Principal independent component analysis

Methods Used in Computer-Aided Diagnosis for Breast Cancer Detection Using Mammograms: A Review

According to the American Cancer Society's forecasts for 2019, there will be about 268,600 new cases in the United States with invasive breast cancer in women, about 62,930 new noninvasive cases, and about 41,760 death cases from breast cancer. As a result, there is a high demand for breast imaging specialists as indicated in a recent report for the Institute of Medicine and National Research Council. One way to meet this demand is through developing Computer-Aided Diagnosis (CAD) systems for breast cancer detection and diagnosis using mammograms. This study aims to review recent advancements and developments in CAD systems for breast cancer detection and diagnosis using mammograms and to give an overview of the methods used in its steps starting from preprocessing and enhancement step and ending in classification step. The current level of performance for the CAD systems is encouraging but not enough to make CAD systems standalone detection and diagnose clinical systems. Unless the performance of CAD systems enhanced dramatically from its current level by enhancing the existing methods, exploiting new promising methods in pattern recognition like data augmentation in deep learning and exploiting the advances in computational power of computers, CAD systems will continue to be a second opinion clinical procedure.

Temporally constrained ICA with threshold and its application to fMRI data

Background

Although independent component analysis (ICA) has been widely applied to functional magnetic resonance imaging (fMRI) data to reveal spatially independent brain networks, the order indetermination of ICA leads to the problem of target component selection. The temporally constrained independent component analysis (TCICA) is capable of automatically extracting the desired spatially independent components by adding the temporal prior information of the task to the mixing matrix for fMRI data analysis. However, the TCICA method can only extract a single component that tends to be a mix of multiple task-related components when there exist several independent components related to one task.

Methods

In this study, we proposed a TCICA with threshold (TCICA-Thres) method that performed TCICA outside the threshold and performed FastICA inside the threshold to automatically extract all the target components related to one task. The proposed approach was tested using simulated fMRI data and was applied to a real fMRI experiment using 13 subjects. Additionally, the performance of TCICA-Thres was compared with that of FastICA and TCICA.

Results

The results from the simulation and the fMRI data demonstrated that TCICA-Thres better extracted the task-related components than TCICA. Moreover, TCICA-Thres outperformed FastICA in robustness to noise, spatial detection power and computational time.

Conclusions

The proposed TCICA-Thres solves the limitations of TCICA and extends the application of TCICA in fMRI data analysis.

Electronic supplementary material

The online version of this article (10.1186/s12880-018-0300-6) contains supplementary material, which is available to authorized users.

A New Constrained Spatiotemporal ICA Method Based on Multi-Objective Optimization for fMRI Data Analysis

Compared with independent component analysis (ICA), constrained ICA (CICA) has unique advantages in functional magnetic resonance image (fMRI) data analysis by introducing some priori information into the estimation process. However, there are still some controversies in the current CICA methods, such as how to choose the threshold parameter to restrain the similarity, and how to reduce the accuracy requirements for a priori information. In this paper, we propose a new constrained spatiotemporal ICA (CSTICA) method based on the framework of multi-objective optimization, where the inequality constraint of the traditional CICA method is transformed into the objective optimization function of the CSTICA, and both temporal and spatial a priori information are included simultaneously. The simulated, hybrid, and real fMRI data experiments are designed to evaluate the performance of the proposed CSTICA method in comparison with the classical ICA and CICA methods. Compared with the traditional CICA methods, the CSTICA has circumvented the problem of threshold parameter selection. Furthermore, the experimental results demonstrate that the source recovery ability of the CSTICA has been improved to a certain extent especially in the cases of a priori information with low accuracies. Meanwhile, the results also indicate that the CSTICA reduces dependency on the accuracy of a priori information.

New Families of Skewed Higher-Order Kernel Estimators to Solve the BSS/ICA Problem for Multimodal Sources Mixtures

This letter suggests two new types of asymmetrical higher-order kernels (HOK) that are generated using the orthogonal polynomials Laguerre (positive or right skew) and Bessel (negative or left skew). These skewed HOK are implemented in the blind source separation/independent component analysis (BSS/ICA) algorithm. The tests for these proposed HOK are accomplished using three scenarios to simulate a real environment using actual sound sources, an environment of mixtures of multimodal fast-changing probability density function (pdf) sources that represent a challenge to the symmetrical HOK, and an environment of an adverse case (near gaussian). The separation is performed by minimizing the mutual information (MI) among the mixed sources. The performance of the skewed kernels is compared to the performance of the standard kernels such as Epanechnikov, bisquare, trisquare, and gaussian and the performance of the symmetrical HOK generated using the polynomials Chebyshev1, Chebyshev2, Gegenbauer, Jacobi, and Legendre to the tenth order. The gaussian HOK are generated using the Hermite polynomial and the Wand and Schucany procedure. The comparison among the 96 kernels is based on the average intersymbol interference ratio (AISIR) and the time needed to complete the separation. In terms of AISIR, the skewed kernels' performance is better than that of the standard kernels and rivals most of the symmetrical kernels' performance. The importance of these new skewed HOK is manifested in the environment of the multimodal pdf mixtures. In such an environment, the skewed HOK come in first place compared with the symmetrical HOK. These new families can substitute for symmetrical HOKs in such applications.

