Independent Component Analysis Filtering Research Articles

Abstract 17924: Machine Learning Analysis of the Atrial ECG in Patients With Persistent Atrial Fibrillation Predicts Long-Term Outcomes

Background: The surface Atrial ECG (A-ECG) time and frequency domains features are not currently used clinically in patients with persistent atrial fibrillation (PeAF). Machine Learning (ML) can provide novel insight into various data sources. Research question: Can ML analysis of the A-ECG predict the outcome of catheter ablation (CA) of PeAF? Aim: To use ML Tools to assess A-ECG prediction of CA outcomes in PeAF patients at 1 and 2 years. Methods: Thirty-two patients (age 63±9 years; 71% males) with PeAF underwent two 5-minute epochs of surface ECG; 4 were excluded for significant artifacts and 2 more for unrelated clinical issues. The Pre-CA A-ECG was derived by QRST subtraction and independent component analysis filtering and divided into 50% overlap 10-second windows for spectral analysis. A-ECG mean dominant frequency DF, mean organization index and median amplitude M-AMP were computed for each lead. Freedom from atrial arrhythmia AA (Responders) was assessed at one and two years. The two 5-minute segments per patient were included in the data set. Classification Learner (Mathworks Inc., Natick, MA, USA) was used to train classifiers, looking for the minimum number of features able to explain the outcomes. Once the best (2-3) features were identified, a MATLAB program was used to visualize the decision regions and correlate with ablation outcomes. Results: ML identified A-ECG features DF and M-AMP of V 1 to well explain outcome. Specifically, an Artificial Neural Network (ANN) with 1 fully connected hidden layer of size 7 can explain the data with 90.4% accuracy. The figure shows the datasets for year 1 and year 2 CA outcomes, superimposed with ANN decision regions, for Responders and non-Responders. High DF and high M-AMP are predictors of responders and Low DF low M-AMP for non-Responders. Conclusion: ML analysis of the A-ECG is a promising tool to predict Responders to PVI CA for treatment of PeAF. This predictive algorithm needs to be tested on a prospective cohort.

Abstract 17011: Correlation of Surface Atrial ECG Dominant Frequency to Intracardiac Atrial Electrogram Dominant Frequency

Background: The surface Atrial ECG (A-ECG) is an underused tool in persistent atrial fibrillation (PeAF) that can provide dominant frequency (DF) of atrial activation. The association between A-ECG DF and left (LA) and right atrial (RA) DF has not been established. Research Question: Does surface A-ECG DF correlate with intracardiac DF? Aims: To investigate the correlation between A-ECG peak DF and peak DF of intracardiac RA and LA electrograms (EGM) in patients with PeAF. Methods: Thirty-two patients (age 63±9 years; 71% males) with PeAF underwent 5-minute epochs of surface ECG and comprehensive LA (261.5±185.1 sites/patient) and RA (211.5±174.6 sites/patient) intracardiac mapping with 15 second recordings. The A-ECG was derived by QRST subtraction and independent component analysis filtering, and divided into overlapping10-second windows which were subjected to Fast Fourier Transform (FFT). 4 were excluded for significant artifact. A-ECG DF was calculated for each lead from the power spectrum as the average of all 10-second segments. Peak A-ECG DF was determined by regional lead location and for all 12 leads. The intracardiac EGM DF was calculated from the FFT, and peak RA and LA DF was determined. Results: A-ECG peak DF was significantly lower than intracardiac peak DF 6.08±0.64 vs 9.72±1.19 Hz, p<0.0001(LA: 9.72±1.20 Hz, p<0.0001; RA: 8.40±0.80 Hz, p<0.0001). Figure shows that A-ECG peak DF correlated with peak RA DF, r=0.77 (p<0.0001), but not with peak LA DF (r=0.31, p=0.10). Regional A-ECG lead group DF correlated with RA DF (Inferior (II, III, aVF): r=0.79, p<0.0001; Lateral (I, aVL, V5-6): r=0.78, p<0.0001; Anterior (V1-3): r=0.75, p<0.0001) but not with peak LA DF. Conclusion: Surface A-ECG DF correlates with intracardiac RA DF and not LA DF. As in atrial flutter, the RA plays a prominent role in the surface ECG manifestation of the f waves. Further study is needed to determine whether A-ECG DF can be used to identify RA versus LA drivers that may require ablation.

