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.

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.

Optimal full ranking from pairwise comparisons

We consider the problem of ranking n players from partial pairwise comparison data under the Bradley–Terry–Luce model. For the first time in the literature, the minimax rate of this ranking problem is derived with respect to the Kendall’s tau distance that measures the difference between two rank vectors by counting the number of inversions. The minimax rate of ranking exhibits a transition between an exponential rate and a polynomial rate depending on the magnitude of the signal-to-noise ratio of the problem. To the best of our knowledge, this phenomenon is unique to full ranking and has not been seen in any other statistical estimation problem. To achieve the minimax rate, we propose a divide-and-conquer ranking algorithm that first divides the n players into groups of similar skills and then computes local MLE within each group. The optimality of the proposed algorithm is established by a careful approximate independence argument between the two steps.

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.

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.

Optimal Permutation Recovery in Permuted Monotone Matrix Model

Motivated by recent research on quantifying bacterial growth dynamics based on genome assemblies, we consider a permuted monotone matrix model , where the rows represent different samples, the columns represent contigs in genome assemblies and the elements represent log-read counts after preprocessing steps and Guanine-Cytosine (GC) adjustment. In this model, Θ is an unknown mean matrix with monotone entries for each row, Π is a permutation matrix that permutes the columns of Θ, and Z is a noise matrix. This article studies the problem of estimation/recovery of Π given the observed noisy matrix Y. We propose an estimator based on the best linear projection, which is shown to be minimax rate-optimal for both exact recovery, as measured by the 0-1 loss, and partial recovery, as quantified by the normalized Kendall’s tau distance. Simulation studies demonstrate the superior empirical performance of the proposed estimator over alternative methods. We demonstrate the methods using a synthetic metagenomics dataset of 45 closely related bacterial species and a real metagenomic dataset to compare the bacterial growth dynamics between the responders and the nonresponders of the IBD patients after 8 weeks of treatment. Supplementary materials for this article are available online.

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.

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.

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.

A novel application of PageRank and user preference algorithms for assessing the relative performance of track athletes in competition.

Ranking enables coaches, sporting authorities, and pundits to determine the relative performance of individual athletes and teams in comparison to their peers. While ranking is relatively straightforward in sports that employ traditional leagues, it is more difficult in sports where competition is fragmented (e.g. athletics, boxing, etc.), with not all competitors competing against each other. In such situations, complex points systems are often employed to rank athletes. However, these systems have the inherent weakness that they frequently rely on subjective assessments in order to gauge the calibre of the competitors involved. Here we show how two Internet derived algorithms, the PageRank (PR) and user preference (UP) algorithms, when utilised with a simple ‘who beat who’ matrix, can be used to accurately rank track athletes, avoiding the need for subjective assessment. We applied the PR and UP algorithms to the 2015 IAAF Diamond League men’s 100m competition and compared their performance with the Keener, Colley and Massey ranking algorithms. The top five places computed by the PR and UP algorithms, and the Diamond League ‘2016’ points system were all identical, with the Kendall’s tau distance between the PR standings and ‘2016’ points system standings being just 15, indicating that only 5.9% of pairs differed in their order between these two lists. By comparison, the UP and ‘2016’ standings displayed a less strong relationship, with a tau distance of 95, indicating that 37.6% of the pairs differed in their order. When compared with the standings produced using the Keener, Colley and Massey algorithms, the PR standings appeared to be closest to the Keener standings (tau distance = 67, 26.5% pair order disagreement), whereas the UP standings were more similar to the Colley and Massey standings, with the tau distances between these ranking lists being only 48 (19.0% pair order disagreement) and 59 (23.3% pair order disagreement) respectively. In particular, the UP algorithm ranked ‘one-off’ victors more highly than the PR algorithm, suggesting that the UP algorithm captures alternative characteristics to the PR algorithm, which may more suitable for predicting future performance in say knockout tournaments, rather than for use in competitions such as the Diamond League. As such, these Internet derived algorithms appear to have considerable potential for objectively assessing the relative performance of track athletes, without the need for complicated points equivalence tables. Importantly, because both algorithms utilise a ‘who beat who’ model, they automatically adjust for the strength of the competition, thus avoiding the need for subjective decision making.

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.

