... mining time series data. Literally hundreds of papers have introduced new algorithms to index, classify, cluster and segment time series. In this work we make the following claim. Much of this work has very little utility because the contribution made (speed in the case of indexing, accuracy in the case of classification and clustering, model accuracy in the case of segmentation) offer an amount of "improvement" that would have been completely dwarfed by the variance that would have been observed by testing on many real world datasets, or the variance that would have been observed by changing minor (unstated) implementation details. To illustrate our point

The anomaly detection problem can be formulated as one of learning to characterize the behaviors of an individual, system, or network in terms of temporal sequences of discrete data. We present an approach to this problem based on instance based learning (IBL) techniques. To cast the anomaly detection task in an IBL framework, we employ an approach that transforms temporal sequences of discrete, unordered observations into a metric space via a similarity measure that encodes intra-attribute dependencies. Classification boundaries are selected from an a posteriori characterization of the valid user's behaviors, coupled with a domain heuristic. An empirical evaluation of the approach on user command data demonstrates that we can accurately differentiate the profiled user from alternative users when the available features encode sufficient information. Furthermore, we demonstrate that the system detects anomalous conditions quickly -- an important quality for reducing potential damage by a malicious user. We present several techniques for reducing the data storage requirements of the user profile, including instance selection methods and clustering. An empirical evaluation shows that a new greedy clustering algorithm reduces the size of the user model by 70 % with only a small loss in accuracy. A comparison of the greedy clustering technique to clustering with K-centers shows that greedy clustering is preferable in terms of accuracy and computation time for this domain.

We investigate techniques for analysis and retrieval of object trajectories in a two or three dimensional space. Such kind of data usually contain a great amount of noise, that makes all previously used metrics fail. Therefore, here we formalize non-metric similarity functions based on the Longest Common Subsequence (LCSS), which are very robust to noise and furthermore provide an intuitive notion of similarity between trajectories by giving more weight to the similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translating of the sequences in space. Efficient approximate algorithms that compute these similarity measures are also provided. We compare these new methods to the widely used Euclidean and Time Warping distance functions (for real and synthetic data) and show the superiority of our approach, especially under the strong presence of noise. We prove a weaker version of the triangle inequality and employ it in an indexing structure to answer nearest neighbor queries. Finally, we present experimental results that validate the accuracy and efficiency of our approach. 1

We consider the problem of finding rules relating patterns in a time series to other patterns in that series, or patterns in one series to patterns in another series. A simple example is a rule such as "a period of low telephone call activity is usually followed by a sharp rise in call volume". Examples of rules relating two or more time series are "if the Microsoft stock price goes up and Intel falls, then IBM goes up the next day," and "if Microsoft goes up strongly for one day, then declines strongly on the next day, and on the same days Intel stays about level, then IBM stays about level." Our emphasis is in the discovery of local patterns in multivariate time series, in contrast to traditional time series analysis which largely focuses on global models. Thus, we search for rules whose conditions refer to patterns in time series. However, we do not want to define beforehand which patterns are to be used; rather, we want the patterns to be formed from the data in t...

In this paper we present the Landmark Model, a model for time series that yields new techniques for similarity-based time series pattern querying. The Landmark Model does not follow traditional similarity models that rely on pointwise Euclidean distance. Instead, it leads to Landmark Similarity, a general model of similarity that is consistent with human intuition and episodic memory. By tracking different specific subsets of features of landmarks, we can efficiently compute different Landmark Similarity measures that are invariant under corresponding subsets of six transformations; namely, Shifting, Uniform

Existing studies on time series are based on two categories of distance functions. The first category consists of the Lp-norms. They are metric distance functions but cannot support local time shifting. The second category consists of distance functions which are capable of handling local time shifting but are nonmetric. The first

Data-driven animation has become the industry standard for computer games and many animated movies and special effects. In particular, motion capture data recorded from live actors, is the most promising approach offered thus far for animating realistic human characters. However, the manipulation of such data for general use and re-use is not yet a solved problem. Many of the existing techniques dealing with editing motion rely on indexing for annotation, segmentation, and re-ordering of the data. Euclidean distance is inappropriate for solving these indexing problems because of the inherent variability found in human motion. The limitations of Euclidean distance stems from the fact that it is very sensitive to distortions in the time axis. A partial solution to this problem, Dynamic Time Warping (DTW), aligns the time axis

In recent years, there has been a lot of interest in the database community in mining time series data. Surprisingly, little work has been done on verifying which measures are most suitable for mining of a given class of data sets. Such work is of crucial importance, since it enables us to identify similarity measures which are useful in a given context and therefore for which efficient algorithms should be further investigated. Moreover, an accurate evaluation of the performance of even existing algorithms is not possible without a good understanding of the data sets occurring in practice. In this work we attempt to fill this gap by studying similarity measures for clustering of similar stocks (which, of course, is an interesting problem on its own). Our approach is to cluster the stocks according to various measures (including several novel ones) and compare the results to the ”groundtruth” clustering based on the Standard and Poor 500 Index. Our experiments reveal several interesting facts about the similarity measures used for stock-market data.

This paper discusses an effective processing of similarity search that supports time warping in large sequence databases. Time warping enables finding sequences with similar patterns even when they are of different lengths. Previous methods for processing similarity search that supports time warping fail to employ multi-dimensional indexes without false dismissal since the time warping distance does not satisfy the triangular inequality. They have to scan all the database, thus suffer from serious performance degradation in large databases. Another method that hires the suffix tree, which does not assume any distance function, also shows poor performance due to the large tree size. In this paper, we propose a new novel method for similarity search that supports time warping. Our primary goal is to innovate on search performance in large databases without permitting any false dismissal. To attain this goal, we devise a new distance function D tw\Gammalb that consistently unde...

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