Kendall Tau Distance Research Articles

A Hybrid Feature Selection through Ensemble Rank Aggregation to Improve Perdition and Classification Accuracy

Today, extending credit is a difficult operation since credit databases contain a large quantity of data as well as redundant and useless information. The surplus and unrelated data can lower the categorization and prediction accuracy. In this case, feature selection is crucial for managing massive data. Different rank aggregation (RA) methods are there to ensemble individual feature selection. However not every dataset will perform at its best when using a single RA technique, the combination of multiple RA techniques are needed to increase the perdition accuracy. This study proposes a hybrid rank aggregation model that select features that are significant across different rank aggregation methods like MC4, Kendall tau distance and Borda. This study observed that the performance of ensemble rank aggregation techniques is better than the existing individual rank aggregation methods.

Beyond kemeny rank aggregation: A parameterizable-penalty framework for robust ranking aggregation with ties

Rank Aggregation has ubiquitous applications in operations research, artificial intelligence, computational social choice, and various other fields. Interest in this problem has increased due in part to the need to consolidate lists of rankings and scores output by different decision-making processes and algorithms. Although most attention has focused on the variant of this problem induced by the Kemeny-Snell distance, other robust rank aggregation problems have been proposed. This work delves into the rank aggregation problem under the generalized Kendall-tau distance —a parameterizable-penalty distance measure for comparing rankings with ties— which contains Kemeny aggregation as a special case. First, it derives exact and heuristic solution methods. Second, it introduces a social choice property (GXCC) that encloses existing variations of the Condorcet criterion as special cases, thereby expanding this seminal social choice concept beyond Kemeny aggregation for the first time. GXCC offers both computational and theoretical advantages. In particular, GXCC may help to divide the original problem into smaller subproblems, while still ensuring that solving them independently yields the optimal solution to the original problem. Experiments on two benchmark datasets conducted herein show that the featured exact and heuristic solution methods can benefit from GXCC. Finally, this work derives new theoretical insights into the effects of the generalized Kendall-tau distance penalty parameter on the optimal ranking and on the proposed social choice property.

CSChO-Deep MaxNet: Cat swam chimp optimization integrated deep maxout network for heart disease detection

Early heart disease identification is of tremendous importance to minimize mortality. As, the medical data is gradually increases, it is more complicate to analyze and process the data. The detection results generated by the existing methods are inaccurate. This research design a Cat Swam Chimp Optimization (CSChO)-based Deep maxout network for detecting the heart disease with medical data. The data is pre-processed using missing data imputation and log transformation. After that, feature fusion mechanism is achieved using Kendall tau distance measure with Deep Belief network (DBN) classifier. Utilizing the features, the suggested CSChO algorithm trained deep maxout network is used to diagnose disease. The Cat Swarm Optimization (CSO) and Chimp Optimization Algorithm (ChOA) are combined to create the CSChO. Testing accuracy, sensitivity, and specificity metrics for training samples show the suggested technique to perform better with values of 0.948, 0.949, and 0.919 respectively, by Hungary dataset.

A Kemeny Distance-Based Robust Fuzzy Clustering for Preference Data

We propose two robust fuzzy clustering techniques in the context of preference rankings to group judges into homogeneous clusters even in the case of contamination due to outliers or, more generally, noisy data. The two fuzzy C-Medoids clustering methods, based on the same suitable exponential transformation of the Kemeny distance, belong to two different approaches and differ in the way they introduce the fuzziness in the membership matrix, the one based on the “m” exponent and the other on the Shannon entropy. As far as the Kemeny distance is concerned, it is equivalent to the Kendall distance in the case of complete rankings but differs from the latter in the way of handling tied rankings. Simulations prove that our methods are able to recover the natural structure of the groups neutralizing the effect of possible noises and outliers. Two applications to real datasets are also provided.

