On the Number of Independent Components: An Adjusted Coefficient of Determination based Approach

Different machine learning algorithms have recently been used for assisting automated classification of independent component analysis (ICA) results from resting-state fMRI data. The success of this approach relies on identification of artifact components and meaningful functional networks. A limiting factor of ICA is the uncertainty of the number of independent components (NIC). We aim to develop a framework based on support vector machines (SVM) and optimized feature-selection for automated classification of independent components (ICs) and use the framework to investigate the effects of input NIC on the ICA results. Seven different resting-state fMRI datasets were studied. 18 features were devised by mimicking the empirical criteria for manual evaluation. The five most significant (p < 0.01) features were identified by general linear modeling and used to generate a classification model for the framework. This feature-optimized classification of ICs with SVM (FOCIS) framework was used to classify both group and single subject ICA results. The classification results obtained using FOCIS and previously published FSL-FIX were compared against manually evaluated results. On average the false negative rate in identifying artifact contaminated ICs for FOCIS and FSL-FIX were 98.27 and 92.34%, respectively. The number of artifact and functional network components increased almost linearly with the input NIC. Through tracking, we demonstrate that incrementing NIC affects most ICs when NIC < 33, whereas only a few limited ICs are affected by direct splitting when NIC is incremented beyond NIC > 40. For a given IC, its changes with increasing NIC are individually specific irrespective whether the component is a potential resting-state functional network or an artifact component. Using FOCIS, we investigated experimentally the ICA dimensionality of resting-state fMRI datasets and found that the input NIC can critically affect the ICA results of resting-state fMRI data.

This paper examines true oscillations in the Northern Hemisphere winter by using independent component analysis (ICA). ICA can distinguish between true and apparent oscillations under the assumption that the true oscillations are mutually independent. Particular attention is paid to the Arctic Oscillation (AO). For this purpose, the NCEP-NCAR reanalysis data (NCEP-NCAR data) and the data of the present climate experiment of the Meteorological Research Institute (MRI data) are used. There may be certain issues in ICA applied to meteorology: the selection of data periods, treatment of noise, and relationship between the number of dimensions in phase space and the number of independent components. We make several considerations and proposals about these issues. ICA should be performed for periods for which the variance is almost the same. Since independent components after whitening are not necessarily uncorrelated with each other under the existence of noise, and the relation between the dimension of phase space and the number of independent components cannot be predetermined, we propose the method for seeking independent components by kurtosis as the most relevant in meteorology. On the basis of the above considerations and proposals, ICA is performed on the NCEP-NCAR data. Independent components are found for the sea level pressure (SLP) and 500 hPa height (Z500) fields. They are the North Atlantic Oscillation (NAO) and the Pacific-North American Oscillation (PNA). Thus, the AO is an apparent mode derived from them. However, since the period of the data is too short, statistical significance cannot be obtained. Then, ICA is performed on the MRI data. Also in this data, the NAO and the PNA-like oscillation are independent for both the SLP and Z500, where the PNA-like oscillation implies that its pattern is somewhat different from the observed PNA pattern. It can be concluded again that the AO is not independent, but this time with statistical significance.

Independent component analysis for noisy data — MEG data analysis

Blind Signal Separation (BSS) and Independent Component Analysis (ICA) are emerging techniques of array processing and data analysis that aim to recover unobserved signals or ldquosourcesrdquo from observed mixtures. When the number of independent components is not very many, using ICA algorithm to separate mixed images, the separated images will have a very strong image artifact noise which will affect the separation efficiency of ICA. In this paper, data fusion technology will be carried out with ICA, firstly, the algorithm used Weiner Filter to preprocess data, and then center the data to make its mean zero; whiten data to make it decorrelation; secondly, use a fast fixed-point algorithm based on negentropy to separate the data, finally, use data fusion based on wavelet algorithm. The results showed that the images after treated by this algorithm become clearer, easier identification, noise significant inhibitory effect. Comparing with the images Peak Signal Noise Ratio (PSNR) before and after the fusion, it proves that the algorithm is feasibility and effectiveness.

ICA (independent component analysis) is a technique for analyzing multi-variant data. Lots of results are reported in the field of neurobiological data analysis such as EEG (electroencephalography), MRI (magnetic resonance imaging), and MEG (magnetoencephalography) using ICA. But there still remain problems. In most of the neurobiological data, there is a large amount of noise, and the number of independent components is unknown which gives difficulties for many ICA algorithms. We discuss an approach to separate noise-contaminated data without knowing the number of independent components. The idea is to replace PCA (principal component analysis), which is used as the preprocessing of many ICA algorithms, with factor analysis. In the new preprocessing, the number of the sources and the amount of the noise are estimated. After the preprocessing, an ICA algorithm is used to estimate the separation matrix and mixing system. Through experiments with MEG data, we show this approach is effective.

