Dynamics of Generalized PCA and MCA Learning Algorithms

Convergence analysis of a simple minor component analysis algorithm

A unified learning algorithm to extract principal and minor components

The incidence and mortality rate of the primary liver cancer are very high and its postoperative metastasis and recurrence have become important factors to the prognosis of patients. Circulating tumor cells (CTC), as a new tumor marker, play important roles in the early diagnosis and individualized treatment. This paper presents an effective method to distinguish liver cancer based on the cellular scattering spectrum, which is a non-fluorescence technique based on the fiber confocal microscopic spectrometer. Combining the principal component analysis (PCA) with back propagation (BP) neural network were utilized to establish an automatic recognition model for backscatter spectrum of the liver cancer cells from blood cell. PCA was applied to reduce the dimension of the scattering spectral data which obtained by the fiber confocal microscopic spectrometer. After dimensionality reduction by PCA, a neural network pattern recognition model with 2 input layer nodes, 11 hidden layer nodes, 3 output nodes was established. We trained the network with 66 samples and also tested it. Results showed that the recognition rate of the three types of cells is more than 90%, the relative standard deviation is only 2.36%. The experimental results showed that the fiber confocal microscopic spectrometer combining with the algorithm of PCA and BP neural network can automatically identify the liver cancer cell from the blood cells. This will provide a better tool for investigating the metastasis of liver cancers in vivo, the biology metabolic characteristics of liver cancers and drug transportation. Additionally, it is obviously referential in practical application.

In this work, a gas sensor array has been designed and developed comprising of Pt, Cu and Ag decorated TiO2 and ZnO functionalized GaN nanowires using industry standard top-down fabrication approach. The receptor metal/metal-oxide combinations within the array have been determined from our prior molecular simulation results using first principle calculations based on density functional theory (DFT). The gas sensing data was collected for both singular and mixture of NO2, ethanol, SO2 and H2 in presence of H2O and O2 gases under UV light at room temperature. Each gas produced a unique response pattern across the sensors within the array by which precise identification of cross-sensitive gases is possible. After pre-processing of raw data, unsupervised principal component analysis (PCA) technique was applied on the array response. It is found that, each analyte gas forms a separate cluster in the score plot for all the target gases and their mixtures, indicating a clear discrimination among them. Then, four supervised machine learning algorithms such as- Decision Tree, Support Vector Machine (SVM), Naive Bayes (kernel) and k-Nearest Neighbor (k-NN) were trained and optimized using their significant parameters with our array dataset for the classification of gas type. Results indicate that the optimized SVM and NB classifier models exhibited 100% classification accuracy on test dataset. Practical applicability of the considered algorithms has been discussed as well. Moreover, this array device works at room-temperature using very low power and low-cost UV light-emitting diode (LED) as compared to high power consuming commercially available metal-oxide sensors.

Prediction model of end-point phosphorus content in BOF steelmaking process based on PCA and BP neural network

This paper introduces a chaotic encryption system using a principal component analysis (PCA) neural network. The PCA neural network can produce the chaotic behaviors under certain conditions so that it serves as a pseudo-random number generator to generate random private keys. In this encryption system, the one-time pad encryption method is used, which is regarded as the most secure encryption method. The proposed system can encrypt any kind of data. The security and high performance of encryption are illustrated via some simulations.

Algorithms that extract the principal or minor components of a signal are widely used in signal processing and control applications. This paper explores new frameworks for generating learning rules for iteratively computing the principal and minor components (or subspaces) of a given matrix. Stability analysis using Lyapunov theory and La Salle invariance principle is provided to determine regions of attraction of these learning rules. Among many derivations, it is specifically shown that Oja's rule and many variations of it are asymptotically globally stable. Lyapunov stability theory is also applied to weighted learning rules. Some of the essential features for the proposed MCA/PCA learning rules are that they are self normalized and can be applied to non-symmetric matrices. Exact solutions for some nonlinear dynamical systems are also provided

Within the last years various principal component analysis (PCA) algorithms have been proposed. In this paper we use a general framework to describe those PCA algorithms which are based on Hebbian learning. For an important subset of these algorithms, the local algorithms, we fully describe their equilibria, where all lateral connections are set to zero and their local stability. We show how the parameters in the PCA algorithms have to be chosen in order to get an algorithm which converges to a stable equilibrium which provides principal component extraction.

