A genetic algorithm and its parallelization for graph matching with similarity measures

Graph matching and similarity measures of graphs have many applications to pattern recognition, machine vision in robotics, and similarity-based approximate reasoning in artificial intelligence. This paper proposes a method of matching and a similarity measure between two directed labeled graphs. We define the degree of similarity, the similar correspondence, and the similarity map which denotes the matching between the graphs. As an approximate computing method, we apply genetic algorithms (GA) to find a similarity map and compute the degree of similarity between graphs. For speed, we make parallel implementations in almost all steps of the GA. We have implemented the sequential GA and the parallel GA in C programs, and made simulations for both GAs. The simulation results show that our method is efficient and useful. This work was presented, in part, at the Second International Symposium on Artificial Life and Robotics, Oita Japan, February 18–20, 1997     

Anytime measures for top-k algorithms on exact and fuzzy data sets

Top-k queries on large multi-attribute data sets are fundamental operations in information retrieval and ranking applications. In this article, we initiate research on the anytime behavior of top-k algorithms on exact and fuzzy data. In particular, given specific top-k algorithms (TA and TA-Sorted) we are interested in studying their progress toward identification of the correct result at any point during the algorithms’ execution. We adopt a probabilistic approach where we seek to report at any point of operation of the algorithm the confidence that the top-k result has been identified. Such a functionality can be a valuable asset when one is interested in reducing the runtime cost of top-k computations. We present a thorough experimental evaluation to validate our techniques using both synthetic and real data sets.     

Characterization and evaluation of similarity measures for pairs of clusterings

In evaluating the results of cluster analysis, it is common practice to make use of a number of fixed heuristics rather than to compare a data clustering directly against an empirically derived standard, such as a clustering empirically obtained from human informants. Given the dearth of research into techniques to express the similarity between clusterings, there is broad scope for fundamental research in this area. In defining the comparative problem, we identify two types of worst-case matches between pairs of clusterings, characterised as independently codistributed clustering pairs and conjugate partition pairs. Desirable behaviour for a similarity measure in either of the two worst cases is discussed, giving rise to five test scenarios in which characteristics of one of a pair of clusterings was manipulated in order to compare and contrast the behaviour of different clustering similarity measures. This comparison is carried out for previously-proposed clustering similarity measures, as well as a number of established similarity measures that have not previously been applied to clustering comparison. We introduce a paradigm apparatus for the evaluation of clustering comparison techniques and distinguish between the goodness of clusterings and the similarity of clusterings by clarifying the degree to which different measures confuse the two. Accompanying this is the proposal of a novel clustering similarity measure, the Measure of Concordance (MoC). We show that only MoC, Powers’s measure, Lopez and Rajski’s measure and various forms of Normalised Mutual Information exhibit the desired behaviour under each of the test scenarios.

Cost-aware query planning for similarity search

Similarity search aims to find all objects similar to a query object. Typically, some base similarity measures for the different properties of the objects are defined, and light-weight similarity indexes for these measures are built. A query plan specifies which similarity indexes to use with which similarity thresholds and how to combine the results. Previous work creates only a single, static query plan to be used by all queries. In contrast, our approach creates a new plan for each query.     

A polygraph test for trustworthy structural similarity

Do similarity or distance measures ever go wrong? The inherent subjectivity in similarity discernment has long supported the view that all judgements of similarity are equally valid, and that any selected similarity measure may only be considered more effective in some chosen domain. This article presents evidence that such a view is incorrect for the specific case of relative structural similarity. In this context, similarity and distance measures occasionally do go wrong, producing judgements that can be considered as errors in judgement. This claim is supported by a novel method for assessing the quality of structural similarity and distance functions, which is based on relative scale of similarity with respect to chosen reference objects. The method may be applied either with synthetic graph datasets or with graphs representing objects in an application domain of interest. This work demonstrates the method over synthetic datasets with common measures of structural similarity in graphs. Finally, the article identifies three distinct kinds of relative similarity judgement errors, and shows how the distribution of these errors is related to graph properties under common similarity measures.     