Abstract 16967: Effect of Catheter Ablation of Persistent Atrial Fibrillation on Surface Atrial ECG Dominant Frequency

Background: There are no standard techniques to track effects of catheter ablation (CA) of persistent atrial fibrillation (PeAF). The Atrial ECG (A-ECG) derived from the standard ECG provides the atrial dominant frequency (DF), an estimation of atrial rate. Research Question: Does CA for PeAF diminish A-ECG DF? Aims: To evaluate change in A-ECG peak DF pre- and post-CA. Methods: We obtained 1-minute epochs of surface ECG pre- and post-CA in 32 patients (age 63±9 years; 71% males) undergoing CA for PeAF. A-ECG was derived by QRST subtraction and independent component analysis filtering, and divided into overlapping10-second windows, each subjected to Fast Fourier Transform. DF was calculated for each lead as the average DF for all 10-sec segments. Peak A-ECG DF was assessed by regional lead group and among all leads. 10 patients were excluded for significant artifact. Of the 22 analyzed patients, all had pulmonary vein isolation and 3 had posterior wall isolation. Two-year outcomes were available in 20 patients (13 were free from recurrent AF). Results: The figure shows the change in the time-frequency plot (left panel) of DF for one subject and the shift in the spectra (right panel) with CA. A-ECG peak DF was significantly lower post- versus pre-CA: 5.96±0.63 vs 6.16±0.64 Hz, p=0.0009. By lead group, peak DFs were all lower post CA - Anterior (V1-3): 5.94±0.62 vs 6.13±0.64 Hz, p=0.0015; Inferior (II, III, aVF): 5.82±0.63 vs 6.01±0.66 Hz, p=0.0040; Lateral (I, aVL, V5-6): 5.82±0.64 vs 5.99±0.63 Hz, p=0.0015. In this small cohort, there was no significant difference in change of peak DF in those free from AF versus with recurrent AF (-2.4±4.3% vs -4.6±3.7%, p=0.26). Conclusion: The A-ECG provides physiologic information of activation rate in PeAF, but despite current, advanced signal processing techniques is analyzable in only 69% of patients. CA results in a significant reduction in DF. Clinical implications of these CA induced changes require further study.

Spatiotemporal Filtering for Continuous GPS Coordinate Time Series in Mainland China by Using Independent Component Analysis

Continuous Global Positioning Systems (GPS) coordinate time series with a high spatiotemporal resolution, and provide a great opportunity to study their noise models and common mode errors (CMEs), thus making it possible to detect and analyse spatiotemporal characteristics of tectonic and non-tectonic signals in time series, and further to estimate a reliable and accurate velocity field of crustal movement in a region by removing CMEs and using the optimal noise model. In this paper, we used GPS coordinate time series from the Crustal Movement Observation Network of China (CMONOC) with an approximate decadal period from 2010 to 2020, to construct optimal noise models by fitting them with several noise combinations according to the Akaike information criterion (AIC). We further adopted independent component analysis (ICA) to extract CMEs and analysed their spatiotemporal characteristics, and then evaluated their effects on noise models and velocity uncertainties, and finally estimated a decennial velocity field of crustal movement with a higher signal-to-noise ratio (SNR) by applying the CME filtering and considering the optimal noise model in Mainland China. Our results show that optimal noise models are dominated by white noise (WN) plus flicker noise (FN) for both east and north components, and WN plus power law noise (PN) with spectral index close to −1 for up component, respectively. ICA filtering can remove the highly spatially correlated CMEs and decrease the mean RMSEs of the residual time series by about 40–60%, providing a more accurate velocity field with a higher SNR in Mainland China, accordingly.

Suppressing tissue clutter in the presence of motion and nonlinear propagation of ultrasound

Visualizing blood flow in small vessel with ultrasound imaging is a useful diagnosis tool for evaluating organ condition. The usage of encapsulated microbubbles that have non-linear response as contrast agents, in combination with pulsing schemes that suppress the linear tissue signal can improve the sensitivity and specificity of ultrasound flow imaging. However, the nonlinear propagation when ultrasound travels through tissue and microbubble clouds reduce contrast detection. Moreover, tissue motion causes clutter artifacts and imprecise combination of the multi-pulse transmission scheme, impairing image quality. We have previously developed an independent component analysis (ICA)-based clutter filter for high framerate imaging, which performed better than the widely used singular value decomposition (SVD) filter in presence of fast tissue motion. In this study, we examined the performance of ICA filter in combination with power modulation (PM) pulsing schemes to detect flow signal. We performed an in vitro- measurement that emulated ultrasound propagation through cloud of microbubbles and fast tissue motion. The results showed that the combination of PM and ICA filter achieved up to 6dB contrast-to-background ratio improvement compared to only PM. This improvement could be significant for myocardial perfusion imaging, where rapid tissue motion and nonlinear propagation through clouds of microbubbles are expected.