General Background: Dimensionality reduction is a critical technique in image processing, especially for multispectral satellite imagery where data redundancy and computational complexity are prevalent challenges. Specific Background: Principal Component Analysis (PCA) and Independent Component Analysis (ICA) are two widely adopted methods for reducing dimensionality while preserving essential image information. Knowledge Gap: Despite their extensive usage, comparative assessments of their performance in multispectral image reconstruction, particularly in geospatial contexts, remain limited. Aims: This study aims to evaluate and compare the effectiveness of PCA and ICA in processing Landsat multispectral images of the Bighorn Basin by assessing image reconstruction fidelity. Results: The findings reveal that PCA outperforms ICA in reconstruction quality, achieving higher Peak Signal-to-Noise Ratio (PSNR) values (up to 27.78 dB) and lower Root Mean Square Error (RMSE), whereas ICA, though proficient in extracting statistically independent features, demonstrated lower fidelity (PSNR = 17.63 dB). Novelty: The work offers a rigorous, side-by-side quantitative analysis of PCA and ICA applied to real-world satellite data, highlighting variance behavior and reconstruction trade-offs. Implications: These insights inform the selection of dimensionality reduction techniques in remote sensing tasks—PCA for optimal reconstruction and noise elimination, and ICA for feature extraction based on statistical independence.Highlights: PCA provides superior image reconstruction accuracy with higher PSNR and lower RMSE. ICA excels in isolating statistically independent features for advanced analysis. PCA components show faster variance decay, making them efficient for compression. Keywords: Dimensionality Reduction, Satellite Imagery, Principal Component Analysis, Independent Component Analysis, Image Reconstruction

Interest in hedge funds has grown tremendously over the past decade. As the market for hedge funds broadens, academics and practitioners are looking for new ways to examine these new financial vehicles. Currently, to uncover the factors that drive hedge fund returns, analysts either implement explicit factor models or implicit factor models such as principal component analysis. In this report, the implicit factor model of independent component analysis is introduced to analyze hedge fund returns. Using 119 equity long/short managers, a number of independent components are extracted along with a number of principal components. A comparison is conducted between the implicit factors indicating that the independent components explain different characteristics of hedge fund returns than the principal components obtained. To show how the independent components and principal components work with factor analysis, a small sample of managers is taken from the 119 hedge funds and all three methods were implemented. Findings indicate that there is value added in implementing independent component analysis in the analysis of hedge fund returns.

Distributed BOLD-response in association cortex vector state space predicts reaction time during selective attention

Study of brain functional images based functional networks helps better understanding of brain function and diagnosis of mental disease.As a data driven method,independent component analysis(ICA) has gained popularity for brain functional networks analysis.However,the order of resulting components is random,the number of independent components needs to be estimated,and the results are affected by initialization.All these shortcomings of ICA bring difficulties to its practical application.The paper firstly explains the principle and disadvantages of ICA,and then reviews the existing ICA methods for brain functional networks analysis.After that,it highlights the recently proposed group information guided ICA method.Finally,potential improvement to methods of brain functional networks is pointed out.

The aim of this study is to apply the Independent Component Analysis (ICA) method in Resting-state Functional MRI (rsfMRI) analysis to estimation somatosensory: motor cortex primary M1 (4, 6, 8) and supplementary SMA (1–3, 5, 31, 32, 40), as well as cerebellum, in patients with Multiple Sclerosis (MS) compared with healthy subjects. The measurements were performed on 3 Tesla scanner using and ICA correlation analysis. Independent component analysis (ICA) was used to post-process the rsfMRI data concerning the sensorimotor networks for two groups in Group ICA of fMRI Toolbox (GIFT) by using the Infomax algorithm. The number of independent components (ICs) influence on sensorimotor network in SM group in comparison with the healthy group is discussed taking into consideration some spectral parameters such as dynamic range and fractional of Amplitude of Low Frequency Fluctuation(fALFF), curtosis of timecourses, and spatial maps.

State-space independent component analysis for nonlinear dynamic process monitoring

BackgroundA key question when analyzing high throughput data is whether the information provided by the measured biological entities (gene, metabolite expression for example) is related to the experimental conditions, or, rather, to some interfering signals, such as experimental bias or artefacts. Visualization tools are therefore useful to better understand the underlying structure of the data in a 'blind' (unsupervised) way. A well-established technique to do so is Principal Component Analysis (PCA). PCA is particularly powerful if the biological question is related to the highest variance. Independent Component Analysis (ICA) has been proposed as an alternative to PCA as it optimizes an independence condition to give more meaningful components. However, neither PCA nor ICA can overcome both the high dimensionality and noisy characteristics of biological data.ResultsWe propose Independent Principal Component Analysis (IPCA) that combines the advantages of both PCA and ICA. It uses ICA as a denoising process of the loading vectors produced by PCA to better highlight the important biological entities and reveal insightful patterns in the data. The result is a better clustering of the biological samples on graphical representations. In addition, a sparse version is proposed that performs an internal variable selection to identify biologically relevant features (sIPCA).ConclusionsOn simulation studies and real data sets, we showed that IPCA offers a better visualization of the data than ICA and with a smaller number of components than PCA. Furthermore, a preliminary investigation of the list of genes selected with sIPCA demonstrate that the approach is well able to highlight relevant genes in the data with respect to the biological experiment.IPCA and sIPCA are both implemented in the R package mixomics dedicated to the analysis and exploration of high dimensional biological data sets, and on mixomics' web-interface.

A STUDY OF THE NOISE FROM DIESEL ENGINES USING THE INDEPENDENT COMPONENT ANALYSIS

Performance comparison of machine learning algorithms and number of independent components used in fMRI decoding of belief vs. disbelief

Using independent component for clustering of time series data