We consider the problem of analyzing market-basket data and present several important contributions. First, we present a new algorithm for finding large itemsets which uses fewer passes over the data than classic algorithms, and yet uses fewer candidate itemsets than methods based on sampling. We investigate the idea of item reordering, which can improve the low-level efficiency of the algorithm. Second, we present a new way of generating "implication rules," which are normalized based on both the antecedent and the consequent and are truly implications (not simply a measure of co-occurrence), and we show how they produce more intuitive results than other methods. Finally, we show how different characteristics of real data, as opposed to synthetic data, can dramatically affect the performance of the system and the form of the results. 1 Introduction Within the area of data mining, the problem of deriving associations from data has recently received a great deal of attention. The prob...

Clustering, in data mining, is useful to discover distribution patterns in the underlying data. Clustering algorithms usually employ a distance metric based (e.g., euclidean) similarity measure in order to partition the database such that data points in the same partition are more similar than points in different partitions. In this paper, we study clustering algorithms for data with boolean and categorical attributes. We show that traditional clustering algorithms that use distances between points for clustering are not appropriate for boolean and categorical attributes. Instead, we propose a novel concept of links to measure the similarity/proximity between a pair of data points. We develop a robust hierarchical clustering algorithm ROCK that employs links and not distances when merging clusters.

Similarity search in large time series databases has attracted much research interest recently. It is a difficult problem because of the typically high dimensionality of the data.. The most promising solutions' involve performing dimensionality reduction on the data, then indexing the reduced data with a multidimensional index structure. Many dimensionality reduction techniques have been proposed, including Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Adaptive Piecewise Constant Approximation (APCA). While previous techniques (e.g., SVD, DFT and DWT) choose a common representation for all the items in the database that minimizes the global reconstruction error, APCA approximates each time series by a set of constant value segments' of varying lengths' such that their individual reconstruction errors' are minimal. We show how APCA can be indexed using a multidimensional index structure. We propose two distance measures in the indexed space that exploit the high fidelity of APCA for fast searching: a lower bounding Euclidean distance approximation, and a non-lower bounding, but very tight Euclidean distance approximation and show how they can support fast exact searchin& and even faster approximate searching on the same index structure. We theoretically and empirically compare APCA to all the other techniques and demonstrate its' superiority.

... 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

Fast similarity searching in large time-sequence databases has attracted a lot of research interest [1, 5, 2, 6, 3, 10]. All of them use the Euclidean distance (L 2 ), or some variation of L p metrics. L p metrics lead to efficient indexing, thanks to feature extraction (e.g., by keeping the first few DFT coefficients) and subsequent use of fast spatial access methods for the points in feature space. In this work we examine a popular, field-tested dissimilarity function, the "time warping" distance function which permits local accelerations and decelerations in the rate of the signals or sequences. This function is natural and suitable for several applications, like matching of voice, audio and medical signals (e.g., electrocardiograms) However, from the indexing viewpoint it presents two major challenges: (a) it does not lead to any natural "features", precluding the use of spatial access methods (b) it is quadratic (O(len 1 len 2 )) on the length of the sequences involved. Here we ...

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

The problem of similarity search in large time series databases has attracted much attention recently. It is a non-trivial problem because of the inherent high dimensionality of the data. The most promising solutions involve first performing dimensionality reduction on the data, and then indexing the reduced data with a spatial access method. Three major dimensionality reduction techniques have been proposed, Singular Value Decomposition (SVD), the Discrete Fourier transform (DFT), and more recently the Discrete Wavelet Transform (DWT). In this work we introduce a new dimensionality reduction technique which we call Piecewise Aggregate Approximation (PAA). We theoretically and empirically compare it to the other techniques and demonstrate its superiority. In addition to being competitive with or faster than the other methods, our approach has numerous other advantages. It is simple to understand and to implement, it allows more flexible distance measures, including weighted Euclidean queries, and the index can be built in linear time.

We introduce an extended representation of time series that allows fast, accurate classification and clustering in addition to the ability to explore time series data in a relevance feedback framework. The representation consists of piecewise linear segments to represent shape and a weight vector that contains the relative importance of each individual linear segment. In the classification context, the weights are learned automatically as part of the training cycle. In the relevance feedback context, the weights are determined by an interactive and iterative process in which users rate various choices presented to them. Our representation allows a user to define a variety of similarity measures that can be tailored to specific domains. We demonstrate our approach on space telemetry, medical and synthetic data.

Real-time production systems and other dynamic environments often generate tremendous (potentially infinite) amount of stream data; the volume of data is too huge to be stored on disks or scanned multiple times. Can we perform on-line, multi-dimensional analysis and data mining of such data to alert people about dramatic changes of situations and to initiate timely, high-quality responses? This is a challenging task. In this paper,

Several important time series data mining problems reduce to the core task of finding approximately repeated subsequences in a longer time series. In an earlier work, we formalized the idea of approximately repeated subsequences by introducing the notion of time series motifs. Two limitations of this work were the poor scalability of the motif discovery algorithm, and the inability to discover motifs in the presence of noise. Here we address these limitations by introducing a novel algorithm inspired by recent advances in the problem of pattern discovery in biosequences. Our algorithm is probabilistic in nature, but as we show empirically and theoretically, it can find time series motifs with very high probability even in the presence of noise or “don’t care ” symbols. Not only is the algorithm fast, but it is an anytime algorithm, producing likely candidate motifs almost immediately, and gradually improving the quality of results over time.