A generic framework for efficient and effective subsequence retrieval

There has been a lot of interest in matching and retrieval of similar time sequences in time series databases. Most of previous work is concentrated on similarity matching and retrieval of time sequences based on the Euclidean distance. However, the Euclidean distance is sensitive to the absolute offsets of time sequences. In addition, the Euclidean distance is not a suitable similarity measurement in terms of shape. In this paper, we propose an indexing scheme for efficient matching and retrieval of time sequences based on the minimum distance. The minimum distance can give a better estimation of similarity in shape between two time sequences. Our indexing scheme can match time sequences of similar shapes irrespective of their vertical positions and guarantees no false dismissals. We experimentally evaluated our approach on real data(stock price movement).

At their core, many time series data mining algorithms reduce to reasoning about the shapes of time series subsequences. This requires an effective distance measure, and for last two decades most algorithms use Euclidean distance or DTW as their core subroutine. We argue that these distance measures are not as robust as the community seems to believe. The undue faith in these measures perhaps derives from an overreliance on the benchmark datasets and self-selection bias. The community is simply reluctant to address more difficult domains, for which current distance measures are ill-suited. In this work, we introduce a novel distance measure MPdist. We show that our proposed distance measure is much more robust than current distance measures. For example, it can handle data with missing values or spurious regions. Furthermore, it allows us to successfully mine datasets that would defeat any Euclidean or DTW distance-based algorithm. Additionally, we show that our distance measure can be computed so efficiently as to allow analytics on very fast arriving streams.

At their core, many time series data mining algorithms can be reduced to reasoning about the shapes of time series subsequences. This requires a distance measure, and most algorithms use Euclidean Distance or Dynamic Time Warping (DTW) as their core subroutine. We argue that these distance measures are not as robust as the community believes. The undue faith in these measures derives from an overreliance on benchmark datasets and self-selection bias. The community is reluctant to address more difficult domains, for which current distance measures are ill-suited. In this work, we introduce a novel distance measure MPdist. We show that our proposed distance measure is much more robust than current distance measures. Furthermore, it allows us to successfully mine datasets that would defeat any Euclidean or DTW distance-based algorithm. Additionally, we show that our distance measure can be computed so efficiently, it allows analytics on fast streams.

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

In this paper, a new version of distance measure for hesitant fuzzy linguistic term sets is developed. The new version of distance measure provides an objective way to handle the diverse dimensions of two HFLTSs, i.e., without shortening the HFLTS to be a linguistic interval or extending the shorter one by adding linguistic terms. The Hamming distance, the Euclidean distance and the corresponding forms are put forward. By the relationship between the distance measure and the similarity measure, some parallel similarity measures are also investigated. As applications of the proposed measures, the issues of pattern recognition, clustering analysis and multi-criteria decision making are considered.

Similarity search is the core procedure for several time series mining tasks. While different distance measures can be used for this purpose, there is clear evidence that the Dynamic Time Warping (DTW) is the most suitable distance function for a wide range of application domains. Despite its quadratic complexity, research efforts have proposed a significant number of pruning methods to speed up the similarity search under DTW. However, the search may still take a considerable amount of time depending on the parameters of the search, such as the length of the query and the warping window width. The main reason is that the current techniques for speeding up the similarity search focus on avoiding the costly distance calculation between as many pairs of time series as possible. Nevertheless, the few pairs of subsequences that were not discarded by the pruning techniques can represent a significant part of the entire search time. In this work, we adapt a recently proposed algorithm to improve the internal efficiency of the DTW calculation. Our method can speed up the UCR suite, considered the current fastest tool for similarity search under DTW. More important, the longer the time needed for the search, the higher the speedup ratio achieved by our method. We demonstrate that our method performs similarly to UCR suite for small queries and narrow warping constraints. However, it performs up to five times faster for long queries and large warping windows.

