Expectation Maximization Principal Component Analysis Research Articles

Multi-channel LFP recording data compression scheme using Cooperative PCA and Kalman Filter

The power consumption and wireless communication bandwidth restrict the channel count and amount of high-resolution intracortical Brain–Computer Interfaces(iBCIs). So, it is necessary to compress the captured data before transmission. Here, we propose a multi-channel data compression method on the correlation between channels for Local Field Potential(LFPs) recorded through Utah microelectrode arrays. The method improves the compression performance of the Stepwise Expectation-Maximization Principal Component Analysis(SEM-PCA) algorithm by implementing the Kalman filter. The multi-channel correlation is sampled with high resolution while the uniqueness of each channel is retained at a low rate. Then, the two parts of information are fused by the Kalman filter, and finally, the data is reconstructed with high precision and high rate. Our testing results verified the effectiveness of the proposed compression scheme. Compared to the traditional SEM-PCA, this algorithm significantly improved neural LFP reconstruction accuracy from 79.61% to 88%.

A New Spatial Filtering Algorithm for Noisy and Missing GNSS Position Time Series Using Weighted Expectation Maximization Principal Component Analysis: A Case Study for Regional GNSS Network in Xinjiang Province

Common Mode Error (CME) presents a kind of spatially correlated error that is widespread in regional Global Navigation Satellite System (GNSS) networks and should be eliminated during postprocessing of a GNSS position time series. Several spatiotemporal filtering methods have been developed to mitigate the effects of CME. However, such methodologies become inappropriate when missing and noisy data exists. In this research, we introduce a novel spatial filtering algorithm called Weighted Expectation Maximization Principal Component Analysis (WEMPCA) for detecting and removing CME from noisy GNSS position time series with missing values, among which formal errors of daily GNSS solutions are utilized to weight the input data. Compared with traditional PCA and the special case of EMPCA, simulation experiments demonstrate that the new WEMPCA algorithm always has outstanding performance over others. The WEMPCA algorithm was then successfully used to extract the CME from real noisy and missing GNSS position time series in Xinjiang province. Our results show that only the first principal component exhibits significant spatial response, with average values of 70.11%, 66.53%, and 52.45% for North, East, and Up (NEU) components, respectively, indicating that it represents the CME of this region. After removing CME, the canonical correlation coefficients and root mean square error of GNSS residual time series, as well as the amplitudes of power-law noises (PLN), are obviously decreased in all three directions. However, the white noise (WN) amplitudes are found to diminish exclusively in the North and East component, not in the Up components. Moreover, the average velocity differences before and after filtering CME are 0.19 mm/year, 0.03 mm/year, and −0.56 mm/year for the NEU components, respectively, indicating that CME has an influence on the GNSS station velocity estimation. The velocity uncertainty is also reduced by 43.51%, 38.64%, and 40.39% on average for the NEU components, respectively, implying that the velocity estimates are more reliable and accurate after removing CME. Therefore, we conclude that the new WEMPCA approach provides an efficient solution to detect and mitigate CME from the noisy and missing GNSS position time series.

Pelton Wheel Bucket Fault Diagnosis Using Improved Shannon Entropy and Expectation Maximization Principal Component Analysis

Pelton Wheel Bucket Fault Diagnosis Using Improved Shannon Entropy and Expectation Maximization Principal Component Analysis

The point spread function reconstruction by using Moffatlets — I

Shear measurement is a crucial task in current and future weak lensing survey projects. The reconstruction of the point spread function (PSF) is one of the essential steps involved in this process. In this work, we present three different methods, Gaussianlets, Moffatlets and Expectation Maximization Principal Component Analysis (EMPCA), and quantify their efficiency on PSF reconstruction using four sets of simulated Large Synoptic Survey Telescope (LSST) star images. Gaussianlets and Moffatlets are two different sets of basis functions whose profiles are based on Gaussian and Moffat functions respectively. EMPCA is a statistical method performing an iterative procedure to find the principal components (PCs) of an ensemble of star images. Our tests show that: (1) Moffatlets always perform better than Gaussianlets. (2) EMPCA is more compact and flexible, but the noise existing in the PCs will contaminate the size and ellipticity of PSF. By contrast, Moffatlets keep the size and ellipticity very well.

Memory Efficient PCA Methods for Large Group ICA.

