Dissimilarity Measure Research Articles

Cyclic generators and an improved linear kernel for the rooted subtree prune and regraft distance

The rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a well-studied measure of topological dissimilarity that is NP-hard to compute. Here we describe an improved linear kernel for the problem. In particular, we show that if the classical subtree and chain reduction rules are augmented with a modified type of chain reduction rule, the resulting trees have at most 9k−3 leaves, where k is the rSPR distance; and that this bound is tight. In comparison, the previous best-known linear kernel is of size at most 28k. To achieve this improvement we introduce cyclic generators, which can be viewed as cyclic analogues of the generators used in the phylogenetic networks literature. As a corollary to our main result we also give an improved weighted linear kernel for the minimum hybridization problem on two rooted binary phylogenetic trees.

The k-nearest Neighbor Classification of Histogram- and Trapezoid-Valued Data

‎A histogram-valued observation is a specific type of symbolic objects that represents its value by a list of bins (intervals) along with their corresponding relative frequencies or probabilities‎.
 ‎In the literature‎, ‎the raw data in bins of all histogram-valued data have been assumed to be uniformly distributed‎. ‎A new representation of such observations is proposed in this paper by assuming that the raw data in each bin are linearly distributed‎, ‎which are called trapezoid-valued data‎.
 ‎Moreover‎, ‎new definitions of union and intersection between trapezoid-valued observations are made‎.
 This study proposes the k-nearest neighbor technique for classifying histogram-valued data using various dissimilarity measures‎.
 ‎Further‎, ‎the limiting behavior of the computational complexities based on the performed dissimilarity measures are compared‎.
 ‎Some simulations are done to study the performance of the proposed procedures‎. ‎Also‎, ‎the results are applied to three various real data sets‎.
 ‎Eventually‎, ‎some conclusions are stated‎.

Divergence measures for circular intuitionistic fuzzy sets and their applications

Circular Intuitionistic Fuzzy Set (C-IFS) is the real extension of the standard Intuitionistic Fuzzy Sets (IFS), where each element is represented by a circle instead of a single value. The divergence measures for fuzzy sets are used to find the discrimination between fuzzy sets. In this study, several divergence functions for C-IFSs are defined. The investigations verify that the divergence functions respect axiomatic properties to be divergence measures. Additional qualities of divergence measures are investigated to assure good performance. Also, the C-IF entropy and dissimilarity measures are explored. Divergence-based VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje” and in English “multi-criteria optimization and compromise solution”) method for C-IFSs is extended and applied to the multi-criteria decision-making problems. In the end, pattern recognition and multi-period medical diagnosis problems are focused on. The numerical examples are provided to illustrate the debated methods.

RSB: Robust Successive Binarization for Change Detection in Bitemporal Hyperspectral Images

The Earth’s observation programs, through the acquisition of remotely sensed hyperspectral images, aim at detecting and monitoring any relevant surface change due to natural or anthropogenic causes. The proposed algorithm, given as input a pair of hyperspectral images, produces as output a binary image denoting in white the changed pixels and in black the unchanged ones. The presented procedure relies on the computation of specific dissimilarity measures and applies successive binarization techniques, which prove to be robust, with respect to the different scenarios produced by the chosen measure, and fully automatic. The numerical tests show superior behavior when other common binarization techniques are used, and very competitive results are achieved when other methodologies are applied on the same benchmarks.

Hierarchical Superpixel Segmentation for PolSAR Images Based on the Boruvka Algorithm

Superpixel segmentation for polarimetric synthetic aperture radar (PolSAR) images plays a key role in remote-sensing tasks, such as ship detection and land-cover classification. However, the existing methods cannot directly generate multi-scale superpixels in a hierarchical style and they will take a long time when multi-scale segmentation is executed separately. In this article, we propose an effective and accurate hierarchical superpixel segmentation method, by introducing a minimum spanning tree (MST) algorithm called the Boruvka algorithm. To accurately measure the difference between neighboring pixels, we obtain the scattering mechanism information derived from the model-based refined 5-component decomposition (RFCD) and construct a comprehensive dissimilarity measure. In addition, the edge strength map and homogeneity measurement are considered to make use of the structural and spatial distribution information in the PolSAR image. On this basis, we can generate superpixels using the distance metric along with the MST framework. The proposed method can maintain good segmentation accuracy at multiple scales, and it generates superpixels in real time. According to the experimental results on the ESAR and AIRSAR datasets, our method is faster than the current state-of-the-art algorithms and preserves somewhat more image details in different segmentation scales.

