Enhancing Blind Source Separation with Dissociative Principal Component Analysis

• URL: http://arxiv.org/abs/2411.12321v1
• Date: Tue, 19 Nov 2024 08:24:01 GMT
• Title: Enhancing Blind Source Separation with Dissociative Principal Component Analysis
• Authors: Muhammad Usman Khalid,
• Abstract summary: Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs) To overcome this limitation, a sophisticated approach is proposed that preserves the interpretability advantages of sPCA while significantly enhancing its source extraction capabilities. This consists of two tailored algorithms, dissociative PCA (DPCA1 and DPCA2), which employ adaptive and firm threshold gradienting alongside and coordinate descent approaches to optimize the proposed model dynamically.
• Score: 0.0
• License:
• Abstract: Sparse principal component analysis (sPCA) enhances the interpretability of principal components (PCs) by imposing sparsity constraints on loading vectors (LVs). However, when used as a precursor to independent component analysis (ICA) for blind source separation (BSS), sPCA may underperform due to its focus on simplicity, potentially disregarding some statistical information essential for effective ICA. To overcome this limitation, a sophisticated approach is proposed that preserves the interpretability advantages of sPCA while significantly enhancing its source extraction capabilities. This consists of two tailored algorithms, dissociative PCA (DPCA1 and DPCA2), which employ adaptive and firm thresholding alongside gradient and coordinate descent approaches to optimize the proposed model dynamically. These algorithms integrate left and right singular vectors from singular value decomposition (SVD) through dissociation matrices (DMs) that replace traditional singular values, thus capturing latent interdependencies effectively to model complex source relationships. This leads to refined PCs and LVs that more accurately represent the underlying data structure. The proposed approach avoids focusing on individual eigenvectors, instead, it collaboratively combines multiple eigenvectors to disentangle interdependencies within each SVD variate. The superior performance of the proposed DPCA algorithms is demonstrated across four varied imaging applications including functional magnetic resonance imaging (fMRI) source retrieval, foreground-background separation, image reconstruction, and image inpainting. They outperformed traditional methods such as PCA+ICA, PPCA+ICA, SPCA+ICA, PMD, and GPower.

Related papers

• Efficient Estimation of Unique Components in Independent Component Analysis by Matrix Representation [1.0282274843007793]
  Independent component analysis (ICA) is a widely used method in various applications of signal processing and feature extraction. In this paper, the unique estimation of ICA is highly accelerated by reformulating the algorithm in matrix representation. Experimental results on artificial datasets and EEG data verified the efficiency of the proposed method.
  arXiv  Detail & Related papers  (2024-08-30T09:01:04Z)
• ESSAformer: Efficient Transformer for Hyperspectral Image Super-resolution [76.7408734079706]
  Single hyperspectral image super-resolution (single-HSI-SR) aims to restore a high-resolution hyperspectral image from a low-resolution observation. We propose ESSAformer, an ESSA attention-embedded Transformer network for single-HSI-SR with an iterative refining structure.
  arXiv  Detail & Related papers  (2023-07-26T07:45:14Z)
• Exploiting Temporal Structures of Cyclostationary Signals for Data-Driven Single-Channel Source Separation [98.95383921866096]
  We study the problem of single-channel source separation (SCSS) We focus on cyclostationary signals, which are particularly suitable in a variety of application domains. We propose a deep learning approach using a U-Net architecture, which is competitive with the minimum MSE estimator.
  arXiv  Detail & Related papers  (2022-08-22T14:04:56Z)
• Personalized PCA: Decoupling Shared and Unique Features [4.976703689624386]
  We propose personalized PCA (PerPCA) to decouple shared and unique features from heterogeneous datasets. We show that, under mild conditions, both unique and shared features can be identified and recovered by a constrained optimization problem. As a systematic approach to decouple shared and unique features from heterogeneous datasets, PerPCA finds applications in several tasks, including video segmentation, topic extraction, and feature clustering.
  arXiv  Detail & Related papers  (2022-07-17T00:09:47Z)
• Pseudo-Spherical Contrastive Divergence [119.28384561517292]
  We propose pseudo-spherical contrastive divergence (PS-CD) to generalize maximum learning likelihood of energy-based models. PS-CD avoids the intractable partition function and provides a generalized family of learning objectives.
  arXiv  Detail & Related papers  (2021-11-01T09:17:15Z)
• Shared Independent Component Analysis for Multi-Subject Neuroimaging [107.29179765643042]
  We introduce Shared Independent Component Analysis (ShICA) that models each view as a linear transform of shared independent components contaminated by additive Gaussian noise. We show that this model is identifiable if the components are either non-Gaussian or have enough diversity in noise variances. We provide empirical evidence on fMRI and MEG datasets that ShICA yields more accurate estimation of the components than alternatives.
  arXiv  Detail & Related papers  (2021-10-26T08:54:41Z)
• Improved Dimensionality Reduction of various Datasets using Novel Multiplicative Factoring Principal Component Analysis (MPCA) [0.0]
  We present an improvement to the traditional PCA approach called Multiplicative factoring Principal Component Analysis. The advantage of MPCA over the traditional PCA is that a penalty is imposed on the occurrence space through a multiplier to make negligible the effect of outliers in seeking out projections.
  arXiv  Detail & Related papers  (2020-09-25T12:30:15Z)
• Exact and Approximation Algorithms for Sparse PCA [1.7640556247739623]
  This paper proposes two exact mixed-integer SDPs (MISDPs) We then analyze the theoretical optimality gaps of their continuous relaxation values and prove that they are stronger than that of the state-of-art one. Since off-the-shelf solvers, in general, have difficulty in solving MISDPs, we approximate SPCA with arbitrary accuracy by a mixed-integer linear program (MILP) of a similar size as MISDPs.
  arXiv  Detail & Related papers  (2020-08-28T02:07:08Z)
• Out-of-distribution Generalization via Partial Feature Decorrelation [72.96261704851683]
  We present a novel Partial Feature Decorrelation Learning (PFDL) algorithm, which jointly optimize a feature decomposition network and the target image classification model. The experiments on real-world datasets demonstrate that our method can improve the backbone model's accuracy on OOD image classification datasets.
  arXiv  Detail & Related papers  (2020-07-30T05:48:48Z)
• Repulsive Mixture Models of Exponential Family PCA for Clustering [127.90219303669006]
  The mixture extension of exponential family principal component analysis ( EPCA) was designed to encode much more structural information about data distribution than the traditional EPCA. The traditional mixture of local EPCAs has the problem of model redundancy, i.e., overlaps among mixing components, which may cause ambiguity for data clustering. In this paper, a repulsiveness-encouraging prior is introduced among mixing components and a diversified EPCA mixture (DEPCAM) model is developed in the Bayesian framework.
  arXiv  Detail & Related papers  (2020-04-07T04:07:29Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.