相关论文: Efficient Approximation of Action Potentials with …

Spikes in the membrane electrical potentials of neurons play a major role in the functioning of nervous systems of animals. Obtaining the spikes from different neurons has been a challenging problem for decades. Several schemes have been…

Function approximation is a generic process in a variety of computational problems, from data interpolation to the solution of differential equations and inverse problems. In this work, a unified approach for such techniques is…

We investigate training and using Gaussian kernel SVMs by approximating the kernel with an explicit finite- dimensional polynomial feature representation based on the Taylor expansion of the exponential. Although not as efficient as the…

Spike sorting plays an irreplaceable role in understanding brain codes. Traditional spike sorting technologies perform feature extraction and clustering separately after spikes are well detected. However, it may often cause many additional…

We propose a construction for joint feature learning and clustering of multichannel extracellular electrophysiological data across multiple recording periods for action potential detection and discrimination ("spike sorting"). Our…

Spike sorting is a valuable tool in understanding brain regions. It assigns detected spike waveforms to their origins, helping to research the mechanism of the human brain and the development of implantable brain-machine interfaces (iBMIs).…

This work proposes and analyzes a compressed sensing approach to polynomial approximation of complex-valued functions in high dimensions. Of particular interest is the setting where the target function is smooth, characterized by a rapidly…

The problem of efficient approximation of a linear operator induced by the Gaussian or softmax kernel is often addressed using random features (RFs) which yield an unbiased approximation of the operator's result. Such operators emerge in…

Spike sorting algorithms are used to separate extracellular recordings of neuronal populations into single-unit spike activities. The development of customized hardware implementing spike sorting algorithms is burgeoning. However, there is…

Sparse polynomial approximation has become indispensable for approximating smooth, high- or infinite-dimensional functions from limited samples. This is a key task in computational science and engineering, e.g., surrogate modelling in…

We propose a fast and scalable optimization method to solve chance or probabilistic constrained optimization problems governed by partial differential equations (PDEs) with high-dimensional random parameters. To address the critical…

Objective. Recent advancements in electrode designs and micro-fabrication technology has allowed existence of microelectrode arrays with hundreds of channels for single-cell recordings. In such electrophysiological recordings, each…

This work is concerned with approximating a trivariate function defined on a tensor-product domain via function evaluations. Combining tensorized Chebyshev interpolation with a Tucker decomposition of low multilinear rank yields function…

An important prerequisite for the analysis of spike synchrony in extracellular recordings is the extraction of single unit activity from the recorded multi unit signal. To identify single units (SUs), potential spikes are detected and…

In this paper, we introduce a method for multivariate function approximation using function evaluations, Chebyshev polynomials, and tensor-based compression techniques via the Tucker format. We develop novel randomized techniques to…

Approximating higher-order tensors by the Tucker format has been applied in many fields such as psychometrics, chemometrics, signal processing, pattern classification, and so on. In this paper, we propose some new Tucker-like approximations…

This paper describes a new algorithm for computing a low-Tucker-rank approximation of a tensor. The method applies a randomized linear map to the tensor to obtain a sketch that captures the important directions within each mode, as well as…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

This paper develops fast and efficient algorithms for computing Tucker decomposition with a given multilinear rank. By combining random projection and the power scheme, we propose two efficient randomized versions for the truncated…

Spike sorting is a critical process for decoding large-scale neural activity from extracellular recordings. The advancement of neural probes facilitates the recording of a high number of neurons with an increase in channel counts, arising a…