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Data-driven decoding (DDD) - learning to decode syndromes of (quantum) error-correcting codes by learning from data - can be a difficult problem due to several atypical and poorly understood properties of the training data. We introduce a…
The singular value decomposition (SVD) is not only a classical theory in matrix computation and analysis, but also is a powerful tool in machine learning and modern data analysis. In this tutorial we first study the basic notion of SVD and…
The singular value decomposition (SVD) and the principal component analysis are fundamental tools and probably the most popular methods for data dimension reduction. The rapid growth in the size of data matrices has lead to a need for…
Dynamic mode (DM) decomposition decomposes spatiotemporal signals into basic oscillatory components (DMs). DMs can improve the accuracy of neural decoding when used with the nonlinear Grassmann kernel, compared to conventional power…
Dynamic mode decomposition (DMD) is a data-driven technique used for capturing the dynamics of complex systems. DMD has been connected to spectral analysis of the Koopman operator, and essentially extracts spatial-temporal modes of the…
Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix…
Dynamic Mode Decomposition (DMD) is a data based modeling tool that identifies a matrix to map a quantity at some time instant to the same quantity in future. We design a new version which we call Adaptive Dynamic Mode Decomposition (ADMD)…
Dynamic mode decomposition (DMD) and its variants have emerged as popular methods for the post-processing of fluid dynamics' simulations in order to visualize dominant coherent structures and to reduce the practical degrees of freedom to a…
Balanced data is required for deep neural networks (DNNs) when learning to perform power system stability assessment. However, power system measurement data contains relatively few events from where power system dynamics can be learnt. To…
We address the problem of data-driven pattern identification and outlier detection in time series. To this end, we use singular value decomposition (SVD) which is a well-known technique to compute a low-rank approximation for an arbitrary…
Presented is an algorithm based on dynamic mode decomposition (DMD) for acceleration of the power method (PM). The power method is a simple technique for determining the dominant eigenmode of an operator $\mathbf{A}$, and variants of the…
The Dynamic Mode Decomposition (DMD) is a Koopman-based algorithm that straightforwardly isolates individual mechanisms from the compound morphology of direct measurement. However, many may be perplexed by the messages the DMD structures…
Sensor-based human activity recognition is important in daily scenarios such as smart healthcare and homes due to its non-intrusive privacy and low cost advantages, but the problem of out-of-domain generalization caused by differences in…
We develop an Iterative version of the Singular Value Decomposition (ISVD) that jointly analyzes a finite number of data matrices to identify signals that correlate among the rows of matrices. It will be illustrated how the supervised…
Single-channel signal separation and deconvolution aims to separate and deconvolve individual sources from a single-channel mixture and is a challenging problem in which no prior knowledge of the mixing filters is available. Both individual…
A novel method for decomposing a nonstationary signal into amplitude- and frequency-modulated (AM-FM) oscillations and discontinuous (jump) components is proposed. Current nonstationary signal decomposition methods are designed to either…
This paper describes several improvements to a new method for signal decomposition that we recently formulated under the name of Differentiable Dictionary Search (DDS). The fundamental idea of DDS is to exploit a class of powerful deep…
We formulate a low-storage method for performing dynamic mode decomposition that can be updated inexpensively as new data become available; this formulation allows dynamical information to be extracted from large datasets and data streams.…
Data segmentation a.k.a. multiple change point analysis has received considerable attention due to its importance in time series analysis and signal processing, with applications in a variety of fields including natural and social sciences,…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…