Symmetric Similarity Measures Research Articles

Fermatean fuzzy copula aggregation operators and similarity measures-based complex proportional assessment approach for renewable energy source selection

Selecting the optimal renewable energy source (RES) is a complex multi-criteria decision-making (MCDM) problem due to the association of diverse conflicting criteria with uncertain information. The utilization of Fermatean fuzzy numbers is successfully treated with the qualitative data and uncertain information that often occur in realistic MCDM problems. In this paper, an extended complex proportional assessment (COPRAS) approach is developed to treat the decision-making problems in a Fermatean fuzzy set (FFS) context. First, to aggregate the Fermatean fuzzy information, a new Fermatean fuzzy Archimedean copula-based Maclaurin symmetric mean operator is introduced with its desirable characteristics. This proposed operator not only considers the interrelationships between multiple numbers of criteria, but also associates more than one marginal distribution, thus avoiding information loss in the process of aggregation. Second, new similarity measures are developed to quantify the degree of similarity between Fermatean fuzzy perspectives more effectively and are further utilized to compute the weights of the criteria. Third, an integrated Fermatean fuzzy-COPRAS approach using the Archimedean copula-based Maclaurin symmetric mean operator and similarity measure has been developed to assess and rank the alternatives under the FFS perspective. Furthermore, a case study of RES selection is presented to validate the feasibility and practicality of the developed model. Comparative and sensitivity analyses are used to check the reliability and strength of the proposed method.

Bipolar Dissimilarity and Similarity Correlations of Numbers

Many papers on fuzzy risk analysis calculate the similarity between fuzzy numbers. Usually, they use symmetric and reflexive similarity measures between parameters of fuzzy sets or “centers of gravity” of generalized fuzzy numbers represented by real numbers. This paper studies bipolar similarity functions (fuzzy relations) defined on a domain with involutive (negation) operation. The bipolarity property reflects a structure of the domain with involutive operation, and bipolar similarity functions are more suitable for calculating a similarity between elements of such domain. On the set of real numbers, similarity measures should take into account symmetry between positive and negative numbers given by involutive negation of numbers. Another reason to consider bipolar similarity functions is that these functions define measures of correlation (association) between elements of the domain. The paper gives a short introduction to the theory of correlation functions defined on sets with an involutive operation. It shows that the dissimilarity function generating Pearson’s correlation coefficient is bipolar. Further, it proposes new normalized similarity and dissimilarity functions on the set of real numbers. It shows that non-bipolar similarity functions have drawbacks in comparison with bipolar similarity functions. For this reason, bipolar similarity measures can be recommended for use in fuzzy risk analysis. Finally, the correlation functions between numbers corresponding to bipolar similarity functions are proposed.

Principle Component Analysis Based on New Symmetric Similarity Measures for Heavy-Tailed Data

We consider the principal component analysis (PCA) for the heavy-tailed distributions. A traditional measure for the classical PCA is the covariance measure. Due to the non-existence of variance of many heavy-tailed distributions, this measure cannot be used for them. We will clarify how to perform PCA in heavy-tailed data by extending a similarity measure based on covariance. We introduce similarity measures based on a new dependence coefficient of heavy-tailed distributions. Using real and artificial datasets, the performance of the proposed PCA is evaluated and compared with the classical one.

An unsupervised approach to generating generic summaries of documents

We present an optimization-based unsupervised approach to automatic document summarization. In the proposed approach, text summarization is modeled as a Boolean programming problem. This model generally attempts to optimize three properties, namely, (1) relevance: summary should contain informative textual units that are relevant to the user; (2) redundancy: summaries should not contain multiple textual units that convey the same information; and (3) length: summary is bounded in length. The approach proposed in this paper is applicable to both tasks: single- and multi-document summarization. In both tasks, documents are split into sentences in preprocessing. We select some salient sentences from document(s) to generate a summary. Finally, the summary is generated by threading all the selected sentences in the order that they appear in the original document(s). We implemented our model on multi-document summarization task. When comparing our methods to several existing summarization methods on an open DUC2005 and DUC2007 data sets, we found that our method improves the summarization results significantly. This is because, first, when extracting summary sentences, this method not only focuses on the relevance scores of sentences to the whole sentence collection, but also the topic representative of sentences. Second, when generating a summary, this method also deals with the problem of repetition of information. The methods were evaluated using ROUGE-1, ROUGE-2 and ROUGE-SU4 metrics. In this paper, we also demonstrate that the summarization result depends on the similarity measure. Results of the experiment showed that combination of symmetric and asymmetric similarity measures yields better result than their use separately.