We consider the similarity problem in time series databases. Given a set of sequences, we are interested in finding those sequences whose behaviors are similar. Several methods have been proposed so far to solve this problem. Among them, [AFS93] mapped a time sequence to the frequency domain using the Discrete Fourier Transformation (DFT), and kept only first few coefficients. The similarity of two sequences is determined by the Euclidean distance between their coefficients. [ALS+95] (hereafter referred to as ALS approach) introduced a new model. Two time-series are said to be similar if they have enough non-overlapping time-ordered pairs of subsequences that are similar. Different from the ALS approach, [DGM97] used another method to find the longest common subsequence. The idea is, given a set of transformation functions, to try to find a linear function y=ax+b such that two subsequences X, Y are e-similar. However no paper up to now, as to our knowledge, had compared these algorithms on the same benchmark. This paper discusses and compares these three popular methods. By overcoming the drawbacks of these algorithms, a new algorithm is proposed. Experiments are conducted on the Nasdaq-100 market.

Sports events, as large-scale events that provide products and services, have received widespread attention for their economic benefits and influence. Event organizers expect to achieve high efficiency by providing high-quality products and services. The quality of competition products and services is mainly evaluated through the subjective feelings of the audience, and usually the audience’s evaluation of service quality is vague. Therefore, this article intends to establish an evaluation index system for the quality of spectator service in sports events, in order to provide a reasonable evaluation of the service products provided by sports event organizers. The audience service quality evaluation for large-scale sports-events is a MAGDM problems. Recently, the EDAS and CRITIC technique has been employed to cope with MAGDM issues. The interval neutrosophic sets (INSs) are employed as a tool for characterizing uncertain information during the audience service quality evaluation for large-scale sports-events. In this paper, the interval neutrosophic number EDAS (INN-EDAS) technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs. The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs. Finally, a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique. The main contributions of this paper are proposed: (1) The INN-EDAS technique based on the Hamming distance and Euclid distance is founded to manage the MAGDM under INSs; (2) The CRITIC technique is employed to obtain the weight information based on the Hamming distance and Euclid distance under INSs; (3) a numerical case study for audience service quality evaluation for large-scale sports-events is employed to validate the proposed technique.

Distance and similarity measures have recently been investigated in-depth within the context of hesitant fuzzy sets. By analyzing the existing studies concerning distance measures for hesitant fuzzy sets, we find that they have some limitations. To address the flaws, this study develops some novel distance measures for hesitant fuzzy sets, including the normalized Euclidean distance measure, the Hausdorff metric distance measure, the normalized generalized distance measure, and their corresponding weighted distance measures. The proposals of this study not only hold many ideal characteristics but also do not consider the lengths of hesitant fuzzy elements as well as the arrangement of their possible values. To deal with the situations where both of the universe of discourse and the weight of element are continuous, some continuous hesitant fuzzy distance measures are also investigated. Based on the relationship between distance measure and similarity measure, some novel similarity measures for hesitant fuzzy sets can be further deduced from the proposed distance measures. Finally, two numerical examples are given to demonstrate the applicability and validity of the proposed hesitant fuzzy distance measures.

Time series forecasting based on pattern matching has received a lot of interest in recent years due to its simplicity and the ability to predict complex nonlinear behaviours. The choice of the metric to measure the similarity between two time series depends mainly on the specific features of the considered data and it can influence on forecasting results. In this paper, unlike the conventional method, we propose an improved pattern matching-based prediction method using a linear combination of two measures, Euclidean distance and dynamic time warping, in order to achieve a better forecasting result. These two distance measures are chosen because they are the two most commonly used metrics for pattern matching in time series. The experimental results showed that our approach can produce better results on time series forecasting work in comparison to the pattern matching-based method under Euclidean distance or dynamic time warping in terms of prediction accuracy.

Effect of feature-type in selecting distance measure for an artificial immune system as a pattern recognizer