Recommending Related Microblogs: A Comparison Between Topic and WordNet based Approaches

Computing similarity between short microblogs is an important step in microblog recommendation. In this paper, we investigate a topic based approach and a WordNet based approach to estimate similarity scores between microblogs and recommend top related ones to users. Empirical study is conducted to compare their recommendation effectiveness using two evaluation measures. The results show that the WordNet based approach has relatively higher precision than that of the topic based approach using 548 tweets as dataset. In addition, the Kendall tau distance between two lists recommended by WordNet and topic approaches is calculated. Its average of all the 548 pair lists tells us the two approaches have the relative high disaccord in the ranking of related tweets.

Distance restricted manipulation in voting

We introduce the notion of Distance Restricted Manipulation, where colluding manipulator(s) need to compute if there exist votes which make their preferred alternative win the election when their knowledge about the others' votes is a little inaccurate. We use the Kendall-Tau distance to model the manipulators' confidence in the non-manipulators' votes. To this end, we study this problem in two settings - one where the manipulators need to compute a manipulating vote that succeeds irrespective of perturbations in others' votes (Distance Restricted Pessimistic Manipulation), and the second where the manipulators need to compute a manipulating vote that succeeds for at least one possible vote profile of the others (Distance Restricted Optimistic Manipulation). We show that Distance Restricted Pessimistic Manipulation admits polynomial-time algorithms for every scoring rule, maximin, Bucklin, and simplified Bucklin voting rules for a single manipulator, and for the k-approval rule for any number of manipulators, but becomes intractable for the Copelandα voting rule for every α∈[0,1] even for a single manipulator. In contrast, Distance Restricted Optimistic Manipulation is intractable for almost all the common voting rules, with the exception of the plurality rule. For a constant number of alternatives, we show that both the problems are polynomial-time solvable for every anonymous and efficient voting rule.

Using the weighted Kendall Distance to analyze rank data in psychology

Using the weighted Kendall Distance to analyze rank data in psychology

Kendall tau sequence distance: Extending Kendall tau from ranks to sequences

An edit distance is a measure of the minimum cost sequence of edit operations to transform one structure into another. Edit distance is most commonly encountered within the context of strings, where Wagner and Fischer's string edit distance is perhaps the most well-known. However, edit distance is not limited to strings. For example, there are several edit distance measures for permutations, including Wagner and Fischer's string edit distance since a permutation is a special case of a string. However, another edit distance for permutations is Kendall tau distance, which is the number of pairwise element inversions. On permutations, Kendall tau distance is equivalent to an edit distance with adjacent swap as the edit operation. A permutation is often used to represent a total ranking over a set of elements. There exist multiple extensions of Kendall tau distance from total rankings (permutations) to partial rankings (i.e., where multiple elements may have the same rank), but none of these are suitable for computing distance between sequences. We set out to explore extending Kendall tau distance in a different direction, namely from the special case of permutations to the more general case of strings or sequences of elements from some finite alphabet. We name our distance metric Kendall tau sequence distance, and define it as the minimum number of adjacent swaps necessary to transform one sequence into the other. We provide two $O(n \lg n)$ algorithms for computing it, and experimentally compare their relative performance. We also provide reference implementations of both algorithms in an open source Java library.

Near-Neighbor Methods in Random Preference Completion

This paper studies a stylized, yet natural, learning-to-rank problem and points out the critical incorrectness of a widely used nearest neighbor algorithm. We consider a model with n agents (users) {xi}i∈[n] and m alternatives (items) {yl}l∈[m], each of which is associated with a latent feature vector. Agents rank items nondeterministically according to the Plackett-Luce model, where the higher the utility of an item to the agent, the more likely this item will be ranked high by the agent. Our goal is to identify near neighbors of an arbitrary agent in the latent space for prediction.We first show that the Kendall-tau distance based kNN produces incorrect results in our model. Next, we propose a new anchor-based algorithm to find neighbors of an agent. A salient feature of our algorithm is that it leverages the rankings of many other agents (the so-called “anchors”) to determine the closeness/similarities of two agents. We provide a rigorous analysis for one-dimensional latent space, and complement the theoretical results with experiments on synthetic and real datasets. The experiments confirm that the new algorithm is robust and practical.

