Comparison on PPCA, KPPCA and MPPCA Based Missing Data Imputing for Traffic Flow

In standard Principal Component Analysis (PCA) comes one problem in addressing the set of incomplete data. The standard PCA procedure on incomplete data is to eliminate (listwise deletion procedure) or using the mean of the variable, this procedure may result in loss information from these observations. Another method used is to integrate Expectation Maximization (EM) to the method of Probabilistic Principal Component Analysis (PPCA). But PPCA can produce overfitting response prediction. In this study discussed the Variational Bayesian Principal Component Analysis (VBPCA) which is a method of development of PPCA method by incorporating prior information from the distribution of the principal components of the model parameters. From the simulation studies by eliminating the data through the concept of missing at random (MAR), obtained results that the value of the correlation scores principal components complete data with the principal component score predicted results PPCA method is superior when compared with VBPCA, as well as to the value of the correlation scores for the various percentages are generally incomplete data. However, judging from the size of a match between the response to predictions by the size normalized root mean square error of prediction (NRMSEP) VBPCA method produces better than PPCA.

This paper proposes a network travel time prediction methodology based on probe data. The model is intended as a tool for traffic management, trip planning, and online vehicle routing, and is designed to be efficient and scalable in calibration and real-time prediction; flexible to changes in network, data, and model extensions; and robust against noisy and missing data. A multivariate probabilistic principal component analysis (PPCA) model is proposed. Spatio-temporal correlations are inferred from historical data based on MLE and an efficient EM algorithm for handling missing data. Prediction is performed in real time by computing the expected distribution of link travel times in future time intervals, conditional on recent current-day observations. A generalization of the methodology partitions the network and applies a distinct PPCA model to each subnetwork. The methodology is applied to the network of downtown Shenzhen, China, using taxi probe data. The model captures variability over months and weekdays as well as other factors. Prediction with PPCA outperforms $k$ -nearest neighbors prediction for horizons from 15 to 45 min, and a hybrid method of PPCA and local smoothing provides the highest accuracy.

Principal Component Analysis (PCA), also known as Proper Orthogonal Decomposition (POD), is one of the prevailing Reduced Order Modeling (ROM) techniques for aerodynamic data analysis. Along with the PCA, its variant for missing data, gappy POD, has recently found its application by transforming problems into missing data problems. In this paper, an alternative based on probability theory, i.e., Probabilistic Principal Component Analysis (PPCA), is employed for aerodynamic data reconstruction problems in lieu of the PCA and the gappy POD. Unlike the PCA, the PPCA generates spanning vectors of low-dimensional space iteratively with an Expectation Maximization (EM) algorithm. The combined algorithm, termed as Expectation-Maximization Probabilistic Principal Component Analysis (EM-PCA), can deal with not only complete data but also incomplete data sets, since the EM algorithm naturally incorporates missing data in its formulation. Therefore, the EM-PCA has potential to be a substitute for both PCA and gappy POD. For illustration, the EM-PCA is applied to complete as well as incomplete snapshot ensembles compiled from aerodynamic simulations, and acquired modes and restored data are verified with those obtained by the PCA and the gappy POD.

In order to evaluate the perceptual quality of images, a full-reference quality index, which is called principal component deviation (PCD), is presented. This research is motivated by the discovery that the filters learned by the probabilistic principal component analysis are closely resemble the neurons of the human visual system. These filters are used as a model of the visual system, which are trained on 100,000 color image patches of size 4×4 by probabilistic principal component analysis. The PCD relates the image quality with the deviation between two sets of features that extracted by the learned filters. Experimental results show that PCD has relatively low computational complexity and high correlation with subjective quality evaluations.

Gaussian mixture model (GMM) techniques are popular for speaker identification. Theoretically, each Gaussian function should have a full covariance matrix. However, the diagonal covariance matrix is usually used because the inverse of diagonal covariance matrix can be easily calculated via expectation maximization (EM) algorithm. This paper proposes a new probabilistic principal component analysis (PPCA) model for speaker identification. The full covariance of speaker’s data is considered. This model is originated from factor analysis theory. The probability distributions using PPCA are well defined. In particular, GMM and PPCA are found to be equivalent when using diagonal covariance matrix. In this study, we derive a novel PPCA model selection and establish models for different speakers. Applying PPCA model selection, we can dynamically determine the numbers of speech features and mixture components. Experiments show that PPCA achieves desirable speaker recognition performance with proper model regularization.

The missing data problem exists in a lot of transportation systems while many traffic applications require accurate traffic data to work well. So, various methods were proposed for traffic data imputation in recent years. However, most of these approaches only consider the information of a single detector. In this paper, we use the temporal and spatial information collected from multiple detectors to improve the traffic data imputation accuracy. Specially, we consider Probabilistic Principal Component Analysis (PPCA) and Mixed Probabilistic Principal Component Analysis (MPPCA), which had been proven to be useful methods to handle data imputation. We examine the performance of these two methods using the temporal and spatial information. Tests show that when only using the spatial information, the errors of these two methods are reduced and MPPCA works even better than PPCA. Moreover, when both of the temporal and spatial information from multiple detectors are used, more imputation accuracy is obtained than only using the spatial information for MPPCA.