Temporally and spatially constrained ICA of fMRI data analysis

Constrained independent component analysis (CICA) is capable of eliminating the order ambiguity that is found in the standard ICA and extracting the desired independent components by incorporating prior information into the ICA contrast function. However, the current CICA method produces constraints that are based on only one type of prior information (temporal/spatial), which may increase the dependency of CICA on the accuracy of the prior information. To improve the robustness of CICA and to reduce the impact of the accuracy of prior information on CICA, we proposed a temporally and spatially constrained ICA (TSCICA) method that incorporated two types of prior information, both temporal and spatial, as constraints in the ICA. The proposed approach was tested using simulated fMRI data and was applied to a real fMRI experiment using 13 subjects who performed a movement task. Additionally, the performance of TSCICA was compared with the ICA method, the temporally CICA (TCICA) method and the spatially CICA (SCICA) method. The results from the simulation and from the real fMRI data demonstrated that TSCICA outperformed TCICA, SCICA and ICA in terms of robustness to noise. Moreover, the TSCICA method displayed better robustness to prior temporal/spatial information than the TCICA/SCICA method.

Fixed-point algorithms for constrained ICA and their applications in fMRI data analysis

Constrained independent component analysis (CICA) eliminates the order ambiguity of standard ICA by incorporating prior information into the learning process to sort the components intrinsically. However, the original CICA (OCICA) and its variants depend on a learning rate, which is not easy to be tuned for various applications. To solve this problem, two learning-rate-free CICA algorithms were derived in this paper using the fixed-point learning concept. A complete stability analysis was provided for the proposed methods, which also made a correction to the stability analysis given to OCICA. Variations for adding constraints either to the components or to the associated time courses were derived too. Using synthetic data, the proposed methods yielded a better stability and a better source separation quality in terms of higher signal-to-noise-ratio and smaller performance index than OCICA. For the artificially generated brain activations, the new CICAs demonstrated a better sensitivity/specificity performance than standard univariate general linear model (GLM) and standard ICA. Original CICA showed a similar sensitivity/specificity gain but failed to converge for several times. Using functional magnetic resonance imaging (fMRI) data acquired with a well-characterized sensorimotor task, the proposed CICAs yielded better sensitivity than OCICA, standard ICA and GLM in all the target functional regions in terms of either higher t values or larger suprathreshold cluster extensions using the same significance threshold. In addition, they were more stable than OCICA and standard ICA for analyzing the sensorimotor fMRI data.

Sequential fixed-point ICA based on mutual information minimization

A new gradient technique is introduced for linear independent component analysis (ICA) based on the Edgeworth expansion of mutual information, for which the algorithm operates sequentially using fixed-point iterations. In order to address the adverse effect of outliers, a robust version of the Edgeworth expansion is adopted, in terms of robust cumulants, and robust derivatives of the Hermite polynomials are used. Also, a new constrained version of ICA is introduced, based on goal programming of mutual information objectives, which is applied to the extraction of the antepartum fetal electrocardiogram from multielectrode cutaneous recordings on the mother's thorax and abdomen.

Approach and Applications of Constrained ICA

This paper presents the technique of constrained independent component analysis (cICA) and demonstrates two applications, less-complete ICA, and ICA with reference (ICA-R). The cICA is proposed as a general framework to incorporate additional requirements and prior information in the form of constraints into the ICA contrast function. The adaptive solutions using the Newton-like learning are proposed to solve the constrained optimization problem. The applications illustrate the versatility of the cICA by separating subspaces of independent components according to density types and extracting a set of desired sources when rough templates are available. The experiments using face images and functional MR images demonstrate the usage and efficacy of the cICA.

Estimation of peroneal and tibial afferent activity from a multichannel cuff placed on the sciatic nerve

The afferent signals recorded with a multi-electrode cuff on the sciatic nerve were employed to investigate the possibility of extracting components ascending from the peroneal and tibial nerves. Two methods, an inverse regression model and principal component method, were studied. The parameters of inverse regression model, determined by data collected in semistatic conditions, were validated by data collected in dynamic conditions. The results showed that the regression model, which used only two channels of the sciatic recordings, was sufficient to separate the distal afferent components. The model, at the expense of requiring distal branch recordings for estimating model parameters, yielded better separation than the principal component method. In conclusion, peroneal and tibial afferent activity can be estimated from the sciatic nerve: the principal component method is suitable for applications focused on acquiring afferent information, whereas the inverse regression model is better for applications in which stimulations will be applied to the branches. The estimation technique provides a powerful tool for in vivo investigation of sensory information transmitted in a peripheral nerve and facilitates implementation of advanced functional neuromuscular stimulation systems.

Extraction of specific signals with temporal structure

In this work we develop a very simple batch learning algorithm for semiblind extraction of a desired source signal with temporal structure from linear mixtures. Although we use the concept of sequential blind extraction of sources and independent component analysis, we do not carry out the extraction in a completely blind manner; neither do we assume that sources are statistically independent. In fact, we show that the a priori information about the autocorrelation function of primary sources can be used to extract the desired signals (sources of interest) from their linear mixtures. Extensive computer simulations and real data application experiments confirm the validity and high performance of the proposed algorithm.