MSeer—An Advanced Technique for Locating Multiple Bugs in Parallel

In practice, a program may contain multiple bugs. The simultaneous presence of these bugs may deteriorate the effectiveness of existing fault-localization techniques to locate program bugs. While it is acceptable to use all failed and successful tests to identify suspicious code for programs with exactly one bug, it is not appropriate to use the same approach for programs with multiple bugs because the due-to relationship between failed tests and underlying bugs cannot be easily identified. One solution is to generate fault-focused clusters by grouping failed tests caused by the same bug into the same clusters. We propose MSeer—an advanced fault localization technique for locating multiple bugs in parallel. Our major contributions include the use of (1) a revised Kendall tau distance to measure the distance between two failed tests, (2) an innovative approach to simultaneously estimate the number of clusters and assign initial medoids to these clusters, and (3) an improved K-medoids clustering algorithm to better identify the due-to relationship between failed tests and their corresponding bugs. Case studies on 840 multiple-bug versions of seven programs suggest that MSeer performs better in terms of effectiveness and efficiency than two other techniques for locating multiple bugs in parallel.

An Analysis on the Negative Effect of Multiple-Faults for Spectrum-Based Fault Localization

This paper aims to investigate the negative effects of multiple-faults on spectrum-based fault localization (SBFL). Previously, researchers validated the fact that the occurrence of multiple-faults could have a significant negative impact on fault localization. However, a very little current research addresses the degree of these impacts through a systemic analysis. Furthermore, the fundamental causes underlying that negative impact have not been investigated and are not fully understood. We conducted experiments on fourteen real-life open source programs to explore and possibly solve these problems. Our results indicate that: 1) although multiple-faults generally do have a negative impact on fault localization, different fault localizations displayed various levels of robustness against that negative impact; 2) restoring pass/fail fault interactions only has a modest effect on that negative impact; 3) our investigation of twelve Fault Localization Interactions (FLI) shows that there is a dominant FLI-1 interaction in multiple-fault programs which should be responsible for that negative impact; 4) restoring FLI-1 can significantly improve the performance of both SBFL and parallel debugging techniques; and 5) furthermore, this paper practically validated the revised Kendall Tau distance as an efficient measure to help locate test cases, which have triggered FLI-1. Based on the revised Kendall Tau distance, a fast search algorithm has been suggested to locate FLI-1 test cases. It is expected that this paper can provide some insight into the fundamental causes of multiple-faults’ negative impact on fault localization and drive the development of more efficient fault localization techniques to improve the identification and handling of multiple-faults.

Weighted Distance-Based Models for Ranking Data Using the R Package rankdist

rankdist is a recently developed R package which implements various distance-based ranking models. These models capture the occurring probability of rankings based on the distances between them. The package provides a framework for fitting and evaluating finite mixture of distance-based models. This paper also presents a new probability model for ranking data based on a new notion of weighted Kendall distance. The new model is flexible and more interpretable than the existing models. We show that the new model has an analytic form of the probability mass function and the maximum likelihood estimates of the model parameters can be obtained efficiently even for ranking involving a large number of objects.

Disease progression timeline estimation for Alzheimer's disease using discriminative event based modeling

