Multi-Channel Factor Analysis With Common and Unique Factors

Abstract

This work presents a generalization of classical factor analysis (FA). Each of M channels carries measurements that share factors with all other channels, but also contains factors that are unique to the channel. Furthermore, each channel carries an additive noise whose covariance is diagonal, as is usual in factor analysis, but is otherwise unknown. This leads to a problem of multi-channel factor analysis with a specially structured covariance model consisting of shared low-rank components, unique low-rank components, and diagonal components. Under a multivariate normal model for the factors and the noises, a maximum likelihood (ML) method is presented for identifying the covariance model, thereby recovering the loading matrices and factors for the shared and unique components in each of the M multiple-input multiple-output (MIMO) channels. The method consists of a three-step cyclic alternating optimization, which can be framed as a block minorization-maximization (BMM) algorithm. Interestingly, the three steps have closed-form solutions and the convergence of the algorithm to a stationary point is ensured. Numerical results demonstrate the performance of the proposed algorithm and its application to passive radar.

Stochastic Majorize-Minimize Subspace Algorithm with Application to Binary Classification

“…MM algorithms are becoming increasingly popular in signal/image processing [18], [36] and machine learning [27], [34], [38]. MM approaches are fast, stable, require limited manual settings, and are often preferred by practitioners in application domains such as medical imaging [16] and telecommunications [29]. The present work introduces novel theoretical convergence guarantees for MM algorithms when approximate gradient terms are employed, generalizing some recent work [11], [27] to a wider class of functions and algorithms.…”

Novel blind full multipath Two Way Relay Network (TWRN), OFDM channel estimation using Machine Learning

“…H and A T are the Toeplitz matrices constructed from h and a respectively. Extending (equation ( 14) in [33]), we have,…”

“…It is here, that a technique called "Factor Analysis" (used in machine learning for separating mixture of distributions [31], [32], and very recently in speech and signal processing [33]), comes to the rescue. The received signal (observation vector) zl can be viewed as filtering white n r through the unknown H factor, (along with other factors) in the factor analysis model (32).…”

“…which falls within the category of EM algorithms, with the last equation in (39), encompassing its E (Expectation) and M (Maximization) steps. Maximization of L, over the pdf f (n r |z l ), followed by maximization over H, are carried out in an alternating fashion, as in [33]. This requires that the pdf p(z l |n r ) be determined first, after which its Expectation (over the hidden variable n r |z l ) is computed in (39).…”

Ultra-short-term prediction of microgrid source load power considering weather characteristics and multivariate correlation

“…Addressing this limitation, this study investigates the simultaneous correlation between source and load power in a microgrid and weather features, conducting research on the joint ultra-short-term prediction of source and load power in a microgrid. Additionally, commonly used dimensionality reduction algorithms include Principal Component Analysis (PCA) (Wang et al, 2023), Independent Component Analysis (ICA) (Kobayashi and Iwai, 2018), Factor Analysis (FA) (Ramirez et al, 2019;Wu et al, 2024), etc. FA merges numerous features into several representative common factors to extract latent factors among features, accurately capturing the relevant information in the data (Zhou et al, 2020).…”