Agglomerative Hierarchical Clustering Without Reversals on Dendrograms Using Asymmetric Similarity Measures

Algorithms of agglomerative hierarchical clustering using asymmetric similarity measures are studied. Two different measures between two clusters are proposed, one of which generalizes the average linkage for symmetric similarity measures. Asymmetric dendrogram representation is considered after foregoing studies. It is proved that the proposed linkage methods for asymmetric measures have no reversals in the dendrograms. Examples based on real data show how the methods work.

WE-E-213CD-03: Inverse-Consistent Symmetric Registration of Inner Colon Surfaces Derived from Prone and Supine CT Colonography.

Robust registration of prone and supine colonie surfaces acquired during CT colonography may lead to faster and more accurate detection of colorectal cancer and polyps. Any directional bias when registering one surface to the other could precipitate incorrect anatomical correspondence and engender reader error. Despite this, non-rigid registration methods are often implemented asymmetrically, which could negatively influence the registration. We aimed to reduce directional bias and so increase robustness by adapting a cylindrical registration algorithm to be both symmetric and inverse-consistent. The registration task can be simplified by mapping both prone and supine colonie surfaces onto regular cylinders. Spatial correspondence can then be established in cylindrical space using the original surfaces' local shape indices. We implemented a symmetric formulation of the popular non-rigid B-spline image registration method in cylindrical space. A symmetric similarity measure computes the sum of squared differences between both cylindrical representations of prone-to-supine and supine-to-prone directions simultaneously. Inverse consistency of the transformation is enforced by adding an appropriately weighted penalty term to the optimisation function. We selected 8 CT colonography patient cases with marked variation in luminal distension and surface morphology. We randomly allocated 4 of these for tuning an optimal set of registration parameters and 4 for validation. The mean inverse-consistency error was reduced by 32% from 4.8mm to 3.2mm by the new symmetric formulation. The mean registration error improved from 8.2mm to 7.3mm for 330 manually chosen reference points on the 4 validation sets. A symmetric formulation of prone and supine surface registration improves the quality of registration. Information from both prone-to-supine and supine-to-prone directions helps enforce convergence towards a more accurate solution due to reduced directional bias. A more robust and accurate registration will facilitate interpretation of CT colonography and has the potential to improve existing computer-aided detection methods. The authors gratefully acknowledge financial support for this work from the NIHR program: “Imaging diagnosis of colorectal cancer: Interventions for efficient and acceptable diagnosis in symptomatic and screening populationsâ€.

Directional distributional similarity for lexical inference

AbstractDistributional word similarity is most commonly perceived as a symmetric relation. Yet, directional relations are abundant in lexical semantics and in many Natural Language Processing (NLP) settings that require lexical inference, making symmetric similarity measures less suitable for their identification. This paper investigates the nature of directional (asymmetric) similarity measures that aim to quantify distributional feature inclusion. We identify desired properties of such measures for lexical inference, specify a particular measure based on Average Precision that addresses these properties, and demonstrate the empirical benefit of directional measures for two different NLP datasets.

Kernel Discriminant Analysis for Positive Definite and Indefinite Kernels

Kernel methods are a class of well established and successful algorithms for pattern analysis thanks to their mathematical elegance and good performance. Numerous nonlinear extensions of pattern recognition techniques have been proposed so far based on the so-called kernel trick. The objective of this paper is twofold. First, we derive an additional kernel tool that is still missing, namely kernel quadratic discriminant (KQD). We discuss different formulations of KQD based on the regularized kernel Mahalanobis distance in both complete and class-related subspaces. Secondly, we propose suitable extensions of kernel linear and quadratic discriminants to indefinite kernels. We provide classifiers that are applicable to kernels defined by any symmetric similarity measure. This is important in practice because problem-suited proximity measures often violate the requirement of positive definiteness. As in the traditional case, KQD can be advantageous for data with unequal class spreads in the kernel-induced spaces, which cannot be well separated by a linear discriminant. We illustrate this on artificial and real data for both positive definite and indefinite kernels.

Low-dimensional Multimodal Deformable Registration of MRI Brain Images in Stereotaxic Space

Deformable image registration is a fundamental technique in computational neuroanatomy. An iterative multilevel block matching technique with the use of several recent inventions is proposed here. A symmetric multimodal similarity measure allows to register subject images to an arbitrary digital brain atlas. Smooth deformations produced by scattered data interpolation based on compactly supported radial basis functions suppress gross inter-subject differences and preserve the localized anatomical variability which may be further studied with selected automated morphometry methods. Four similarity measures are tested in an experiment with image data obtained from the Simulated Brain Database and a quantitative evaluation of the algorithm is presented.