Optimal rotation alignment of 3D objects using a GPU-based similarity function

In this paper, we address the challenging task of finding the best alignment between two 3D objects by solving a global optimization problem in the space of rotations SO(3). The objective function to be optimized is a newly developed rotation-variant similarity measure, which is obtained directly from the object's geometry and is entirely implemented on the GPU. By exploiting the modern GPU's parallel architecture, we can process considerably greater amounts of data than a CPU implementation can do in the same amount of time. This allows us to create a similarity measure which combines speed and accuracy. The actual problem of rotation alignment is then solved by finding the global maximum of this similarity function in the space of rotations. A special rotation representation allows for an efficient local optimization on the manifold SO(3). Furthermore, unwanted local maxima can be avoided by a heuristic global optimization procedure which exploits rotational symmetry. Due to this common sense heuristics, the global search can be gradually reduced to a lower-dimensional problem up to a 1D line search to handle objects with high rotational symmetry. We show that our method is superior to existing normalization techniques such as PCA and provides a high degree of precision despite remarkably short runtimes.     

A comparative study of ranking methods, similarity measures and uncertainty measures for interval type-2 fuzzy sets

Ranking methods, similarity measures and uncertainty measures are very important concepts for interval type-2 fuzzy sets (IT2 FSs). So far, there is only one ranking method for such sets, whereas there are many similarity and uncertainty measures. A new ranking method and a new similarity measure for IT2 FSs are proposed in this paper. All these ranking methods, similarity measures and uncertainty measures are compared based on real survey data and then the most suitable ranking method, similarity measure and uncertainty measure that can be used in the computing with words paradigm are suggested. The results are useful in understanding the uncertainties associated with linguistic terms and hence how to use them effectively in survey design and linguistic information processing.     

一种基于直觉模糊集相似度的多属性决策方法

直觉模糊集（ＩＦＳ）是对模糊集理论的一种扩充,能更好地处理模糊概念．首先给出一种新的直觉模糊集相似度;然后提出基于直觉模糊集相似度的多属性决策方法;最后通过线性目标规划模型和直觉模糊集相似度,得到属性的最优权重和相应的方案排序．数值实例表明,该方法是有效而可行的．     

Machining feature-based similarity assessment algorithms for prismatic machined parts

This paper presents algorithms for identifying machined parts in a database that are similar to a given query part based on machining features. In this paper we only consider parts that are machined on 3-axis machining centers. We utilize reduced feature vectors consisting of machining feature access directions, feature types, feature volumes, feature dimensional tolerances and feature group cardinality as a basis for assessing shape similarity. We have defined a distance function between two sets of reduced feature vectors to assess the similarity between them from the machining effort point of view. To assess the similarity between the two parts, one set of reduced feature vectors is transformed in space using rigid body transformations with respect to the other set such that the distance between them is minimized. The distance between the two sets of aligned reduced feature vectors is used as a measure of similarity between the two parts. The existing machined parts are rank ordered based on the value of the distance with respect to the query part. The cost of previously machined parts that have a very small distance from the query part can be used as a basis for estimating the cost of machining the new part.     

Distance and similarity measures for fuzzy operators

We introduce and study a new family of normalized distance measures between binary fuzzy operators, along with its dual family of similarity measures. Both are based on matrix norms and arise from the study of the aggregate plausibility of set-operations. We also suggest a new family of normalized distance measures between fuzzy sets, based on binary operators and matrix norms, and discuss its qualitative and quantitative features. All measures proposed are intended for applications and may be customized according to the needs and intuition of the user.     

Distance and similarity measures for hesitant fuzzy sets

In this paper, we propose a variety of distance measures for hesitant fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant ordered weighted distance measures and hesitant ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Several numerical examples are provided to illustrate these distance and similarity measures.     

Symmetric deformable image registration via optimization of information theoretic measures

The use of information theoretic measures (ITMs) has been steadily growing in image processing, bioinformatics, and pattern classification. Although the ITMs have been extensively used in rigid and affine registration of multi-modal images, their computation and accuracy are critical issues in deformable image registration. Three important aspects of using ITMs in multi-modal deformable image registration are considered in this paper: computation, inverse consistency, and accuracy; a symmetric formulation of the deformable image registration problem through the computation of derivatives and resampling on both source and target images, and sufficient criteria for inverse consistency are presented for the purpose of achieving more accurate registration. The techniques of estimating ITMs are examined and analytical derivatives are derived for carrying out the optimization in a computationally efficient manner. ITMs based on Shannon’s and Renyi’s definitions are considered and compared. The obtained evaluation results via registration functions, and controlled deformable registration of multi-modal digital brain phantom and in vivo magnetic resonance brain images show the improved accuracy and efficiency of the developed formulation. The results also indicate that despite the recent favorable studies towards the use of ITMs based on Renyi’s definitions, these measures are seen not to provide improvements in this type of deformable registration as compared to ITMs based on Shannon’s definitions.     