To Explore the Potentials of Independent Component Analysis in Brain-Computer Interface of Motor Imagery.

This paper is focused on the experimental approach to explore the potential of independent component analysis (ICA) in the context of motor imagery (MI)-based brain-computer interface (BCI). We presented a simple and efficient algorithmic framework of ICA-based MI BCI (ICA-MIBCI) for the evaluation of four classical ICA algorithms (Infomax, FastICA, Jade, and Sobi) as well as a simplified Infomax (sInfomax). Two novel performance indexes, self-test accuracy and the number of invalid ICA filters, were employed to assess the performance of MIBCI based on different ICA variants. As a reference method, common spatial pattern (CSP), a commonly-used spatial filtering method, was employed for the comparative study between ICA-MIBCI and CSP-MIBCI. The experimental results showed that sInfomax-based spatial filters exhibited significantly better transferability in session to session and subject to subject transfer as compared to CSP-based spatial filters. The online experiment was also introduced to demonstrate the practicability and feasibility of sInfomax-based MIBCI. However, four classical ICA variants, especially FastICA, Jade, and Sobi, performed much worse as compared to sInfomax and CSP in terms of classification accuracy and stability. We consider that conventional ICA-based spatial filtering methods tend to be overfitting while applied to real-life electroencephalogram data. Nevertheless, the sInfomax-based experimental results indicate that ICA methods have a great space for improvement in the application of MIBCI. We believe that this paper could bring forth new ideas for the practical implementation of ICA-MIBCI.

Spatiotemporal Filtering and Noise Analysis for Regional GNSS Network in Antarctica Using Independent Component Analysis

The common mode error (CME) and optimal noise model are the two most important factors affecting the accuracy of time series in regional Global Navigation Satellite System (GNSS) networks. Removing the CME and selecting the optimal noise model can effectively improve the accuracy of GNSS coordinate time series. The CME, a major source of error, is related to the spatiotemporal distribution; hence, its detrimental effects on time series can be effectively reduced through spatial filtering. Independent component analysis (ICA) is used to filter the time series recorded by 79 GPS stations in Antarctica from 2010 to 2018. After removing stations exhibiting strong local effects using their spatial responses, the filtering results of residual time series derived from principal component analysis (PCA) and ICA are compared and analyzed. The Akaike information criterion (AIC) is then used to determine the optimal noise model of the GPS time series before and after ICA/PCA filtering. The results show that ICA is superior to PCA regarding both the filter results and the consistency of the optimal noise model. In terms of the filtering results, ICA can extract multisource error signals. After ICA filtering, the root mean square (RMS) values of the residual time series are reduced by 14.45%, 8.97%, and 13.27% in the east (E), north (N), and vertical (U) components, respectively, and the associated speed uncertainties are reduced by 13.50%, 8.06% and 11.82%, respectively. Furthermore, different GNSS time series in Antarctica have different optimal noise models with different noise characteristics in different components. The main noise models are the white noise plus flicker noise (WN+FN) and white noise plus power law noise (WN+PN) models. Additionally, the spectrum index of most PN is close to that of FN. Finally, there are more stations with consistent optimal noise models after ICA filtering than there are after PCA filtering.

An Automatic Channel Selection Approach for ICA-Based Motor Imagery Brain Computer Interface.

Independent component analysis (ICA) is a potential spatial filtering method for the implementation of motor imagery brain-computer interface (MIBCI). However, ICA-based MIBCI (ICA-MIBCI) is sensitive to electroencephalogram (EEG) channels and the quality of the training data, which are two crucial factors affecting the stability and classification performance of ICA-MIBCI. To address these problems, this paper is mainly focused on the investigation of EEG channel optimization. As a reference, we constructed a single-trial-based ICA-MIBCI system with commonly used channels and common spatial pattern-based MIBCI (CSP-MIBCI). To minimize the impact of artifacts on EEG channel optimization, a data-quality evaluation method, named "self-testing" in this paper, was used in a single-trial-based ICA-MIBCI system to evaluate the quality of single trials in each dataset; the resulting self-testing accuracies were used for the selection of high-quality trials. Given several candidate channel configurations, ICA filters were calculated using selected high-quality trials and applied to the corresponding ICA-MIBCI implementation. Optimal channels for each dataset were assessed and selected according to the self-testing results related to various candidate configurations. Forty-eight MI datasets of six subjects were employed in this study to validate the proposed methods. Experimental results revealed that the average classification accuracy of the optimal channels yielded a relative increment of 2.8% and 8.5% during self-testing, 14.4% and 9.5% during session-to-session transfer, and 36.2% and 26.7% during subject-to-subject transfer compared to CSP-MIBCI and ICA-MIBCI with fixed the channel configuration. This work indicates that the proposed methods can efficiently improve the practical feasibility of ICA-MIBCI.

