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This paper introduces a novel methodology of adapting the representation of videos based on the dynamics of their scene content variation. In particular, we demonstrate how the clustering of dynamic mode decomposition eigenvalues can be…
We study the basic problem of robust subspace recovery. That is, we assume a data set that some of its points are sampled around a fixed subspace and the rest of them are spread in the whole ambient space, and we aim to recover the fixed…
Minor Component Adaptation (MiCA) is a novel parameter-efficient fine-tuning method for large language models that focuses on adapting underutilized subspaces of model representations. Unlike conventional methods such as Low-Rank Adaptation…
A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
The Multiple Signal Classification (MUSIC) algorithm based on the orthogonality between the signal subspace and noise subspace is one of the most frequently used method in the estimation of Direction Of Arrival (DOA), and its performance of…
In order to encode additional statistical information in data fusion and transfer learning applications, we introduce a generalized covariance constraint for the matching component analysis (MCA) transfer learning technique. We provide a…
In this paper, we consider multivariate response regression models with high dimensional predictor variables. One way to model the correlation among the response variables is through the low rank decomposition of the coefficient matrix,…
Multiple-input multiple-output (MIMO) systems play an essential role in direction-of-arrival (DOA) estimation. A large number of antennas used in a MIMO system imposes a huge complexity burden on the popular DOA estimation algorithms, such…
Principal component analysis is an important pattern recognition and dimensionality reduction tool in many applications. Principal components are computed as eigenvectors of a maximum likelihood covariance $\widehat{\Sigma}$ that…
Classical methods of DOA estimation such as the MUSIC algorithm are based on estimating the signal and noise subspaces from the sample covariance matrix. For a small number of samples, such methods are exposed to performance breakdown, as…
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a…
Principal Component Analysis (PCA) is the workhorse tool for dimensionality reduction in this era of big data. While often overlooked, the purpose of PCA is not only to reduce data dimensionality, but also to yield features that are…
We introduce Monte-Carlo Attention (MCA), a randomized approximation method for reducing the computational cost of self-attention mechanisms in Transformer architectures. MCA exploits the fact that the importance of each token in an input…
Independent component analysis (ICA) is a powerful computational tool for separating independent source signals from their linear mixtures. ICA has been widely applied in neuroimaging studies to identify and characterize underlying brain…
Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…
Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. It extends principal component analysis (PCA) and can extract important and complicated components with small…
Principal components analysis (PCA) is a classical method for the reduction of dimensionality of data in the form of n observations (or cases) of a vector with p variables. For a simple model of factor analysis type, it is proved that…
Covariance matrix estimates are an essential part of many signal processing algorithms, and are often used to determine a low-dimensional principal subspace via their spectral decomposition. However, exact eigenanalysis is computationally…
The development of neuromorphic hardware and modeling of biological neural networks requires algorithms with local learning rules. Artificial neural networks using local learning rules to perform principal subspace analysis (PSA) and…