Traditional Principal Component Analysis Method Research Articles

Principal component analysis for non-stationary time series based on detrended cross-correlation analysis

The principal component analysis (PCA) has been extensively studied and proved to be a sophisticated technique for the dimension reduction and the index construction of multidimensional stationary time series. However, the PCA method is often susceptible to external trends of original variables in real-world applications, when data present non-stationarity. In this paper, we propose a non-stationary principal component analysis (NSPCA) for multidimensional time series in the presence of non-stationarity. The new method is based on detrended cross-correlation analysis. We theoretically derive the coefficients relating to the combinations of original variables in the NSPCA method. We also apply the NSPCA method to the autoregressive model, Gaussian distributed variables as well as stock sectors in Chinese stock markets, and compare it with the traditional PCA method. We find that the NSPCA method has the advantage to detect intrinsic cross-correlations among variables and identify the patterns of data in the case of non-stationarity, minimizing the effects of external trends which often make the PCA yields few components assigning similar loadings to all variables.

On-line monitoring of batch processes using generalized additive kernel principal component analysis

Based on analyzing the special structure of three-way array and generalizing the concept of additive kernels, this paper proposes the generalized additive kernel principal component analysis (GAKPCA) method for on-line monitoring of batch processes. The proposed method is a special nonlinear principal component analysis (PCA) method which can handle the nonlinear relationships between different monitoring variables and/or time intervals. It inherits the good properties of traditional multiway PCA (MPCA) method for on-line monitoring, and solves some problems that exist in traditional multiway kernel PCA (MKPCA) method. For example, based on the decomposition of batch samples in the feature space, the total squared prediction error (SPE) statistic of an entire batch can be divided into K components corresponding to K time intervals respectively, and its score vectors can be directly estimated on-line by the least squares approach without filling the unknown observations. As a special case, when the Gaussian kernel is used as the kernel function at each time interval, the proposed method is connected with the concept of correntropy which can bring robustness to our method. The experimental results on a fed-batch penicillin fermentation process demonstrate the validity of the proposed GAKPCA-based on-line monitoring method.

Multiple Component Analysis and Its Application in Process Monitoring With Prior Fault Data

Traditional principal component analysis (PCA) based process monitoring method is unsupervised learning method, which builds a statistical model only based on the normal operating dataset. However, in industrial process database, there are also some faulty operating datasets available which are omitted by PCA but may be helpful for fault detection performance improvement. To better utilize both normal operating data and prior faulty data, a modified PCA method, called multiple component analysis (MCA) is presented for monitoring process faults. MCA statistical modelling involves two kinds of data feature extractions. Firstly, based on normal operating data, MCA applies conventional PCA transformation to obtain the principal component features, which describe normal data distribution directions. Then, for the known fault data, non-local preservation projection technique is used to compute fault discriminant features, which describe the fault data distribution directions. Lastly these features are integrated to construct monitoring statistics for fault detection. Simulations on Tennessee Eastman benchmark process show that the proposed method outperforms traditional PCA method in terms of fault detection performance.

Steady State Power Quality Evaluation of Grid-Connected Photovoltaic System Based on Improved Principal Component Analysis Method

The comprehensive quantified evaluation of power quality is one of the main foundations in power quality appraisal. This paper presents the improved principal component analysis (PCA) method to evaluate steady state power quality of grid-connected photovoltaic system synthetically. Some improvements are made to traditional PCA method for the purpose of taking subjective factors into account and normalizing the final assessment results. Furthermore, the assessment results are graded on the basis of the Chinese national standard. The result shows that this method is simple, practical and efficient on power quality comprehensive evaluation. This method is the basis of a number of patents on power quality evaluation. Keywords: Comprehensive evaluation, G1 method, principal component analysis, power quality.

Adaptive neuro-fuzzy inference system based faulty sensor monitoring of indoor air quality in a subway station

A new faulty sensor monitoring method based on an adaptive neuro-fuzzy inference system (ANFIS) is proposed to improve the monitoring performance of indoor air quality (IAQ) in subway stations. To enhance network performance, a data preprocessing step for detecting outliers and treating missing data is implemented before building the monitoring models. A squared prediction error (SPE) monitoring index based on the ANFIS prediction model is proposed to detect sensor faults, where the confidence limit for the SPE index is determined by using the kernel density estimation method. The proposed monitoring approach is applied to detect four typical kinds of sensor faults that may happen in the indoor space of a subway. The prediction results in the subway system indicate that the prediction accuracy of an ANFIS structure with 15 clusters is superior to that of an appropriate artificial neural network structure. Specifically, when detecting one kind of complete failure fault that happened within the normal range, the detection performance of ANFIS-based SPE outperforms that of a traditional principal component analysis method. The developed sensor monitoring technique could work well for other kinds of sensor faults resulting from a noxious underground environment.