ICANet: a simple cascade linear convolution network for face recognition

Recently, deep convolutional networks have demonstrated their capability of improving the discriminative power compared with other machine learning method, but its feature learning mechanism is not very clear. In this paper, we present a cascaded linear convolutional network, based on independent component analysis (ICA) filters, named ICANet. ICANet consists of three parts: a convolutional layer, a binary hash, and a block histogram. It has the following advantages over other methods: (1) the network structure is simple and computationally efficient, (2) the ICA filter is trained with an unsupervised algorithm using unlabeled samples, which is practical, and (3) compared to deep learning models, each layer parameter in ICANet can be easily trained. Thus, ICANet can be used as a benchmark for the application of a deep learning framework for large-scale image classification. Finally, we test two public databases, AR and FERET, showing that ICANet performs well in facial recognition tasks.

Common mode error in Antarctic GPS coordinate time-series on its effect on bedrock-uplift estimates

Spatially correlated common mode error (CME) always exists in regional, or-larger, global positioning system (GPS) networks. We applied independent component analysis (ICA) to GPS vertical coordinate time-series in Antarctica from 2010 to 2014 and made a comparison with the principal component analysis (PCA). Using PCA/ICA, the time-series can be decomposed into a set of temporal components and their spatial responses. We assume the components with common spatial responses are CME. An average reduction of ∼40 per cent about the root-mean-square (RMS) values was achieved in both PCA and ICA filtering. However, the common mode components obtained from the two approaches have different spatial and temporal features. ICA time-series present interesting correlations with modelled atmospheric and non-tidal ocean loading displacements. A white noise plus power law (PL) noise model was adopted in the GPS velocity estimation using maximum likelihood estimation analysis, with ∼55 per cent reduction of the velocity uncertainties after filtering using ICA. Meanwhile, spatiotemporal filtering reduces the amplitude of PL and periodic terms in the GPS time-series. Finally, we compare the GPS uplift velocities, after correction for elastic effects, with recent models of glacial isostatic adjustment (GIA). The agreements of the GPS observed velocities and four GIA models are generally improved after the spatiotemporal filtering, with a mean reduction of ∼0.9 mm yr−1 of the weighted RMS values, possibly allowing for more confident separation of various GIA model predictions.

Unsupervised Feature Learning with Single Layer ICANet for Face Recognition

Compared to supervised learning, unsupervised learning allows systems to learn consistent patterns from cheap and abundant unlabeled data, without the need for manual annotation. In this paper, we present a novel unsupervised feature learning method with single layer (SL) network based independent component analysis (ICA) filters called SL-ICANet, with the goal of achieving compact and robust facial feature representation. Our contributions are twofold: (i) We developed a single-layer convolutional network for unsupervised learning wherein the trainable kernels are replaced by ICA filters. (ii) We extended our SL-ICANet to use multi-scale information for better feature learning. Extensive experiments on two popular face recognition benchmarks, namely, labeled faces in the wild and facial recognition technology show that the proposed method might serve as a simple but highly competitive baseline for face recognition.

Multi-Fold Gabor, PCA, and ICA Filter Convolution Descriptor for Face Recognition

This paper devises a new means of filter diversification, dubbed multi-fold filter convolution (M-FFC), for face recognition. On the assumption that M-FFC receives single-scale Gabor filters of varying orientations as input, these filters are self-cross convolved by M-fold to instantiate a filter offspring set. The M-FFC flexibility also permits cross convolution amongst Gabor filters and other filter banks of profoundly dissimilar traits, e.g., principal component analysis (PCA) filters, and independent component analysis (ICA) filters. The 2-FFC of Gabor, PCA and ICA filters thus yields three offspring sets: (1) Gabor filters solely, (2) Gabor-PCA filters, and (3) Gabor-ICA filters, to render the learning-free and the learning-based 2-FFC descriptors. To facilitate a sensible Gabor filter selection for M-FFC, the 40 multi-scale, multi-orientation Gabor filters are condensed into 8 elementary filters. Aside from that, an average histogram pooling operator is employed to leverage the 2-FFC histogram features, prior to the final whitening PCA compression. The empirical results substantiate that the 2-FFC descriptors prevail over, or on par with, other face descriptors on both identification and verification tasks.

