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- All Subjects: Block based tensor decomposition
- Genre: Academic theses
- Creators: Sapino, Maria Luisa
Description
The amount of time series data generated is increasing due to the integration of sensor technologies with everyday applications, such as gesture recognition, energy optimization, health care, video surveillance. The use of multiple sensors simultaneously
for capturing different aspects of the real world attributes has also led to an increase in dimensionality from uni-variate to multi-variate time series. This has facilitated richer data representation but also has necessitated algorithms determining similarity between two multi-variate time series for search and analysis.
Various algorithms have been extended from uni-variate to multi-variate case, such as multi-variate versions of Euclidean distance, edit distance, dynamic time warping. However, it has not been studied how these algorithms account for asynchronous in time series. Human gestures, for example, exhibit asynchrony in their patterns as different subjects perform the same gesture with varying movements in their patterns at different speeds. In this thesis, we propose several algorithms (some of which also leverage metadata describing the relationships among the variates). In particular, we present several techniques that leverage the contextual relationships among the variates when measuring multi-variate time series similarities. Based on the way correlation is leveraged, various weighing mechanisms have been proposed that determine the importance of a dimension for discriminating between the time series as giving the same weight to each dimension can led to misclassification. We next study the robustness of the considered techniques against different temporal asynchronies, including shifts and stretching.
Exhaustive experiments were carried on datasets with multiple types and amounts of temporal asynchronies. It has been observed that accuracy of algorithms that rely on data to discover variate relationships can be low under the presence of temporal asynchrony, whereas in case of algorithms that rely on external metadata, robustness against asynchronous distortions tends to be stronger. Specifically, algorithms using external metadata have better classification accuracy and cluster separation than existing state-of-the-art work, such as EROS, PCA, and naive dynamic time warping.
for capturing different aspects of the real world attributes has also led to an increase in dimensionality from uni-variate to multi-variate time series. This has facilitated richer data representation but also has necessitated algorithms determining similarity between two multi-variate time series for search and analysis.
Various algorithms have been extended from uni-variate to multi-variate case, such as multi-variate versions of Euclidean distance, edit distance, dynamic time warping. However, it has not been studied how these algorithms account for asynchronous in time series. Human gestures, for example, exhibit asynchrony in their patterns as different subjects perform the same gesture with varying movements in their patterns at different speeds. In this thesis, we propose several algorithms (some of which also leverage metadata describing the relationships among the variates). In particular, we present several techniques that leverage the contextual relationships among the variates when measuring multi-variate time series similarities. Based on the way correlation is leveraged, various weighing mechanisms have been proposed that determine the importance of a dimension for discriminating between the time series as giving the same weight to each dimension can led to misclassification. We next study the robustness of the considered techniques against different temporal asynchronies, including shifts and stretching.
Exhaustive experiments were carried on datasets with multiple types and amounts of temporal asynchronies. It has been observed that accuracy of algorithms that rely on data to discover variate relationships can be low under the presence of temporal asynchrony, whereas in case of algorithms that rely on external metadata, robustness against asynchronous distortions tends to be stronger. Specifically, algorithms using external metadata have better classification accuracy and cluster separation than existing state-of-the-art work, such as EROS, PCA, and naive dynamic time warping.
ContributorsGarg, Yash (Author) / Candan, Kasim Selcuk (Thesis advisor) / Chowell-Punete, Gerardo (Committee member) / Tong, Hanghang (Committee member) / Davulcu, Hasan (Committee member) / Sapino, Maria Luisa (Committee member) / Arizona State University (Publisher)
Created2015
Description
Tensors are commonly used for representing multi-dimensional data, such as Web graphs, sensor streams, and social networks. As a consequence of the increase in the use of tensors, tensor decomposition operations began to form the basis for many data analysis and knowledge discovery tasks, from clustering, trend detection, anomaly detection to correlationanalysis [31, 38]. It is well known that Singular Value matrix Decomposition (SVD) [9] is used to extract latent semantics for matrix data. When apply SVD to tensors, which have more than two modes, it is tensor decomposition. The two most popular tensor decomposition algorithms are the Tucker [54] and the CP [19] decompositions. Intuitively, they both generalize SVD to tensors. However, one key problem with tensor decomposition is its computational complexity which may cause system bottleneck. Therefore, two phase block-centric CP tensor decomposition (2PCP) was proposed to partition the tensor into small sub-tensors, execute sub-tensor decomposition in parallel and combine the factors from each sub-tensor into final decomposition factors through iterative rerefinement process. Consequently, I proposed Sub-tensor Impact Graph (SIG) to account for inaccuracy propagation among sub-tensors and measure the impact of decomposition of sub-tensors on the other's decomposition, Based on SIG, I proposed several optimization strategies to optimize 2PCP's phase-2 refinement process. Furthermore, I applied SIG and optimization strategies for data focus, data evolution, and focus shifting in tensor analysis. Personalized Tensor Decomposition (PTD) is proposed to account for the users focus given the observations that in many applications, the user may have a focus of interest i.e., part of the data for which the user needs high accuracy and beyond this area focus, accuracy may not be as critical. PTD takes as input one or more areas of focus and performs the decomposition in such a way that, when reconstructed, the accuracy of the tensor is boosted for these areas of focus. A related challenge of data evolution in tensor analytics is incremental tensor decomposition since re-computation of the whole tensor decomposition with each update will cause high computational costs and incur large memory overheads. Especially for applications where data evolves over time and the tensor-based analysis results need to be continuouslymaintained. To avoid re-decomposition, I propose a two-phase block-incremental CP-based tensor decomposition technique, BICP, that efficiently and effectively maintains tensor decomposition results in the presence of dynamically evolving tensor data. I further extend the research focus on user focus shift. User focus may change over time as data is evolving along the time. Although PTD is efficient, re-computation for each user preference update can be the bottleneck for the system. Therefore I propose dynamic evolving user focus tensor decomposition which can smartly reuse the existing decomposition result to improve the efficiency of evolving user focus block decomposition.
ContributorsHuang, shengyu (Author) / Candan, K. Selcuk (Thesis advisor) / Davulcu, Hasan (Committee member) / Sapino, Maria Luisa (Committee member) / Tong, Hanghang (Committee member) / Zou, Jia (Committee member) / Arizona State University (Publisher)
Created2021