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The Dynamic Time Warping (DTW) is a popular similarity measure between time series. The DTW fails to satisfy the triangle inequality and its computation requires quadratic time. Hence, to find closest neighbors quickly, we use bounding…
Time Series Alignment is a critical task in signal processing with numerous real-world applications. In practice, signals often exhibit temporal shifts and scaling, making classification on raw data prone to errors. This paper introduces a…
We propose regularizing the empirical loss for semi-supervised learning by acting on both the input (data) space, and the weight (parameter) space. We show that the two are not equivalent, and in fact are complementary, one affecting the…
The proliferation and ubiquity of temporal data across many disciplines has sparked interest for similarity, classification and clustering methods specifically designed to handle time series data. A core issue when dealing with time series…
We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…
Consider the problem of minimizing the expected value of a cost function parameterized by a random variable. The classical sample average approximation (SAA) method for solving this problem requires minimization of an ensemble average of…
Stochastic Gradient Descent (SGD) is one of the simplest and most popular stochastic optimization methods. While it has already been theoretically studied for decades, the classical analysis usually required non-trivial smoothness…
Multivariate time series naturally exist in many fields, like energy, bioinformatics, signal processing, and finance. Most of these applications need to be able to compare these structured data. In this context, dynamic time warping (DTW)…
Data augmentation have been intensively used in training deep neural network to improve the generalization, whether in original space (e.g., image space) or representation space. Although being successful, the connection between the…
Anomaly Detection in multivariate time series is a major problem in many fields. Due to their nature, anomalies sparsely occur in real data, thus making the task of anomaly detection a challenging problem for classification algorithms to…
This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…
Dynamic Time Warping (DTW) is an algorithm to align temporal sequences with possible local non-linear distortions, and has been widely applied to audio, video and graphics data alignments. DTW is essentially a point-to-point matching method…
Temporal alignment of sequences is a fundamental challenge in many applications, such as computer vision and bioinformatics, where local time shifting needs to be accounted for. Misalignment can lead to poor model generalization, especially…
Dynamic Time Warping (DTW) is widely used for temporal data processing. However, existing methods can neither learn the discriminative prototypes of different classes nor exploit such prototypes for further analysis. We propose…
The Dynamic Time Warping (DTW) distance is a popular measure of similarity for a variety of sequence data. For comparing polygonal curves $\pi, \sigma$ in $\mathbb{R}^d$, it provides a robust, outlier-insensitive alternative to the…
We study statistical inference on the similarity/distance between two time-series under uncertain environment by considering a statistical hypothesis test on the distance obtained from Dynamic Time Warping (DTW) algorithm. The sampling…
Similarity measures for time series are important problems for time series classification. To handle the nonlinear time distortions, Dynamic Time Warping (DTW) has been widely used. However, DTW is not learnable and suffers from a trade-off…
Purpose: To develop an algorithm for the retrospective correction of signal dropout artifacts in abdominal diffusion-weighted imaging (DWI) resulting from cardiac motion. Methods: Given a set of image repetitions for a slice, a locally…
Additive spatial statistical models with weakly stationary process assumptions have become standard in spatial statistics. However, one disadvantage of such models is the computation time, which rapidly increases with the number of data…
Over the last decade, time series motif discovery has emerged as a useful primitive for many downstream analytical tasks, including clustering, classification, rule discovery, segmentation, and summarization. In parallel, there has been an…