A Fully Automated Trial Selection Method for Optimization of Motor Imagery Based Brain-Computer Interface.

Independent component analysis (ICA) as a promising spatial filtering method can separate motor-related independent components (MRICs) from the multichannel electroencephalogram (EEG) signals. However, the unpredictable burst interferences may significantly degrade the performance of ICA-based brain-computer interface (BCI) system. In this study, we proposed a new algorithm frame to address this issue by combining the single-trial-based ICA filter with zero-training classifier. We developed a two-round data selection method to identify automatically the badly corrupted EEG trials in the training set. The “high quality” training trials were utilized to optimize the ICA filter. In addition, we proposed an accuracy-matrix method to locate the artifact data segments within a single trial and investigated which types of artifacts can influence the performance of the ICA-based MIBCIs. Twenty-six EEG datasets of three-class motor imagery were used to validate the proposed methods, and the classification accuracies were compared with that obtained by frequently used common spatial pattern (CSP) spatial filtering algorithm. The experimental results demonstrated that the proposed optimizing strategy could effectively improve the stability, practicality and classification performance of ICA-based MIBCI. The study revealed that rational use of ICA method may be crucial in building a practical ICA-based MIBCI system.

Visual learning and classification of human epithelial type 2 cell images through spontaneous activity patterns

Identifying the presence of anti-nuclear antibody (ANA) in human epithelial type 2 (HEp-2) cells via the indirect immunofluorescence (IIF) protocol is commonly used to diagnose various connective tissue diseases in clinical pathology tests. As it is a labour and time intensive diagnostic process, several computer aided diagnostic (CAD) systems have been proposed. However, the existing CAD systems suffer from numerous shortcomings due to the selection of features, which is commonly based on expert experience. Such a choice of features may not work well when the CAD systems are retasked to another dataset. To address this, in our previous work, we proposed a novel approach that learns a set of filters from HEp-2 cell images. It is inspired by the receptive fields in the mammalian's vision system, since the receptive fields can be thought as a set of filters for similar shapes. We obtain robust filters for HEp-2 cell classification by employing the independent component analysis (ICA) framework. Although, this approach may be held back due to one particular problem; ICA learning requires a sufficiently large volume of training data which is not always available. In this paper, we demonstrate a biologically inspired solution to address this issue via the use of spontaneous activity patterns (SAP). The spontaneous activity patterns, which are related to the spontaneous neural activities initialised by the chemical release in the brain, are found as the typical stimuli for the visual cell development of newborn animals. In the classification system for HEp-2 cells, we propose to model SAP as a set of small image patches containing randomly positioned Gaussian spots. The SAP image patches are generated and mixed with the training images in order to learn filters via the ICA framework. The obtained filters are adopted to extract the set of responses from a HEp-2 cell image. We then employ regions from this set of responses and stack them into “cubic regions”, and apply a classification based on the correlation information of the features. We show that applying the additional SAP leads to a better classification performance on HEp-2 cell images compared to using only the existing patterns for training ICA filters. The improvement on classification is particularly significant when there are not enough specimen images available in the training set, as SAP adds more variations to the existing data that makes the learned ICA model more robust. We show that the proposed approach consistently outperforms three recently proposed CAD systems on two publicly available datasets: ICPR HEp-2 contest and SNPHEp-2.

Double-gabor filters are independent components of small translation-invariant image patches.

The analysis of natural images with independent component analysis (ICA) yields localized bandpass Gabor-type filters similar to receptive fields of simple cells in visual cortex. We applied ICA on a subset of patches called position-centered patches, selected for forming a translation-invariant representation of small patches. The resulting filters were qualitatively different in two respects. One novel feature was the emergence of filters we call double-Gabor filters. In contrast to Gabor functions that are modulated in one direction, double-Gabor filters are sinusoidally modulated in two orthogonal directions. In addition the filters were more extended in space and frequency compared to standard ICA filters and better matched the distribution in experimental recordings from neurons in primary visual cortex. We further found a dual role for double-Gabor filters as edge and texture detectors, which could have engineering applications.