Entropy for evaluation of Dempster-Shafer belief function models

Applications of Dempster-Shafer (D-S) belief functions to practical problems involve difficulties arising from their high computational complexity. One can use space-saving factored approximations such as graphical belief function models to solve them. Using an analogy with probability distributions, we represent these approximations in the form of compositional models. Since no theoretical apparatus similar to probabilistic information theory exists for D-S belief functions (e.g., dissimilarity measure analogous to the Kullback-Liebler divergence measure), the problems arise not only in connection with the design of algorithms seeking optimal approximations but also in connection with a criterion comparing two different approximations. In this respect, the application of the analogy with probability theory fails. Therefore, in this paper, we conduct some synthetic experiments and describe the results designed to reveal whether some belief function entropy definitions described in the literature can detect optimal approximations, i.e., that achieve their minimum for an optimal approximation.

Feature Clustering of Noisy Data and Application in the Currency Market

With the increase in high-dimensional data, researchers pay more attention to dimensionality reduction techniques because there are many noisy, redundant and irrelevant features in high-dimensional data. The existence of noisy features leads to decrease performance when analyzing high-dimensional data. Also, unsupervised dimensionality reduction techniques are widely used due to the lack of available labels. Feature clustering is an unsupervised dimensionality reduction technique to partition features into clusters in which features are strongly related. In addition, the Pearson correlation coefficient is widely used as a similarity tool for feature clustering. However, the Pearson correlation coefficient is easily influenced by outliers and noises, thus leading to misleading results. This paper focuses on the influence of dissimilarity measures on the clustering of noisy features. Heavy-tailed distributions are used for modeling data with outliers and noises. Therefore, we introduce a new dissimilarity measure based on a new dependence coefficient of heavy-tailed distributions. The performance of feature clustering using the proposed dissimilarity is evaluated using ARI and internal criteria on artificial and real currency market datasets. Experiment results have demonstrated the effectiveness of the proposed feature clustering method.

A hierarchically low-rank optimal transport dissimilarity measure for structured data

We develop a class of hierarchically low-rank, scalable optimal transport dissimilarity measures for structured data, bringing the current state-of-the-art optimal transport solvers to a higher level of performance. Given two n-dimensional discrete probability measures supported on two structured grids in \({\mathbb {R}}^d\), we present a fast method for computing an entropically regularized optimal transport distance, referred to as the debiased Sinkhorn distance. The method combines Sinkhorn’s matrix scaling iteration with a low-rank hierarchical representation of the scaling matrices to achieve a near-linear complexity \({{\mathscr {O}}}(n \ln ^4 n)\). This provides a fast, scalable, and easy-to-implement algorithm for computing a class of optimal transport dissimilarity measures, enabling their applicability to large-scale optimization problems, where the computation of the classical Wasserstein metric is not feasible. We carry out a rigorous error-complexity analysis for the proposed algorithm and present several numerical examples to verify the accuracy and efficiency of the algorithm and to demonstrate its applicability in tackling real-world problems.

Hierarchical clustered multiclass discriminant analysis via cross-validation

Linear discriminant analysis (LDA) is a well-known method for multiclass classification and dimensionality reduction. However, in general, ordinary LDA does not achieve high prediction accuracy when observations in some classes are difficult to be classified. A novel cluster-based LDA method is proposed that significantly improves prediction accuracy. Hierarchical clustering is adopted, and the dissimilarity measure of two clusters is defined by the cross-validation (CV) value. Therefore, clusters are constructed such that the misclassification error rate is minimized. The proposed approach involves a heavy computational load because the CV value must be computed at each step of the hierarchical clustering algorithm. To address this issue, a regression formulation for LDA is developed and an efficient algorithm that computes an approximate CV value is constructed. The performance of the proposed method is investigated by applying it to both artificial and real datasets. The proposed method provides high prediction accuracy with fast computation from both numerical and theoretical viewpoints.

A scalable and unbiased discordance metric with H.

A standard unsupervised analysis is to cluster observations into discrete groups using a dissimilarity measure, such as Euclidean distance. If there does not exist a ground-truth label for each observation necessary for external validity metrics, then internal validity metrics, such as the tightness or separation of the clusters, are often used. However, the interpretation of these internal metrics can be problematic when using different dissimilarity measures as they have different magnitudes and ranges of values that they span. To address this problem, previous work introduced the "scale-agnostic" $G_{+}$ discordance metric; however, this internal metric is slow to calculate for large data. Furthermore, in the setting of unsupervised clustering with $k$ groups, we show that $G_{+}$ varies as a function of the proportion of observations assigned to each of the groups (or clusters), referred to as the group balance, which is an undesirable property. To address this problem, we propose a modification of $G_{+}$, referred to as $H_{+}$, and demonstrate that $H_{+}$ does not vary as a function of group balance using a simulation study and with public single-cell RNA-sequencing data. Finally, we provide scalable approaches to estimate $H_{+}$, which are available in the $\mathtt{fasthplus}$ R package.

