Tau Distance Research Articles

Comparative Analysis of DTW based Outlier Segregation Algorithms for Wrist Pulse Analysis

Background/Objectives: Quantification of Wrist Pulse Signals is helpful to take benefit of ancient approach i.e. Pulse Diagnosis. The objective of this paper is to effectively segregate outliers present within wrist pulses. Methods/Statistical Analysis: This work presents modification in Dynamic Time Warping (DTW) algorithm. The existing DTW algorithm searches for an optimal path using squared Euclidean distance to measure the local distance between segments. Here, we are discussing and integrating different local distance measures such as Correlation Distance, Manhattan Distance, Kendall’s τ Distance and Canberra Distance with DTW. All the discussed local distance measures were compared with existing Euclidean based DTW algorithm on the basis of Similarity Index parameter. Findings: Results shown that Manhattan Distance and Canberra Distance based DTW algorithm was efficient in optimal path selection and segregation of segments which lose their shape characteristics. In euclidean based DTW, outlier segregation was difficult as all values lied between 0 to 1.Correlation distance and Kendall’s tau distance algorithm were inappropriate in detecting outliers as results were not matched with visual observations. It was noticed that combination of Manhattan Distance and Canberra Distance based DTW algorithm were giving better outlier finding.

Guidance for representing uncertainty on global temperature change maps

ABSTRACTUncertainty in the spatial distribution of projected climate changes can be represented along with the magnitudes of those changes using coincident‐bivariate maps. While these maps are popular in climate change assessment reports, limited empirical research has tested which combinations of colour (including variation in the visual variables of hue, lightness, and saturation) and pattern (including variation in the visual variables of size, shape, spacing, orientation, and arrangement) are best suited to mapping projected changes coincident with uncertainty. We evaluate eight coincident‐bivariate techniques for mapping global temperature (CMIP5 ensemble using RCP8.5 and RCP4.5 scenarios) and its uncertainty, each using 20‐classes: five temperature change classes combined with four uncertainty classes. Subjects ranked rectangular map regions by overall amounts of temperature change and uncertainty; response accuracy was evaluated using Kendall's Tau Distance. Maps using colour for representing temperature change and pattern for uncertainty appear most suitable for retaining separability of temperature and uncertainty information. Spot symbols for uncertainty (combining arrangement and lightness) overlaid on hue/lightness for temperature performed best for uncertainty ranking, second best for temperature ranking, and were map users' preferred representation. If colour alone must be used for both variables, then a classed overlay of lightness/saturation differences for uncertainty with hue/lightness for temperature change was preferred; such maps were strong performers on the uncertainty‐ranking task but interfered with map users' ability to rank temperature change. Such a masking approach may be the best choice if the goal is to actively prevent map users from making erroneous inferences based on highly uncertain model output for climate change.

Theoretical and empirical evaluation of data reduction for exact Kemeny Rank Aggregation

Kemeny Rank Aggregation is a consensus finding problem important in many areas ranging from classical voting over web search and databases to bioinformatics. The underlying decision problem Kemeny Score is NP-complete even in case of four input rankings to be aggregated into a "median ranking". We analyze efficient polynomial-time data reduction rules with provable performance bounds that allow us to find even all optimal median rankings. We show that our reduced instances contain at most [InlineEquation not available: see fulltext.] candidates where $$d_a$$ d a denotes the average Kendall's tau distance between the input votes. On the theoretical side, this improves a corresponding result for a "partial problem kernel" from quadratic to linear size. In this context we provide a theoretical analysis of a commonly used data reduction. On the practical side, we provide experimental results with data based on web search and sport competitions, e.g., computing optimal median rankings for real-world instances with more than 100 candidates within milliseconds. Moreover, we perform experiments with randomly generated data based on two random distribution models for permutations.

COMPARING AND AGGREGATING PARTIAL ORDERS WITH KENDALL TAU DISTANCES

Comparing and ranking information is an important topic in social and information sciences, and in particular on the web. Its objective is to measure the difference of the preferences of voters on a set of candidates and to compute a consensus ranking. Commonly, each voter provides a total order or a bucket order of all candidates, where bucket orders allow ties.In this work we consider the generalization of total and bucket orders to partial orders and compare them by the nearest neighbor and the Hausdorff Kendall tau distances. For total and bucket orders these distances can be computed in [Formula: see text] time. We show that the computation of the nearest neighbor Kendall tau distance is NP-hard, 2-approximable and fixed-parameter tractable for a total and a partial order. The computation of the Hausdorff Kendall tau distance for a total and a partial order is shown to be coNP-hard.The rank aggregation problem is known to be NP-complete for total and bucket orders, even for four voters and solvable in [Formula: see text] time for two voters. We show that it is NP-complete for two partial orders and the nearest neighbor Kendall tau distance. For the Hausdorff Kendall tau distance it is in [Formula: see text], but not in NP or coNP unless NP = coNP, even for four voters.