Facial Recognition Using Tensor-Tensor Decompositions

A tensor is a multidimensional array. First-order tensors and second-order tensors can be viewed as vectors and matrices, respectively. Tensors of higher order, with the ability to include more information, appear more frequently nowadays in image and signal processing, data mining, biomedical engineering, and so on. With the recent work of Kilmer and Martin, familiar matrix-based factorizations in linear algebra can be extended in a straightforward way to third-order tensors based on their new tensor multiplication and concepts. Our method has an advantage over a popular tensor-based face recognition algorithm called TensorFaces, which is based on the higher-order SVD of an arrangement of the images in a database, in that it does not require a least squares solve for the coefficients. In this paper, we give a brief introduction to the new tensor framework and apply the induced tensor decompositions to the application of facial recognition. In the numerical results, we compare our new approaches with the traditional principal component analysis method based on matrix decomposition (also known as eigenfaces) and with TensorFaces.

Performance Monitoring of MPC Based on Dynamic Principal Component Analysis

AbstractA unified framework based on the dynamic principal component analysis (PCA) is proposed for performance monitoring of constrained multi-variable model predictive control (MPC) systems. In the proposed performance monitoring framework, the dynamic PCA based performance benchmark is adopted for performance assessment, while performance diagnosis is carried out using a unified weighted dynamic PCA similarity measure. Simulation results obtained from the case study of the Shell process demonstrate that the use of the dynamic PCA performance benchmark can detect the performance deterioration more quickly compared with the traditional PCA method, and the proposed unified weighted dynamic PCA similarity measure can correctly locate the root cause for poor performance of MPC controller.

Symplectic Principal Component Analysis: A New Method for Time Series Analysis

Experimental data are often very complex since the underlying dynamical system may be unknown and the data may heavily be corrupted by noise. It is a crucial task to properly analyze data to get maximal information of the underlying dynamical system. This paper presents a novel principal component analysis (PCA) method based on symplectic geometry, called symplectic PCA (SPCA), to study nonlinear time series. Being nonlinear, it is different from the traditional PCA method based on linear singular value decomposition (SVD). It is thus perceived to be able to better represent nonlinear, especially chaotic data, than PCA. Using the chaotic Lorenz time series data, we show that this is indeed the case. Furthermore, we show that SPCA can conveniently reduce measurement noise.

Rapid Authentication of Olive Oil Adulteration by Raman Spectrometry

The authentication of olive oil and its adulteration with lower priced oils are still serious problems in the olive oil industry. In this study, a method based on the intensity ratio of the Raman spectroscopy vibration bands, especially on the intensity ratio of the cis ( ==C-H) and cis (C=C) bonds normalized by the band at 1441 cm(-1) (CH(2)), was established to authenticate genuine/fake olive oil. These intensity ratios of the vibration bands given in the form of a two-dimensional chart allow first the discrimination between the various grades of olive oil and the seed oils and then the detection of olive oil fraud by the line of y = 0.7, which is observed under most experiments and dot charts. This method can reliably distinguish the genuine olive oils from the olive oils containing 5% (volume percentage) or more of other edible oils, such as soybean oil, rapeseed oil, sunflower seed oil, or corn oil. Compared to the traditional principal component analysis method, this method is more intuitive, more precise, and easier to use. Moreover, this method also has the advantages of simplicity efficiency and has no need for sample preprocessing, being especially suitable for on-site testing in field applications.

Fusion algorithm for multi‐sensor images based on PCA and lifting wavelet transformation

Anovel fast image fusion scheme based on principal component analysis (PCA) and lifting wavelet transformation (LWT) is proposed. Firstly, the principal component images of the registered original colour image are obtainedby PCA transformation. Then, the first principal component image and near infrared imagery are merged using lifting wavelet transformation (LWT) based on regional features. The fused image replaces the first principal component of the visual colour image. Finally, the final composite image is obtained by inverse PCA transformation. Compared with other fusing algorithms, the experimental results demonstrate that this fusion scheme is more effective in fusing image quality than the traditional PCA or wavelet transformation fusion methods. The obtained image conforms to human vision features. The standard deviation (ó) and average gradients (g) are a little smaller with this fusion algorithm than the wavelet transformation method, but they are bigger with this fusion algorithm than the PCA method; however, entropy (EN) and correlation coefficients are larger with this fusion algorithm than with the PCA or wavelet transformation method. The fusion image contains more information and stronger spatial detail performance. The merged image is more advantageous to be further analysed, understood and recognised.

Supervised locality pursuit embedding for pattern classification

In pattern recognition research, dimensionality reduction techniques are widely used since it may be difficult to recognize multidimensional data especially if the number of samples in a data set is not large comparing with the dimensionality of data space. Locality pursuit embedding (LPE) is a recently proposed method for unsupervised linear dimensionality reduction. LPE seeks to preserve the local structure, which is usually more significant than the global structure preserved by principal component analysis (PCA) and linear discriminant analysis (LDA). In this paper, we investigate its extension, called supervised locality pursuit embedding (SLPE), using class labels of data points to enhance its discriminant power in their mapping into a low dimensional space. We compare the proposed SLPE approach with traditional LPE, PCA and LDA methods on real-world data sets including handwritten digits, character data set and face images. Experimental results demonstrate that SLPE is superior to other three methods in terms of recognition accuracy.