Combined Independent Component Analysis and Kalman Filter Based Real-Time Digital Video Stabilization

We present an online approach for digital video stabilization. This paper builds upon the work presented in where the authors have proposed the use of Independent Component Analysis (ICA) for video stabilization. Their scheme however is intended for offline systems and cannot be used for online systems. We propose a window based approach to combine the ICA based technique with Kalman filter, in order to make the method suitable for online systems. The proposed approach is tested using simulations and the mean square error between the outcome and the ground truth is used as performance measure. The performances of the proposed method, separate ICA and separate Kalman filter application are compared. The performance of the proposed method turns out to be better than separate application of Kalman filtering or ICA alone. 

TVICA - Time Varying Independent Component Analysis and Its Application to Financial Data

Source extraction and dimensionality reduction are important in analyzing high dimensional and complex financial time series that are neither Gaussian distributed nor stationary. Independent component analysis (ICA) method can be used to factorize the data into a linear combination of independent components, so that the high dimensional problem is converted to a set of univariate ones. However conventional ICA methods implicitly assume stationarity or stochastic homogeneity of the analyzed time series, which leads to a low accuracy of estimation in case of a changing stochastic structure. A time varying ICA (TVICA) is proposed here. The key idea is to allow the ICA filter to change over time, and to estimate it in so-called local homogeneous intervals. The question of how to identify these intervals is solved by the LCP (local change point) method. Compared to a static ICA, the dynamic TVICA provides good performance both in simulation and real data analysis. The data example is concerned with independent signal processing and deals with a portfolio of highly traded stocks.

Separation and Tracking of Maneuvering Sources with ICA and Particle Filters using a New Switching Dynamic Model

The problem addressed in this work is to simultaneously separate multiple maneuvering sources and track their kinematics (position, velocity, and acceleration) in the working space. It is developed upon the incorporation of the nonstationary independent component analysis (ICA) and the nonlinear state estimator problems in a noisy environment. The sampling importance resampling (SIR) particle filter is exploited as the nonlinear state estimator to track current kinematics of the sources even though the state densities are non-Gaussian, and the observation equations are nonlinear. Given source kinematics, nonstationary ICA with a generalized Gaussian density function is used to separate each source signal. Also a novel scheme is proposed as a better alternative for the conventional interacting multiple model (IMM) algorithm to cover the unpredictable movement of the source over time. The proposed scheme deals with the uncertainty of each source motion by incorporating multiple dynamic models in the tracking process. The single best dynamic mode is identified at each time step for all the sources rather than tracking sources for several IMMs as in the IMM algorithm by finding the mode that tracks an indicator source with minimum root mean square error (RMSE). The method is strictly causal and can be used for online tracking. The algorithm performance has been verified by illustrating some simulation results.

Natural image coding in V1: how much use is orientation selectivity?

Orientation selectivity is the most striking feature of simple cell coding in V1 that has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding, it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. To assess the tenability of this hypothesis, it is an important empirical question how much more redundancy can be removed with ICA in comparison to PCA or other second-order decorrelation methods. Although some previous studies have concluded that the amount of higher-order correlation in natural images is generally insignificant, other studies reported an extra gain for ICA of more than 100%. A consistent conclusion about the role of higher-order correlations in natural images can be reached only by the development of reliable quantitative evaluation methods. Here, we present a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss, we compute complete rate–distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is small. At the same time, we show that a simple spherically symmetric distribution with only two parameters can fit the data significantly better than the probabilistic model underlying ICA. This finding suggests that, although the amount of higher-order correlation in natural images can in fact be significant, the feature of orientation selectivity does not yield a large contribution to redundancy reduction within the linear filter bank models of V1 simple cells.

MICA: A Multilinear ICA Decomposition for Natural Scene Modeling

We refine the classical independent component analysis (ICA) decomposition using a multilinear expansion of the probability density function of the source statistics. In particular, we introduce a specific nonlinear system that allows us to elegantly capture the statistical dependences between the responses of the multilinear ICA (MICA) filters. The resulting multilinear probability density is analytically tractable and does not require Monte Carlo simulations to estimate the model parameters. We demonstrate the MICA model on natural image textures and envision that the new model will prove useful for analyzing nonstationarity natural images using natural scene statistics models.