In aerospace engineering, various problems such as restoring impaired experimental flow data can be handled by gappy proper orthogonal decomposition (POD). Similarly to gappy POD, probabilistic principal component analysis (PPCA) can approximate missing data with the help of an expectation-maximization (EM) algorithm, yielding an EM algorithm applied to PPCA (EM-PCA). Although both gappy POD and EM-PCA address the same missing date estimation problem, their antithetical formulation perspectives hinder their direct comparison; the development of the former is deterministic whereas that of the latter is probabilistic. In order to effectively differentiate both methods, this research provides a unifying least squares perspective to qualitatively dissect them within a unified least squares framework. By virtue of the unifying least squares perspective, gappy POD and the EM-PCA 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 EM-PCA, unlike gappy POD, dispenses with either a gappy norm or a POD 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 EM-PCA is simpler and thereby more efficient than gappy POD.

Soft sensor modeling with a selective updating strategy for Gaussian process regression based on probabilistic principle component analysis

This study proposes a probabilistic principal component analysis- (PPCA-) based method for online monitoring of water-quality contaminant events by UV-Vis (ultraviolet-visible) spectroscopy. The purpose of this method is to achieve fast and sound protection against accidental and intentional contaminate injection into the water distribution system. The method is achieved first by properly imposing a sliding window onto simultaneously updated online monitoring data collected by the automated spectrometer. The PPCA algorithm is then executed to simplify the large amount of spectrum data while maintaining the necessary spectral information to the largest extent. Finally, a monitoring chart extensively employed in fault diagnosis field methods is used here to search for potential anomaly events and to determine whether the current water-quality is normal or abnormal. A small-scale water-pipe distribution network is tested to detect water contamination events. The tests demonstrate that the PPCA-based online monitoring model can achieve satisfactory results under the ROC curve, which denotes a low false alarm rate and high probability of detecting water contamination events.

A framework is suggested to segment the foreground in image sequences using background subtraction based on the reconstructed background image for each frame. First, the consecutive frames are taken as inputs for a motion estimation algorithm to calculate the motion vector between frames. Second, an incomplete background image can be achieved by cutting moving parts from origin images. Then, all the incomplete background images from the same sequence can be used to model the background by probabilistic principle component analysis with missing data. The background image can be estimated for each frame. Finally, a simple background subtraction can segment the foreground. The effectiveness of our method is demonstrated in different illumination conditions and compared to the commonly used Gaussian mixture models method.

This paper describes methods for recovering time-varying shape and motion of non-rigid 3D objects from uncalibrated 2D point tracks. For example, given a video recording of a talking person, we would like to estimate the 3D shape of the face at each instant, and learn a model of facial deformation. Time-varying shape is modeled as a rigid transformation combined with a non-rigid deformation. Reconstruction is ill-posed if arbitrary deformations are allowed, and thus additional assumptions about deformations are required. We first suggest restricting shapes to lie within a low-dimensional subspace, and describe estimation algorithms. However, this restriction alone is insufficient to constrain reconstruction. To address these problems, we propose a reconstruction method using a Probabilistic Principal Components Analysis (PPCA) shape model, and an estimation algorithm that simultaneously estimates 3D shape and motion for each instant, learns the PPCA model parameters, and robustly fills-in missing data points. We then extend the model to model temporal dynamics in object shape, allowing the algorithm to robustly handle severe cases of missing data.

Process Monitoring with Sparse Bayesian Model for Industrial Methanol Distillation

Ultrasound (US) imaging is the initial phase in the preliminary diagnosis for the treatment of kidney diseases, particularly to estimate kidney size, shape and position, to give information about kidney function, and to help in diagnosis of abnormalities like cysts, stones, junctional parenchyma and tumors which is shown in Figs. 7–9. This study proposes Grey Level Co-occurrence Matrix (GLCM)-based Probabilistic Principal Component Analysis (PPCA) and Artificial Neural Network (ANN) method for the classification of kidney images. Grey Wolf Optimization (GWO) is used to update the current positions of abnormal kidney images in the discrete searching space, thus getting the optimal feature subset for better classification purposes based on Feed Forward Neural Network (FFNN). The scanned image is pre-processed and the required features are extracted by GLCM, among those, some features are selected by PPCA. Feed Forward Back propagation Neural Network (FFBN) is used to classify the normalities and abnormalities in the part of kidney images. The proposed methodology is implemented in MATLAB platform and the analyzed result produces 98% accuracy using GWO-FFBN technique.

Rolling element bearing fault detection using PPCA and spectral kurtosis

A Motion Data Automatic Segmentation using a Probabilistic/Kernel principal component analysis (P/KPCA) method is proposed. This approach utilizes Kernel principal component analysis (KPCA) to construct a kernel function while using Probabilistic principal component analysis (PPCA) to reduce motion noise. Formulate the feature function to obtain the derivative of projection error, and detect the segmentation point of data through analyzing the change of geometric features to realize the automatic segmentation. It is indicated in the experiment that the motion capture technique has certain feasibility. The paper presents the automatic segmentation approach of the motion capture data, in which the motion data is automatic segmented through KPCA combined with PPCA to reduce the dimension and project the 56 dimensional data in 2 dimensional space; formulate the feature function to obtain the derivative of projection error, and detect the segmentation point of data through analyzing the change of geometric features to realize the automatic segmentation. It is indicated in the experiment that the motion capture technique has certain feasibility.