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- All Subjects: time series
- All Subjects: Human behavior--Mathematical models.
- Creators: Chowell-Punete, Gerardo
Description
With improvements in technology, intensive longitudinal studies that permit the investigation of daily and weekly cycles in behavior have increased exponentially over the past few decades. Traditionally, when data have been collected on two variables over time, multivariate time series approaches that remove trends, cycles, and serial dependency have been used. These analyses permit the study of the relationship between random shocks (perturbations) in the presumed causal series and changes in the outcome series, but do not permit the study of the relationships between cycles. Liu and West (2016) proposed a multilevel approach that permitted the study of potential between subject relationships between features of the cycles in two series (e.g., amplitude). However, I show that the application of the Liu and West approach is restricted to a small set of features and types of relationships between the series. Several authors (e.g., Boker & Graham, 1998) proposed a connected mass-spring model that appears to permit modeling of more general cyclic relationships. I showed that the undamped connected mass-spring model is also limited and may be unidentified. To test the severity of the restrictions of the motion trajectories producible by the undamped connected mass-spring model I mathematically derived their connection to the force equations of the undamped connected mass-spring system. The mathematical solution describes the domain of the trajectory pairs that are producible by the undamped connected mass-spring model. The set of producible trajectory pairs is highly restricted, and this restriction sets major limitations on the application of the connected mass-spring model to psychological data. I used a simulation to demonstrate that even if a pair of psychological time-varying variables behaved exactly like two masses in an undamped connected mass-spring system, the connected mass-spring model would not yield adequate parameter estimates. My simulation probed the performance of the connected mass-spring model as a function of several aspects of data quality including number of subjects, series length, sampling rate relative to the cycle, and measurement error in the data. The findings can be extended to damped and nonlinear connected mass-spring systems.
ContributorsMartynova, Elena (M.A.) (Author) / West, Stephen G. (Thesis advisor) / Amazeen, Polemnia (Committee member) / Tein, Jenn-Yun (Committee member) / Arizona State University (Publisher)
Created2019
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