Nine oat cultivars and experimental lines from four diverse germ plasm sources were crossed in a diallel mating design, without reciprocals. Heterosis for grain yield was evaluated in two experiments and 48 F2-derived lines from each of the 36 matings were evaluated for bundle weight, grain yield, straw yield, harvest index, and heading date in two experiments. The number of transgressive segregates per trait and generalized genetic variances were calculated for each mating. Euclidean distance between parents was calculated by using the first five principal components of the parental correlation matrix. The distance measures of W. D. Hanson and E. Casas (1968. Biometrics, 24: 867–880) and T. S. Cervantes, M. M. Goodman, E. Casas, and J. O. Rawlings (1978. Genetics, 90: 339–348) were calculated for each of two experiments. The relationships between the three distance measures and the three types of breeding behavior were examined via correlation and regression. Euclidean distance was negatively correlated with transgressive segregation and generalized genetic variances. Hanson and Casas' distance measure was positively correlated with transgressive segregation and generalized genetic variances. The distance measure of Cervantes et al. was negatively correlated with heterosis in one experiment. Regressions on the three distances measures, when significant, were linear. The single exception was the regression of heterosis on Euclidean distance, which had significant linear and quadratic coefficients and high R2. No distance measure was closely associated with all three types of breeding behavior. Using information from more than one measure improved the R2 value for polynomial regressions. Key words: oats, genetic distance, heterosis, generalized variances.

BackgroundGene expression divergence is a phenotypic trait reflecting evolution of gene regulation and characterizing dissimilarity between species and between cells and tissues within the same species. Several distance measures, such as Euclidean and correlation-based distances have been proposed for measuring expression divergence.ResultsWe show that different distance measures identify different trends in gene expression patterns. When comparing orthologous genes in eight rat and human tissues, the Euclidean distance identified genes uniformly expressed in all tissues near the expression background as genes with the most conserved expression pattern. In contrast, correlation-based distance and generalized-average distance identified genes with concerted changes among homologous tissues as those most conserved. On the other hand, correlation-based distance, Euclidean distance and generalized-average distance highlight quite well the relatively high similarity of gene expression patterns in homologous tissues between species, compared to non-homologous tissues within species.ConclusionsDifferent trends exist in the high-dimensional numeric data, and to highlight a particular trend an appropriate distance measure needs to be chosen. The choice of the distance measure for measuring expression divergence can be dictated by the expression patterns that are of interest in a particular study.ReviewersThis article was reviewed by Mikhail Gelfand, Eugene Koonin and Subhajyoti De (nominated by Sarah Teichmann).

Hellwig’s method is a multi-criteria decision-making technique designed to facilitate the ranking of alternatives based on their proximity to the ideal solution. Typically, this approach calculates distances using the Euclidean norm, assuming implicitly that the considered criteria are independent. However, in real-world situations, the assumption of criteria independence is rarely met. The paper aims to propose an extension of Hellwig’s method by incorporating the Mahalanobis distance. Substituting the Euclidean distance with the Mahalanobis distance has proven to be effective in handling correlations among criteria, especially in the context of asymmetrical relationships between criteria. Subsequently, we investigate the impact of the Euclidean and Mahalanobis distance measures on the several variants of Hellwig procedures, analyzing examples based on various illustrative data with 10 alternatives and 4 criteria. Additionally, we examine the influence of three normalization formulas in Hellwig’s aggregation procedures. The investigation results indicate that both the distance measure and normalization formulas have some impact on the final rankings. The evaluation and ranking of alternatives using the Euclidean distance measure are influenced by the normalization formula, albeit to a limited extent. In contrast, the Mahalanobis distance-based Hellwig’s method remains unaffected by the choice of normalization formulas. The study concludes that the ranking of alternatives is strongly dependent on the distance measure employed, whether it is Euclidean or Mahalanobis. The Mahalanobis distance-based Hellwig method is deemed a valuable tool for decision-makers in real-life situations. It enables the evaluation of alternatives by considering interactions between criteria, providing a more comprehensive perspective for decision-making.

A common problem in many types of databases is retrieving the most similar matches to a query object. Finding those matches in a large database can be too slow to be practical, especially in domains where objects are compared using computationally expensive similarity (or distance) measures. This paper proposes a novel method for approximate nearest neighbor retrieval in such spaces. Our method is embedding-based, meaning that it constructs a function that maps objects into a real vector space. The mapping preserves a large amount of the proximity structure of the original space, and it can be used to rapidly obtain a short list of likely matches to the query. The main novelty of our method is that it constructs, together with the embedding, a distance measure that should be used when measuring distances in the vector space. The term query-sensitive means that the distance measure changes depending on the current query object. We report experiments with an image database of handwritten digits, and a time-series database. In both cases, the proposed method outperforms existing state-of-the-art embedding methods, meaning that it provides significantly better trade-offs between efficiency and retrieval accuracy.