This general similarity measure, called SimRank, is based on a simple and intuitive graph-theoretic model. For a given domain, SimRank can be combined with other domain-specific similarity measures. We suggest techniques for efficient computation of SimRank scores, and provide experimental results on two application domains showing the computational feasibility and effectiveness of our approach.