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Dynamic mode decomposition (DMD) is a leading tool for equation-free analysis of high-dimensional dynamical systems from observations. In this work, we focus on a combination of delay-coordinates embedding and DMD, i.e., delay-coordinates…
This paper presents an efficient approach to image segmentation that approximates the piecewise-smooth (PS) functional in [12] with explicit solutions. By rendering some rational constraints on the initial conditions and the final solutions…
Semantic segmentation is a core task in computer vision with applications in biomedical imaging, remote sensing, and autonomous driving. While standard loss functions such as cross-entropy and Dice loss perform well in general cases, they…
In this paper, for the purpose of data centre energy consumption monitoring and analysis, we propose to detect the running programs in a server by classifying the observed power consumption series. Time series classification problem has…
Neural network-based solvers for partial differential equations (PDEs) have attracted considerable attention, yet they often face challenges in accuracy and computational efficiency. In this work, we focus on time-dependent PDEs and observe…
The classification of time series data is a well-studied problem with numerous practical applications, such as medical diagnosis and speech recognition. A popular and effective approach is to classify new time series in the same way as…
Dynamic magnetic resonance imaging (MRI) plays an indispensable role in cardiac diagnosis. To enable fast imaging, the k-space data can be undersampled but the image reconstruction poses a great challenge of high-dimensional processing.…
Systems are commonly monitored for health and security through collection and streaming of multivariate time series. Advances in time series forecasting due to adoption of multilayer recurrent neural network architectures make it possible…
The Dynamic Time Warping ("DTW") distance is widely used in time series analysis, be it for classification, clustering or similarity search. However, its quadratic time complexity prevents it from scaling. Strategies, based on early…
Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long…
A time series consists of a series of values or events obtained over repeated measurements in time. Analysis of time series represents and important tool in many application areas, such as stock market analysis, process and quality control,…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…
Objective. Imaging dynamic object with high temporal resolution is challenging in magnetic resonance imaging (MRI). Partial separable (PS) model was proposed to improve the imaging quality by reducing the degrees of freedom of the inverse…
Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…
Distance metric learning is successful in discovering intrinsic relations in data. However, most algorithms are computationally demanding when the problem size becomes large. In this paper, we propose a discriminative metric learning…
Many smart grid applications involve data mining, clustering, classification, identification, and anomaly detection, among others. These applications primarily depend on the measurement of similarity, which is the distance between different…
Time-series forecasting has gained significant attention in machine learning due to its crucial role in various domains. However, most existing forecasting models rely heavily on point-wise loss functions like Mean Square Error, which treat…
Dynamic mode decomposition (DMD) is a widely used data-driven algorithm for predicting the future states of dynamical systems. However, its standard formulation often struggles with poor long-term predictive accuracy. To address this…
Dynamic or temporal networks enable representation of time-varying edges between nodes. Conventional adjacency-based data structures used for storing networks such as adjacency lists were designed without incorporating time and can thus…
The Random Walks (RW) algorithm is one of the most e - cient and easy-to-use probabilistic segmentation methods. By combining contrast terms with prior terms, it provides accurate segmentations of medical images in a fully automated manner.…