Alzheimer's Disease (AD) is characterized by a cascade of biomarkers becoming abnormal, the pathophysiology of which is very complex and largely unknown. Event-based modeling (EBM) is a data-driven technique to estimate the sequence in which biomarkers for a disease become abnormal based on cross-sectional data. It can help in understanding the dynamics of disease progression and facilitate early diagnosis and prognosis by staging patients. In this work we propose a novel discriminative approach to EBM, which is shown to be more accurate than existing state-of-the-art EBM methods. The method first estimates for each subject an approximate ordering of events. Subsequently, the central ordering over all subjects is estimated by fitting a generalized Mallows model to these approximate subject-specific orderings based on a novel probabilistic Kendall's Tau distance. We also introduce the concept of relative distance between events which helps in creating a disease progression timeline. Subsequently, we propose a method to stage subjects by placing them on the estimated disease progression timeline. We evaluated the proposed method on Alzheimer's Disease Neuroimaging Initiative (ADNI) data and compared the results with existing state-of-the-art EBM methods. We also performed extensive experiments on synthetic data simulating the progression of Alzheimer's disease. The event orderings obtained on ADNI data seem plausible and are in agreement with the current understanding of progression of AD. The proposed patient staging algorithm performed consistently better than that of state-of-the-art EBM methods. Event orderings obtained in simulation experiments were more accurate than those of other EBM methods and the estimated disease progression timeline was observed to correlate with the timeline of actual disease progression. The results of these experiments are encouraging and suggest that discriminative EBM is a promising approach to disease progression modeling.

Can eye-tracking metrics be used to better pair radiologists in a mammogram reading task?

To propose a framework for optimal pairing of radiologists when reading mammograms based on their search patterns. Four experienced and four less-experienced radiologists were asked to assess 120 cases (59 with cancers) while their eye positions were tracked. Fourteen eye-tracking metrics were extracted to quantify the differences among radiologists' visual search pattern. For each radiologist and metric, less-experienced radiologists and expert readers were ranked based on the level of similarities in gaze patterns (from the most different to the most similar). Less-experienced readers and experts were also ranked based on the values of area under the receiver operating characteristic curve (AUC) after pairing (the best possible way of ranking). Using the Kendall's tau distance, rankings based on different metrics were compared with the best possible ranking. Using paired Wilcoxon signed-rank test, the AUC values when pairing in the best way were compared with pairing based on different metrics. Finally, we investigated the robustness of pairing strategies against the small sample size. For ranking the experienced radiologists, results from eight metrics were as good as the best possible ranking. For the less-experienced ones, only one metric resulted in a ranking comparable to the best possible way of ranking. The AUC values of pairings based on these metrics did not differ significantly from the best pairing scenario. Compared to the pairings based on the cognitive metrics, the ranking based on AUC values varied more greatly with the sample size, suggesting that it is less robust against the small sample size compared to the cognitive metrics. Different pairings may have different effects on performance; some are detrimental while some improve the performance of the pair. Using the suggested cognitive metrics, we can optimize the pairings even with a small dataset.

A Genetic Algorithm Approach for Group Recommender System Based on Partial Rankings

Abstract Many recommender systems frequently make suggestions for group consumable items to the individual users. There has been much work done in group recommender systems (GRSs) with full ranking, but partial ranking (PR) where items are partially ranked still remains a challenge. The ultimate objective of this work is to propose rank aggregation technique for effectively handling the PR problem. Additionally, in real applications, most of the studies have focused on PR without ties (PRWOT). However, the rankings may have ties where some items are placed in the same position, but where some items are partially ranked to be aggregated may not be permutations. In this work, in order to handle problem of PR in GRS for PRWOT and PR with ties (PRWT), we propose a novel approach to GRS based on genetic algorithm (GA) where for PRWOT Spearman foot rule distance and for PRWT Kendall tau distance with bucket order are used as fitness functions. Experimental results are presented that clearly demonstrate that our proposed GRS based on GA for PRWOT (GRS-GA-PRWOT) and PRWT (GRS-GA-PRWT) outperforms well-known baseline GRS techniques.