Constructions of Rank Modulation Codes

Rank modulation is a way of encoding information to correct errors in flash memory devices as well as impulse noise in transmission lines. Modeling rank modulation involves construction of packings of the space of permutations equipped with the Kendall tau distance. As our main set of results, we present several general constructions of codes in permutations that cover a broad range of code parameters. In particular, we show a number of ways in which conventional error-correcting codes can be modified to correct errors in the Kendall space. Our constructions are nonasymptotic and afford simple encoding and decoding algorithms of essentially the same complexity as required to correct errors in the Hamming metric. As an example, from binary Bose-Chaudhuri-Hocquenghem codes, we obtain codes correcting t Kendall errors in n memory cells that support the order of n!/(log2n!)t messages, for any constant t=1,2,.... We give many examples of rank modulation codes with specific parameters. Turning to asymptotic analysis, we construct families of rank modulation codes that correct a number of errors that grows with n at varying rates, from Θ(n) to Θ(n2). One of our constructions gives rise to a family of rank modulation codes for which the tradeoff between the number of messages and the number of correctable Kendall errors approaches the optimal scaling rate.

Codes in Permutations and Error Correction for Rank Modulation

Codes for rank modulation have been recently proposed as a means of protecting flash memory devices from errors. We study basic coding theoretic problems for such codes, representing them as subsets of the set of permutations of $n$ elements equipped with the Kendall tau distance. We derive several lower and upper bounds on the size of codes. These bounds enable us to establish the exact scaling of the size of optimal codes for large values of $n$. We also show the existence of codes whose size is within a constant factor of the sphere packing bound for any fixed number of errors.

Fixed-parameter algorithms for Kemeny rankings

The computation of Kemeny rankings is central to many applications in the context of rank aggregation. Given a set of permutations (votes) over a set of candidates, one searches for a “consensus permutation” that is “closest” to the given set of permutations. Unfortunately, the problem is NP-hard. We provide a broad study of the parameterized complexity for computing optimal Kemeny rankings. Besides the three obvious parameters “number of votes”, “number of candidates”, and solution size (called Kemeny score), we consider further structural parameterizations. More specifically, we show that the Kemeny score (and a corresponding Kemeny ranking) of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large. In other words, Kemeny Score is fixed-parameter tractable with respect to the parameter “average pairwise Kendall–Tau distance d a ”. We describe a fixed-parameter algorithm with running time 1 6 ⌈ d a ⌉ ⋅ poly . Moreover, we extend our studies to the parameters “maximum range” and “average range” of positions a candidate takes in the input votes. Whereas Kemeny Score remains fixed-parameter tractable with respect to the parameter “maximum range”, it becomes NP-complete in the case of an average range of two. This excludes fixed-parameter tractability with respect to the parameter “average range” unless P=NP. Finally, we extend some of our results to votes with ties and incomplete votes, where in both cases one no longer has permutations as input.

Evaluating the effectiveness of FDM in identifying important factors in a dynamic flowshop

Dynamic events such as machine breakdown and hot jobs may induce problems on the production system such as order delay, increasing machine load, and changing inventory level. Past studies of dynamic events often use traditional design of experiments (DOE) to analyze the effects of dynamic events on system's performance. The shortcoming of this approach is that the number of experimental runs conducted would become exponentially increased as the number of factors increased. This study tries to use frequency domain methodology (FDM) instead so as to detect the higher order effects and rank important factors in a few experimental runs. Spectrum analysis is used to comprehend the effects of different location of machine breakdown and different size of hot jobs on the system's performance of flowshops with different traffic (utilization) and stability (oscillation). This study finds that the important factors identified by the FDM analysis are the same as that of DOE. However, only in some cases can the rankings of important factors be the same for both approaches. The dissimilarity between rankings of important factors found by these two methods is further measured using Kendall tau distance.

Frequency‐ and ordering‐based similarity measure for host‐based intrusion detection

This paper discusses a new similarity measure for the anomaly‐based intrusion detection scheme using sequences of system calls. With the increasing frequency of new attacks, it is getting difficult to update the signatures database for misuse‐based intrusion detection system (IDS). While anomaly‐based IDS has a very important role to play, the high rate of false positives remains a cause for concern. Defines a similarity measure that considers the number of similar system calls, frequencies of system calls and ordering‐of‐system calls made by the processes to calculate the similarity between the processes. Proposes the use of Kendall Tau distance to calculate the similarity in terms of ordering of system calls in the process. The k nearest neighbor (kNN) classifier is used to categorize a process as either normal or abnormal. The experimental results, performed on 1998 DARPA data, are very promising and show that the proposed scheme results in a high detection rate and low rate of false positives.