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.
There are also other similarity measures such as Longest Common Subsequence (LCSS) @cite_23 @cite_10 , but rather than concerning generalizability, they either focus on a specific type of data or problem related to the @math -norm and DTW. They therefore did not attract much attention in the past decade. Interested readers are again referred to the comparison work by @cite_4 for more details on similarity measures.
@cite_4 @cite_10 @cite_23
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While most time series data mining research has concentrated on providing solutions for a single distance function, in this work we motivate the need for an index structure that can support multiple distance measures. Our specific area of interest is the efficient retrieval and analysis of similar trajectories. Trajectory datasets are very common in environmental applications, mobility experiments, and video surveillance and are especially important for the discovery of certain biological patterns. Our primary similarity measure is based on the longest common subsequence (LCSS) model that offers enhanced robustness, particularly for noisy data, which are encountered very often in real-world applications. However, our index is able to accommodate other distance measures as well, including the ubiquitous Euclidean distance and the increasingly popular dynamic time warping (DTW). While other researchers have advocated one or other of these similarity measures, a major contribution of our work is the ability to support all these measures without the need to restructure the index. Our framework guarantees no false dismissals and can also be tailored to provide much faster response time at the expense of slightly reduced precision recall. The experimental results demonstrate that our index can help speed up the computation of expensive similarity measures such as the LCSS and the DTW. We investigate techniques for analysis and retrieval of object trajectories in two or three dimensional space. Such data usually contain a large amount of noise, that has made previously used metrics fail. Therefore, 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 similar portions of the sequences. Stretching of sequences in time is allowed, as well as global translation 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 in 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. Abstract When dealing with the registration of information from different image sources, the de facto similarity measure used is Mutual Information (MI). Although MI gives good performance in many image registration applications, recent works in thermal–visible registration have shown that other similarity measures can give results that are as accurate, if not more than MI. Furthermore, some of these measures also have the advantage of being calculated independently from each image to register, which allows them to be integrated more easily in energy minimization frameworks. In this article, we investigate the accuracy of similarity measures for thermal–visible image registration of human silhouettes, including MI, Sum of Squared Differences (SSD), Normalized Cross-Correlation (NCC), Histograms of Oriented Gradients (HOG), Local Self-Similarity (LSS), Scale-Invariant Feature Transform (SIFT), Speeded-Up Robust Features (SURF), Census, Fast Retina Keypoint (FREAK), and Binary Robust Independent Elementary Feature (BRIEF). We tested the various similarity measures in dense stereo matching tasks over 25,000 windows to have statistically significant results. To do so, we created a new dataset in which one to five humans are walking in a scene in various depth planes. Results show that even if MI is a very strong performer, particularly for large regions of interest (ROI), LSS gives better accuracies when ROI are small or segmented into small fragments because of its ability to capture shape. The other tested similarity measures did not give consistently accurate results. In Semantic Textual Similarity (STS), systems rate the degree of semantic equivalence, on a graded scale from 0 to 5, with 5 being the most similar. This year we set up two tasks: (i) a core task (CORE), and (ii) a typed-similarity task (TYPED). CORE is similar in set up to SemEval STS 2012 task with pairs of sentences from sources related to those of 2012, yet different in genre from the 2012 set, namely, this year we included newswire headlines, machine translation evaluation datasets and multiple lexical resource glossed sets. TYPED, on the other hand, is novel and tries to characterize why two items are deemed similar, using cultural heritage items which are described with metadata such as title, author or description. Several types of similarity have been defined, including similar author, similar time period or similar location. The annotation for both tasks leverages crowdsourcing, with relative high interannotator correlation, ranging from 62 to 87 . The CORE task attracted 34 participants with 89 runs, and the TYPED task attracted 6 teams with 14 runs.