Robust Plackett–Luce model for k-ary crowdsourced preferences

The aggregation of k-ary preferences is an emerging ranking problem, which plays an important role in several aspects of our daily life, such as ordinal peer grading and online product recommendation. At the same time, crowdsourcing has become a trendy way to provide a plethora of k-ary preferences for this ranking problem, due to convenient platforms and low costs. However, k-ary preferences from crowdsourced workers are often noisy, which inevitably degenerates the performance of traditional aggregation models. To address this challenge, in this paper, we present a RObust PlAckett–Luce (ROPAL) model. Specifically, to ensure the robustness, ROPAL integrates the Plackett–Luce model with a denoising vector. Based on the Kendall-tau distance, this vector corrects k-ary crowdsourced preferences with a certain probability. In addition, we propose an online Bayesian inference to make ROPAL scalable to large-scale preferences. We conduct comprehensive experiments on simulated and real-world datasets. Empirical results on “massive synthetic” and “real-world” datasets show that ROPAL with online Bayesian inference achieves substantial improvements in robustness and noisy worker detection over current approaches.

Comparison of rank aggregation methods based on inherent ability

AbstractRanking is a common task for selecting and evaluating alternatives. In the past few decades, combining rankings results from various sources into a consensus ranking has become an increasingly active research topic. In this study, we focus on the evaluation of rank aggregation methods. We first develop an experimental data generation method, which can provide ground truth ranking for alternatives based on their “inherent ability.” This experimental data generation method can generate the required individual synthetic rankings with adjustable accuracy and length. We propose characterizing the effectiveness of rank aggregation methods by calculating the Kendall tau distance between the aggregated ranking and the ground truth ranking. We then compare four classical rank aggregation methods and present some useful findings on the relative performances of the four methods. The results reveal that both the accuracy and length of individual rankings have a remarkable effect on the comparison results between rank aggregation methods. Our methods and results may be helpful to both researchers and decision‐makers.

Rank aggregation using ant colony approach for metasearch

Metasearch engines provide a plethora of information to the user through World Wide Web. They are the prominent sources of query-based search and centralized human–world interactions. Metasearch engine shows a list of Web sites to a particular query as per the rank assigned to a web link. The effectiveness of metasearch engine is also examined on the basis of ranks assigned to Web sites for a particular query. Assigning top rank to a web link with most relevant information pertaining to a query by the search engine is formulated as research problem. Here, we have formulated the rank aggregation optimization problem by using metaheuristic approach. Search engines are facing widely two problems such as biasing of search solutions and giving irrelevant rank to similar kind of documents. Both these problems can be overcome by applying an effective rank aggregation technique for combining the search results from various search engines. This paper presents a metaheuristic approach to optimize Spearman’s footrule and Kendall-tau distance measures which are used to compare ranking methods. The performance of proposed ant colony-based strategy is compared with GA technique and is validated through experimental results for real-world queries. Likewise, Precision, Recall and F-Measure-based performance metrics are employed to test the effectiveness of various metasearch engines.

Ranking, clustering and fusing the normalized LBP temporal facial features for face recognition in video sequences

This paper proposes a novel approach for recognizing faces in videos with high recognition rate. Initially, the feature vector based on Normalized Local Binary Patterns is obtained for the face region. A set of training and testing videos are used in this face recognition procedure. Each frame in the query video is matched with the signature of the faces in the database using Euclidean distance and a rank list is formed. Each ranked list is clustered and its reliability is analyzed for re-ranking. Multiple re-ranked lists of the query video is fused together to form a video signature. This video signature embeds diverse intra-personal variations such as poses, expressions and facilitates in matching two videos with large variations. For matching two videos, their composite ranked lists are compared using a Kendall Tau distance measure. The developed methods are deployed on the YouTube and ChokePoint videos, and they exhibit significant performance improvement owing to their novel approach when compared with the existing techniques.

Rank aggregation in cyclic sequences

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic rank with respect to a set of elements. This problem originates from the Rank Aggregation Problem for combining different linear ranks of elements. Next, we also introduce the problem of finding the cyclic sequence with minimum expected cost with respect to a probability measure based on dissimilarity between cyclic sequences on the Kendall Tau metric. Finally, we establish certain relationships among some classical problems and the new problems that we have proposed.