Similarity and dissimilarity measures of basic uncertain information and their applications in group decision-making

Similarity and dissimilarity measures of basic uncertain information and their applications in group decision-making

Quantile-based fuzzy C-means clustering of multivariate time series: Robust techniques

Robust fuzzy clustering of multivariate time series is addressed when the clustering purpose is grouping together series generated from similar stochastic processes. Robustness to the presence of anomalous series is attained by considering three well-known robust versions of a fuzzy C-means model based on a spectral dissimilarity measure with high discriminatory power. The dissimilarity measure compares principal component scores obtained from estimates of quantile cross-spectral densities, and the robust techniques follow the so-called metric, noise and trimmed approaches. The metric approach incorporates in the objective function a distance aimed at neutralizing the effect of the outliers, the noise approach builds an artificial cluster expected to contain the outlying series, and the trimmed approach removes the most atypical series in the dataset. As result, the proposed clustering methods take advantage of both the robust nature of these techniques and the capability of the quantile cross-spectral density to identify complex dependence structures. An extensive simulation study including multivariate linear, nonlinear and GARCH processes shows that the algorithms are substantially effective in coping with the presence of outlying series, clearly outperforming other alternative procedures. Two specific applications regarding financial and environmental series illustrate the usefulness of the presented methods.

Group-based public opinion polarisation in multi-party systems

Public opinion polarisation can impair society’s ability to reach a democratic consensus in different political issue areas. This appears particularly true when the polarisation of opinions coincides with clearly identifiable social groups. The literature on public opinion polarisation has mostly focussed on the US two-party context. We lack concepts and measures that can be adapted to European countries with multi-party systems and multi-layered group identities. This article proposes a conceptualisation of polarisation between groups in society. It presents a measure that captures the overlap of ideology distributions between groups. The two-step empirical framework includes hierarchical IRT models and a measure for dissimilarity of distributions. The second part presents an empirical application of the measure based on survey data from Switzerland (1994–2016), which reveals insightful dynamics of public opinion polarisation between party supporters and education groups.

Out‐of‐bag stability estimation for k‐means clustering

AbstractClustering data is a challenging problem in unsupervised learning where there is no gold standard. Results depend on several factors, such as the selection of a clustering method, measures of dissimilarity, parameters, and the determination of the number of reliable groupings. Stability has become a valuable surrogate to performance and robustness that can provide insight to an investigator on the quality of a clustering, and guidance on subsequent cluster prioritization. This work develops a framework for stability measurements that is based on resampling and OB estimation. Bootstrapping methods for cluster stability can be prone to overfitting in a setting that is analogous to poor delineation of test and training sets in supervised learning. Stability that relies on OB items from a resampling overcomes these issues and does not depend on a reference clustering for comparisons. Furthermore, OB stability can provide estimates at the level of the item, cluster, and as an overall summary, which has good interpretive value. This framework is extended to develop stability estimates for determining the number of clusters (model selection) through contrasts between stability estimates on clustered data, and stability estimates of clustered reference data with no signal. These contrasts form stability profiles that can be used to identify the largest differences in stability and do not require a direct threshold on stability values, which tend to be data specific. These approaches can be implemented using the R package bootcluster that is available on the Comprehensive R Archive Network.

How representative are social partners in Europe? The role of dissimilarity

AbstractSocial partners (trade unions and employers' associations [EA]) and their representativeness can shape labour institutions and economic and social outcomes in many countries. In this paper, we argue that, when examining social partners' representativeness, it is important to consider both affiliation rates and dissimilarity measures. The latter concerns the extent to which affiliated and non‐affiliated firms or workers are distributed similarly across relevant dimensions, including firm size. In our analysis of the European Company Survey, we find that affiliation density and dissimilarity measures correlate positively across countries, particularly in the case of EA in which we focus. This result also holds across EA when we use more detailed, firm population data for Portugal. We conclude that higher affiliation densities do not necessarily correspond to more representative social partners as they can involve greater dissimilarity between affiliated and non‐affiliated firms.

Is traditional back translation enough? Comparison of translation methodology for an ASD screening tool.