The problem of ranking CO2 abatement measures: A methodological proposal

Marginal Abatement Cost curves are considered a standard tool for analysing the impacts of mitigation measures and are one of the most used methodologies for evaluating abatement options by comparing their cost-effectiveness. Nevertheless some discrepancies regarding their construction and interpretation arose in the last few years. In this paper, we analyse the methods found in the literature for evaluating and ranking abatement measures, identify unsolved issues and propose three alternative methods. The first method, Gain Maximizing (GM), supports an environmentalist attitude and performs a direct comparison of measures with both negative and positive costs. The second, Extended MAC method (EMAC), considers an economically driven point of view, weighting the negative cost options according to its economic savings over its reduction potential. The third is a Balanced Ordering Method (BOM), consisting in a linear weighted combination of two discretional seed methods, which allows decision makers to create new rankings adjustable to a specific greenhouse gases policy, whether it is fully or partially driven by economical or environmental positions. Finally, the authors propose a methodology for comparing methods based on their Kendal tau distance to the benchmarks considered relevant in the decision making process (economical profit and environmental benefit).

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.

Ranking chain sum orders

Ranking information is an important topic in information sciences, Internet searching, voting systems, and sports. In the full information approach, a ranking is a total order of the candidates. We compare two rankings by pairwise comparisons under the nearest neighbor Kendall tau distance and study the distance and rank aggregation problems.In many settings, the information is incomplete and a ranking is given by a partial order. A bucket order is obtained if a ranking allows ties and treats tied candidates as equivalent. Then the distance and rank aggregation problems can be solved efficiently in almost linear time. A chain sum order is complementary to a bucket order and consists of a set of disjoint total orders. Its width and height is the number and the maximum size of the total orders, respectively.We show that the distance and rank aggregation problems of a total order and a chain sum order of bounded width or of height at most two can be solved in polynomial time and are NP-complete for a total and a chain sum order of height at least 12. Both problems remain NP-complete for a total and a heap order which is the partial order obtained from a single-elimination tournament (in sports). However, the problems are fixed-parameter tractable with respect to the distance and the Ulam distance, but are fixed-parameter intractable with respect to the order dimension.

Ranking of Dystonia Severity by Pairwise Video Comparison.

Reviewers of dystonia rating scales agree on the need to assess symptoms more comprehensively. During the development of a quantitative dystonia assessment by video-perceptive computing, we devised a video-based severity ranking as a procedure to create a validation standard without the use of clinical scales. Thirty-four patients with dystonia (17 with dystonic tremor) and 2 controls were assessed with clinical scales and video-recordings of 24 short movement tasks. Two to 4 raters compared multiple permutations of videos from 22 subjects, including 2 healthy controls, until a complete rank order was achieved. Inter-rater agreement was expressed as normalized Kendall tau distance. Spearman correlations of video rank order with clinical scales and self-rating were repeated for tremor/nontremor subgroups. Normalized Kendall tau distances were <0.3 for 15 items. The video rank order for sitting and head movements correlated with clinical scales for the whole group (rho 0.52-0.87) and in the subgroup without tremor. In the tremor subgroup such correlation was perceived in the 2 items involving sitting. Video rank order correlated with quality of life self-rating only in 1 item (arms held in front, palm down). The agreement of video rankings between raters is remarkable. The lack of correlation in the tremor subgroup in several items may be interpreted as tremor being considered in video comparisons but not in clinical scales. This supports video-based ranking as a more comprehensive rating of dystonia and as a possible validation instrument applicable in situations in which no reference standard is available.

Reconstructing Hidden Permutations Using the Average-Precision (AP) Correlation Statistic

We study the problem of learning probabilistic models for permutations, where the order between highly ranked items in the observed permutations is more reliable (i.e., consistent in different rankings) than the order between lower ranked items, a typical phenomena observed in many applications such as web search results and product ranking. We introduce and study a variant of the Mallows model where the distribution is a function of the widely used Average-Precision (AP) Correlation statistic, instead of the standard Kendall’s tau distance. We present a generative model for constructing samples from this distribution and prove useful properties of that distribution. Using these properties we develop an efficient algorithm that provably computes an asymptotically unbiased estimate of the center permutation, and a faster algorithm that learns with high probability the hidden central permutation for a wide range of the parameters of the model. We complement our theoretical analysis with extensive experiments showing that unsupervised methods based on our model can precisely identify ground-truth clusters of rankings in real-world data. In particular, when compared to the Kendall’s tau based methods, our methods are less affected by noise in low-rank items.

Optimal Aggregation of Uncertain Preferences

A paradigmatic problem in social choice theory deals with the aggregation of subjective preferences of individuals --- represented as rankings of alternatives --- into a social ranking. We are interested in settings where individuals are uncertain about their own preferences, and represent their uncertainty as distributions over rankings. Under the classic objective of minimizing the (expected) sum of Kendall tau distances between the input rankings and the output ranking, we establish that preference elicitation is surprisingly straightforward and near-optimal solutions can be obtained in polynomial time. We show, both in theory and using real data, that ignoring uncertainty altogether can lead to suboptimal outcomes.