We propose an approximation algorithm for efficient correlation search in time series data. In our method, we use Fourier transform and neural network to embed time series into a low-dimensional Euclidean space. The given space is learned such that time series correlation can be effectively approximated from Euclidean distance between corresponding embedded vectors. Therefore, search for correlated time series can be done using an index in the embedding space for efficient nearest neighbor search. Our theoretical analysis illustrates that our method's accuracy can be guaranteed under certain regularity conditions. We further conduct experiments on real-world datasets and the results show that our method indeed outperforms the baseline solution. In particular, for approximation of correlation, our method reduces the approximation loss by a half in most test cases compared to the baseline solution. For top- @math highest correlation search, our method improves the precision from 5 to 20 while the query time is similar to the baseline approach query time.
Consider the problem of monitoring tens of thousands of time series data streams in an online fashion and making decisions based on them. In addition to single stream statistics such as average and standard deviation, we also want to find high correlations among all pairs of streams. A stock market trader might use such a tool to spot arbitrage opportunities. This paper proposes efficient methods for solving this problem based on Discrete Fourier Transforms and a three level time interval hierarchy. Extensive experiments on synthetic data and real world financial trading data show that our algorithm beats the direct computation approach by several orders of magnitude. It also improves on previous Fourier Transform approaches by allowing the efficient computation of time-delayed correlation over any size sliding window and any time delay. Correlation also lends itself to an efficient grid-based data structure. The result is the first algorithm that we know of to compute correlations over thousands of data streams in real time. The algorithm is incremental, has fixed response time, and can monitor the pairwise correlations of 10,000 streams on a single PC. The algorithm is embarrassingly parallelizable. We propose an indexing method for time sequences for processing similarity queries. We use the Discrete Fourier Transform (DFT) to map time sequences to the frequency domain, the crucial observation being that, for most sequences of practical interest, only the first few frequencies are strong. Another important observation is Parseval's theorem, which specifies that the Fourier transform preserves the Euclidean distance in the time or frequency domain. Having thus mapped sequences to a lower-dimensionality space by using only the first few Fourier coefficients, we use R * -trees to index the sequences and efficiently answer similarity queries. We provide experimental results which show that our method is superior to search based on sequential scanning. Our experiments show that a few coefficients (1–3) are adequate to provide good performance. The performance gain of our method increases with the number and length of sequences.   Most time series data mining algorithms use similarity search as a core subroutine, and thus the time taken for similarity search is the bottleneck for virtually all time series data mining algorithms. The difficulty of scaling search to large datasets largely explains why most academic work on time series data mining has plateaued at considering a few millions of time series objects, while much of industry and science sits on billions of time series objects waiting to be explored. In this work we show that by using a combination of four novel ideas we can search and mine truly massive time series for the first time. We demonstrate the following extremely unintuitive fact; in large datasets we can exactly search under DTW much more quickly than the current state-of-the-art Euclidean distance search algorithms. We demonstrate our work on the largest set of time series experiments ever attempted. In particular, the largest dataset we consider is larger than the combined size of all of the time series datasets considered in all data mining papers ever published. We show that our ideas allow us to solve higher-level time series data mining problem such as motif discovery and clustering at scales that would otherwise be untenable. In addition to mining massive datasets, we will show that our ideas also have implications for real-time monitoring of data streams, allowing us to handle much faster arrival rates and or use cheaper and lower powered devices than are currently possible. We present an efficient indexing method to locate 1-dimensional subsequences within a collection of sequences, such that the subsequences match a given (query) pattern within a specified tolerance. The idea is to map each data sequences into a small set of multidimensional rectangles in feature space. Then, these rectangles can be readily indexed using traditional spatial access methods, like the R*-tree [9]. In more detail, we use a sliding window over the data sequence and extract its features; the result is a trail in feature space. We propose an efficient and effective algorithm to divide such trails into sub-trails, which are subsequently represented by their Minimum Bounding Rectangles (MBRs). We also examine queries of varying lengths, and we show how to handle each case efficiently. We implemented our method and carried out experiments on synthetic and real data (stock price movements). We compared the method to sequential scanning, which is the only obvious competitor. The results were excellent: our method accelerated the search time from 3 times up to 100 times. Most existing work on sequence databases use correlation (e.g., Euclidean distance and Pearson correlation) as a core function for various analytical tasks. Typically, it requires users to set a length for the similarity queries. However, there is no steady way to define the proper length on different application needs. In this work we focus on discovering longest-lasting highly correlated subsequences in sequence databases, which is particularly useful in helping those analyses without prior knowledge about the query length. Surprisingly, there has been limited work on this problem. A baseline solution is to calculate the correlations for every possible subsequence combination. Obviously, the brute force solution is not scalable for large datasets. In this work we study a space-constrained index that gives a tight correlation bound for subsequences of similar length and offset by intra-object grouping and inter-object grouping techniques. To the best of our knowledge, this is the first index to support normalized distance metric of arbitrary length subsequences. Extensive experimental evaluation on both real and synthetic sequence datasets verifies the efficiency and effectiveness of our proposed methods.