Early identification of autism spectrum disorders (ASD) in non-English speaking children often relies on translation of English ASD screening measures. Most measures employ a forward-back translation approach, despite data suggesting that this method may result in poor psychometric properties. Some studies in non-ASD fields have suggested that a rigorous method of translation with cultural adaptation may yield better psychometric properties, but no studies in the ASD field have compared the two approaches directly. This investigation compares these two translation methodologies to determine if they produce psychometrically similar or dissimilar measures. Three hundred and eighty US-based Spanish-speaking caregivers of children 8-16 months old were randomly assigned to complete either a forward-back Spanish translation or a rigorous translation with cultural adaptation of a parent-report ASD screening tool. Measurement invariance analyses determined that the two translations were psychometrically dissimilar. Additional qualitative explanatory methods using cognitive interviews examined textual differences and participant preferences between non-invariant items. LAY SUMMARY: Autism screening questionnaires created in English need to be translated into other languages so non-English speaking parents can fill them out accurately. Traditionally, researchers have not considered cultural differences when they translate these questionnaires. When we compared a direct translation to a translation with cultural adaptations, the two questionnaires were statistically different. Parents interpreted and responded to the same questions differently, depending on which version they filled out.

Multidimensional Scaling Clustering Based on Weighted-Permutation Patterns and Symmetrical Kullback–Leibler Divergence

In this paper, the symmetrical Kullback–Leibler divergence is proposed to capture the dynamical features of various complex time series more accurately. The symmetrical Kullback–Leibler divergence is modified from the Kullback–Leibler divergence to make it possess the properties of a normal distance measure. A new multidimensional scaling (MDS) method with the proposed symmetrical Kullback–Leibler divergence is established, which is an efficient clustering and visualization technique. The proposed method also includes the probability distribution of the weighted-permutation patterns, which not only provides a modified time series quantification process with more possible patterns, but also facilitates the reduction of error when extracting the hidden information from time series. The upper and lower bounds of the proposed divergence are also presented. Through simulation and reality-based data experiments, it is affirmed that the MDS based on this novel dissimilarity measure is capable of presenting more distinctive and rational clustering results by comparing it with the MDS methods based on conventional dissimilarities.

Picture fuzzy large-scale group decision-making in a trust- relationship-based social network environment

Traditional large-scale group decision-making (LSGDM) methods assume that the decision-makers (DMs) are independent, and the trust relationships among DMs in the social network (SN) are complete. However, DMs always influence each other, and practical trust relationships among DMs in the SN are often incomplete. In this study, we propose a picture fuzzy LSGDM approach in a trust-relationship-based SN environment to solve decision-making problems. To achieve this, the incomplete trust relationship of SNs was considered first and the missing information was estimated using a picture fuzzy trust propagation operator. Next, a novel picture fuzzy Jensen a-norm dissimilarity measure was defined and the corresponding consensus detection model was developed for LSGDM in a trust-relationship-based SN environment. Afterward, based on the technique for order of preference by similarity to ideal solution (TOPSIS) approach, a picture fuzzy dissimilarity-based selection method was proposed for the selection process. Finally, two case studies were provided to demonstrate the effectiveness of the proposed approach. The sensitivity and comparison analyses demonstrated the stability and reliability of the decision-making results obtained using this method.

Wilks’ dissimilarity for gene clustering: computational issues

Clustering methods are widely used in the analysis of gene expression data for their ability to uncover coordinated expression profiles. One important goal of clustering is to discover co–regulated genes because it has been postulated that co–regulation implies a similar function. In the context of agglomerative hierarchical clustering, we introduced a dissimilarity measure based on the Wilks’ Λ statistic that they called the Wilks’ dissimilarity and showed its usefulness in the identification of transcription modules. In this paper, we discuss the ability of the Wilks’ dissimilarity to identify clusters of co-expressed genes by providing an example where the most commonly used dissimilarity measures fail. Furthermore, we carry out a set of simulations aimed to investigate the use of a sparse canonical correlation technique in the estimation of the Wilks’ dissimilarity and provide guidelines for its use.

Supervised Nonparametric Classification in the Context of Replicated Point Patterns

A spatial point pattern is a collection of points in space, representing, e.g. observed locations of trees, bird nests, centers of cells in a histological sample, etc. When several independent realizations of the underlying stochastic process are observed, these realizations are referred to as replicated point patterns. The main objective of this paper is to classify a newly observed pattern into one of the existing classes using a supervised nonparametric classification method, namely the Bayes classifier in combination with the k-nearest neighbors algorithms and the kernel regression method. The dissimilarity between a pair of patterns is defined using the functional summaries extracted from the point patterns via the Cramér-von Mises or Kolmogorov-Smirnov type formula. A set of simulation experiments is presented to investigate the performance of the proposed classifier with a dissimilarity measure based on functional summaries, such as the pair correlation function. The application of such a classifier to a real point pattern dataset is also illustrated.