Graph-based representation for similarity retrieval of symbolic images

Image retrieval from an image database by the image objects and their spatial relationships has emerged as an important research subject in these decades. To retrieve images similar to a given query image, retrieval methods must assess the similarity degree between a database image and the query image by the extracted features with acceptable efficiency and effectiveness. This paper proposes a graph-based model SRG (spatial relation graph) to represent the semantic information of the contained objects and their spatial relationships in an image with no file annotation. In an SRG graph, the image objects are symbolized by the predefined class names as vertices and the spatial relations between object pairs are represented as arcs. The proposed model assesses the similarity degree between two images by calculating the maximum common subgraph of two corresponding SRG’s through intersection, which has quadratic time complexity owing to the characteristics of SRG. Its efficiency remains quadratic regardless of the duplication rate of the object symbols. The extended model SRG_T is also proposed, with the same time complexity, for the applications that need to consider the topological relations among objects. A synthetic symbolic image database and an existing image dataset are used in the conducted experiments to verify the performance of the proposed models. The experimental results show that the proposed models have compatible retrieval quality with remarkable efficiency improvements compared with three well-known methods LCS_Clique, SIM_R, and 2D Be-string, where LCS_Clique utilizes the number of objects in the maximum common subimage as its similarity function, SIM_R uses accumulation-based similarity function of similar object pairs, and 2D Be-string calculates the similarity of 2D patterns by the linear combination of two 1D similarities.     

互信息启发的相似度组合图像检索算法

图像的视觉特征与用户描述之间的差距一直是影响基于内容的图像检索准确度的最主要因素。对多种相似度进行组合来检索图像是近几年图像检索领域涌现出的一个研究热点,也是缩小这种差距的一种有效途径。如何选择更好的组合方法则是该领域很多研究者关注的核心问题。提出一种新的相似度组合算法。该算法基于互信息度量相对熵的原理,计算连续变量相似度与离散变量相似性之间的相关性,对多种相似度进行选择,以“和规则”组合相似度。在公用数据集上进行检索实验,该算法优于当前其他的“和规则”下的组合方法。     

Parallel strategies for the local biological sequence alignment in a cluster of workstations

Recently, many organisms have had their DNA entirely sequenced. This reality presents the need for comparing long DNA sequences, which is a challenging task due to its high demands for computational power and memory. Sequence comparison is a basic operation in DNA sequencing projects, and most sequence comparison methods currently in use are based on heuristics, which are faster but offer no guarantees of producing the best alignments possible. In order to alleviate this problem, Smith–Waterman proposed an algorithm. This algorithm obtains the best local alignments but at the expense of very high computing power and huge memory requirements. In this article, we present and evaluate our experiments involving three strategies to run the Smith–Waterman algorithm in a cluster of workstations using a Distributed Shared Memory System. Our results on an eight-machine cluster presented very good speed-up and indicate that impressive improvements can be achieved depending on the strategy used. In addition, we present a number of theoretical remarks concerning how to reduce the amount of memory used.     

A high performance multiple sequence alignment system for pyrosequencing reads from multiple reference genomes

Genome resequencing with short reads generated from pyrosequencing generally relies on mapping the short reads against a single reference genome. However, mapping of reads from multiple reference genomes is not possible using a pairwise mapping algorithm. In order to align the reads w.r.t each other and the reference genomes, existing multiple sequence alignment(MSA) methods cannot be used because they do not take into account the position of these short reads with respect to the genome, and are highly inefficient for a large number of sequences. In this paper, we develop a highly scalable parallel algorithm based on domain decomposition, referred to as P-Pyro-Align, to align such a large number of reads from single or multiple reference genomes. The proposed alignment algorithm accurately aligns the erroneous reads, and has been implemented on a cluster of workstations using MPI library. Experimental results for different problem sizes are analyzed in terms of execution time, quality of the alignments, and the ability of the algorithm to handle reads from multiple haplotypes. We report high quality multiple alignment of up to 0.5 million reads. The algorithm is shown to be highly scalable and exhibits super-linear speedups with increasing number of processors.