Principal component analysis (PCA) is widely used for data reduction in group independent component analysis (ICA) of fMRI data. Commonly, group-level PCA of temporally concatenated datasets is computed prior to ICA of the group principal components. This work focuses on reducing very high dimensional temporally concatenated datasets into its group PCA space. Existing randomized PCA methods can determine the PCA subspace with minimal memory requirements and, thus, are ideal for solving large PCA problems. Since the number of dataloads is not typically optimized, we extend one of these methods to compute PCA of very large datasets with a minimal number of dataloads. This method is coined multi power iteration (MPOWIT). The key idea behind MPOWIT is to estimate a subspace larger than the desired one, while checking for convergence of only the smaller subset of interest. The number of iterations is reduced considerably (as well as the number of dataloads), accelerating convergence without loss of accuracy. More importantly, in the proposed implementation of MPOWIT, the memory required for successful recovery of the group principal components becomes independent of the number of subjects analyzed. Highly efficient subsampled eigenvalue decomposition techniques are also introduced, furnishing excellent PCA subspace approximations that can be used for intelligent initialization of randomized methods such as MPOWIT. Together, these developments enable efficient estimation of accurate principal components, as we illustrate by solving a 1600-subject group-level PCA of fMRI with standard acquisition parameters, on a regular desktop computer with only 4 GB RAM, in just a few hours. MPOWIT is also highly scalable and could realistically solve group-level PCA of fMRI on thousands of subjects, or more, using standard hardware, limited only by time, not memory. Also, the MPOWIT algorithm is highly parallelizable, which would enable fast, distributed implementations ideal for big data analysis. Implications to other methods such as expectation maximization PCA (EM PCA) are also presented. Based on our results, general recommendations for efficient application of PCA methods are given according to problem size and available computational resources. MPOWIT and all other methods discussed here are implemented and readily available in the open source GIFT software.

Incremental expectation maximization principal component analysis for missing value imputation for coevolving EEG data

Missing values occur in bio-signal processing for various reasons, including technical problems or biological characteristics. These missing values are then either simply excluded or substituted with estimated values for further processing. When the missing signal values are estimated for electroencephalography (EEG) signals, an example where electrical signals arrive quickly and successively, rapid processing of high-speed data is required for immediate decision making. In this study, we propose an incremental expectation maximization principal component analysis (iEMPCA) method that automatically estimates missing values from multivariable EEG time series data without requiring a whole and complete data set. The proposed method solves the problem of a biased model, which inevitably results from simply removing incomplete data rather than estimating them, and thus reduces the loss of information by incorporating missing values in real time. By using an incremental approach, the proposed method also minimizes memory usage and processing time of continuously arriving data. Experimental results show that the proposed method assigns more accurate missing values than previous methods.

Unifying Perspective for Gappy Proper Orthogonal Decomposition and Probabilistic Principal Component Analysis

In aerospace engineering, various problems such as restoring impaired experimental flow data can be handled by gappy proper orthogonal decomposition. Similar to gappy proper orthogonal decomposition, probabilistic principal component analysis can approximate missing data with the help of an expectation-maximization algorithm, yielding an expectation-maximization algorithm for probabilistic principal component analysis (expectation-maximization principal component analysis). Although both gappy proper orthogonal decomposition and expectationmaximization principal component analysis address the same missing-data-estimation problem, their antithetical formulation perspectives hinder their direct comparison; the development of the former is deterministic, whereas that of the latter is probabilistic. To effectively differentiate both methods, this research provides a unifying leastsquares perspective to qualitatively dissect them within a unified least-squares framework. By virtue of the unifying least-squares perspective, gappy proper orthogonal decomposition and the expectation-maximization principal component analysis turn out to be similar in that they are twofold: basis and least-squares coefficient evaluations. On the other hand, they are dissimilar because the expectation-maximization principal component analysis, unlike gappy proper orthogonal decomposition, dispenses with either a gappy norm or a proper orthogonal decomposition basis. To illustrate the theoretical analysis of both methods, numerical experiments using simple and complex data sets quantitatively examine their performance in terms of convergence rates and computational cost. Finally, comprehensive comparisons, including theoretical and numerical aspects, establish that the expectationmaximization principal component analysis is simpler and thereby more efficient than gappy proper orthogonal decomposition.

Predictive modeling of pharmaceutical processes with missing and noisy data

AbstractLack of knowledge of the first principles, that describe the behavior of processed particulate mixtures, has created significant attention to data‐driven models for characterizing the performance of pharmaceutical processes—which are often treated as black—box operations. Uncertainty contained in the experimental data sets, however, can decrease the quality of the produced predictive models. In this work, the effect of missing and noisy data on the predictive capability of surrogate modeling methodologies such as Kriging and Response Surface Method (RSM) is evaluated. The key areas that affect the final error of prediction and the computational efficiency of the algorithm were found to be: (a) the method used to assign initial estimate values to the missing elements and (b) the iterative procedure used to further improve these initial estimates. The proposed approach includes the combination of the most appropriate initialization technique and the Expectation Maximization Principal Component Analysis algorithm to impute missing elements and minimize noise. Comparative analysis of the use of different initial imputation techniques such as mean, matching procedure, and a Kriging‐based approach proves that the two former used approaches give more accurate, “warm‐start” estimates of the missing data points that can significantly reduce computational time requirements. Experimental data from two case studies of different unit operations of the pharmaceutical powder tablet production process (feeding and mixing) are used as examples to illustrate the performance of the proposed methodology. Results show that by introducing an extra imputation step, the pseudo complete data sets created, produce very accurate predictive responses, whereas discarding incomplete observations leads to loss of valuable information and distortion of the predictive response. Results are also given for different percentages of missing data and different missing patterns. © 2010 American Institute of Chemical Engineers AIChE J, 2010