CLUE: cluster-based retrieval of images by unsupervised learning

In a typical content-based image retrieval (CBIR) system, target images (images in the database) are sorted by feature similarities with respect to the query. Similarities among target images are usually ignored. This paper introduces a new technique, cluster-based retrieval of images by unsupervised learning (CLUE), for improving user interaction with image retrieval systems by fully exploiting the similarity information. CLUE retrieves image clusters by applying a graph-theoretic clustering algorithm to a collection of images in the vicinity of the query. Clustering in CLUE is dynamic. In particular, clusters formed depend on which images are retrieved in response to the query. CLUE can be combined with any real-valued symmetric similarity measure (metric or nonmetric). Thus, it may be embedded in many current CBIR systems, including relevance feedback systems. The performance of an experimental image retrieval system using CLUE is evaluated on a database of around 60,000 images from COREL. Empirical results demonstrate improved performance compared with a CBIR system using the same image similarity measure. In addition, results on images returned by Google's Image Search reveal the potential of applying CLUE to real-world image data and integrating CLUE as a part of the interface for keyword-based image retrieval systems.

A fast document copy detection model

Text similarity measure is a common issue in Information Retrieval, Text Mining, Web Mining, Text Classification/Clustering and Document Copy Detection etc. The most popular approach is word frequency based scheme, which uses a word frequency vector to represent a document. Cosine function, dot product and proportion function are regular similarity measures of vector. But they are symmetric similarity measures, which cannot find out the subset copies. In this paper we present the concepts of asymmetric similarity model and heavy frequency vector (HFV). The former can detect subset copies well, and the latter can save a great resources and CPU time. We have developed two new asymmetric measures: heavy frequency vector (HFM) and Heavy inclusion proportion model HIPM. The HFM and HIPM are derived from cosine function and proportion function by combining asymmetric similarity concept with HFV. The HFV is to truncate the original full frequency vector to a short vector. We can adjust the parameter of HFV to balance the model’s performance. The paper illustrates the aspects of asymmetric similarity and HFV models by several experiments.

Visualizing asymmetric proximities with SOM and MDS models

Multidimensional scaling (MDS) and self organizing maps (SOM) algorithms are useful to visualize object relationships in a data set. These algorithms rely on the use of symmetric distances or similarity measures; for instance the Euclidean distance. There are a number of relevant applications, such as text mining and DNA microarray processing for which it is worth considering non symmetric similarity measures, that allow us to properly represent hierarchical relationships. In this paper we present asymmetric versions of SOM and MDS algorithms able to deal with asymmetric proximity matrices. We also compare these approaches to the corresponding symmetric versions. Experimental work on text databases and gene expression data sets show that the asymmetric proposed algorithms outperform their symmetric counterparts.

Modelling asymmetric similarity with prominence.

This paper introduces and discusses a geometrically based model, the relative prominence model, which is inspired by Tversky's finding that a factor behind asymmetric similarity seems to be 'relative prominence'. The model proposes that the experienced directed similarity from I to J is proportional to some symmetric similarity measure between I and J, and the quotient between the 'prominences' for J and I. Analysis of several empirical data sets shows that it is possible for a procedure to estimate the parameters of the model quite well. The differences between the relative prominence model and related models that handle asymmetry in terms of 'stimulus bias' are discussed.

Molecular Similarity. 1. Analytical Description of the Set of Graph Similarity Measures

The elaboration of methods for defining molecular similarity measures is one of the important fields of modern theoretical chemistry. These measures are used for solving a number of problems of theoretical and computer chemistry, in particular the prediction of properties of chemical compounds. For the construction of any molecular similarity measures molecules are represented as some mathematical objects {M}, on which quantitative similarity measures d(M1, M2) (M1, M2 ∈ {M}) are introduced. The most widely used way of molecular representation is based on picturing molecules as labeled graphs, labels of which encode types of atoms and bonds. There are many different similarity measures defined for graphs, expressed in terms of vectors of graph invariant, sequences, and sets derived from graphs or in terms of maximal common subgraph, etc. In general, there exists an infinite number of graph similarity measures. In the present paper an analytical description of the set of symmetric similarity measures defin...