Remote sensing technology provides an unprecedented tool for the continuous and real-time monitoring of atmospheric SO2 from volcanic eruption and anthropogenic emission. The Global Ozone Monitoring Experiment (GOME), SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY), and Ozone Monitoring Instrument (OMI) have high SO2 monitoring capability. The OMI, which was launched on the EOS/Aura platform in July 2004, has the same hyperspectral measurements as the GOME and SCIAMACHY, but offers the improved spatial resolution at nadir (1324 km2) and daily global coverage for short-lifetime SO2. For OMI operational SO2 planetary boundary layer (PBL) retrieval, the previous band residual difference (BRD) algorithm has been replaced by principal component analysis (PCA) algorithm, which effectively reduces the systematic biases in SO2 column retrievals. However, there are few studies on the evaluations and validations of PCA SO2 retrievals over China, and the long-term comparisons with BRD SO2 retrievals also need to be conducted. In this study, the accuracies of PCA and BRD SO2 retrievals are validated by using ground-based multi axis differential optical absorption spectroscopy (MAX-DOAS) located in Beijing, and regional atmospheric modeling system, community multi-scale air quality (RAMS-CMAQ) modeling system model which can simulate the vertical distribution of atmospheric SO2. Moreover, BRD and PCA SO2 retrievals from oceanic area, eastern China and Reunion volcanic eruption are compared to find the long-term trend and spatiotemporal differences between SO2 columns. Finally, the uncertainty of SO2 retrieval, caused by measurement errors, band selection and input parameter errors in radiative transfer model, are analysed to understand the limitations of BRD and PCA algorithms. Results show that both PCA and BRD SO2 retrievals over Beijing are lower than ground-based MAX-DOAS measurements of SO2. PCA and BRD SO2 retrievals over eastern China are lower than the simulated SO2 columns from RAMS-CMAQ in winter 2008, but in July and August BRD SO2 columns are higher than RAMS-CMAQ simulations. The values of SO2 columns from BRD over China are more consistent with those from ground-based MAX-DOAS and RAMS-CMAQ model than from PCA. Although PCA algorithm effectively reduces the noise in SO2 column retrieval, SO2 columns from PCA over China are lower than those from BRD. For oceanic area where SO2 amount is nearly zero, the standard deviation of PCA results is lower than that of BRD, but the absolute value of averaged PCA SO2 column is larger than that of BRD. In the case of Reunion volcanic eruption with SO2 columns larger than 25 DU, the BRD SO2 columns are lower than PCA retrievals. Meanwhile, with the increase of SO2 column, the difference between BRD and PCA SO2 retrievals increases. Detailed uncertainty analysis shows the influences of measurement errors, band selection and inputs of radiative transfer model on the retrieval results. This study is important for developing the retrieval algorithm, and can also improve the application of OMI SO2 products.

Principal Component Analysis Network (PCANet) is a feature learning algorithm which is widely used in face recognition and object classification. However, original PCANet still has some shortages. One is that PCA algorithm only extracts features by considering the global structure. The other lies in that the original PCANet only employs one particular single layer convolutional results, which loses the information of other convolutional layers. In this paper, we propose a new simple and efficient convolutional neural network called global and local structure network (GLSNet) to address the problems. The network extracts the features both from the global structure and the local structure of the original data space. Specifically, a principal component analysis (PCA) convolutional layer which learns the filters by PCA algorithm is used to remove the noises and redundant information at the first stage. Then at the second stage, another PCA convolution is added to extract features by considering the global structure. As for the local structure, we use the neighborhood preserving embedding (NPE) algorithm to learn the convolutional filters. At the output stage, the global structure feature extracted by PCA convolution and the local structure feature extracted by NPE convolution is concatenated as a united feature. Furthermore, the first layer convolutional feature is also taken into consideration to obtain shallow-level information. Finally, these features are concatenated as a united feature, and a spatial pyramid pooling layer is followed to pool above the united features. To test the effectiveness of the proposed algorithm, the experiments on some image datasets, including three types: human face dataset, object dataset, and handprinted dataset, proceeded. And it performs better than the original PCANet and some improvement algorithms of PCANet, such as PLDANet, and MMPCANet.

The prognosis of childhood nephrotic syndrome directly hinges on the accurate prediction of negative conversion days (NCDs). Therefore, this paper designs a hybrid approach of principal component analysis (PCA) and backpropagation (BP)-adaptive boosting (AdaBoost) neural network (NN), and applies the method to predict the NCDs for children with nephrotic syndrome. Specifically, PCA method was employed for dimension reduction. Six principal components were extracted from multiple physiological features, and taken as input variables of three-tiered neural networks. The boosted predictor of BP-AdaBoost model, together with three predictors of BP NN, support vector machine (SVM) and radial basis function (RBF) NN, was trained for NCDs prediction. The experimental results show that the predictor of BP-AdaBoost NN achieves the mean absolute error of 0.2334, the mean relative error of 3.2789%, the SD of 4.6804 and the RSD of 50.8053% in NCDs prediction, and it outperforms other predictors of BP NN, SVM and RBF NN on both accuracy and precision. Furthermore, comparison experiments are conducted on PCA processed testing data and raw testing data for BP-AdaBoost NN and demonstrate the excellent effect of PCA. The hybrid approach of PCA and BP-AdaBoost NN is simple and reliable for NCDs prediction of childhood nephrotic syndrome, and it can help pediatricians prognose childhood nephrotic syndrome accurately and further provide patients with better care and treatment.

This article presents a method based on support vector machines (SVMs) and the Osuna–Platt algorithm used to diagnose the ischemic heart disease. It also includes the necessary concepts from the optimization theory which make it possible to formulate the problem for support vectors and the Osuna–Platt algorithm applied. Next, a principal component analysis (PCA) algorithm used is also presented. Heart images acquired using Single Photon Emission Computed Tomography (SPECT) have been used in the experimental part. Results of classifying cardiac SPECT images using SVM, PCA and neural networks are compared here with those obtained using another method of machine learning – CLIP3 – a combination of the decision tree algorithm and the rule induction algorithm. Tests against an SPECT image database have shown that SVMs are generally more accurate and specific, while the PCA algorithm is the most sensitive for all data sets analysed in this research project.

A de-noising method based on PCA (Principal Component Analysis) is proposed to suppress the noise of LLL (Low-Light Level) image. At first, the feasibility of de-noising with the algorithm of PCA is analyzed in detail. Since the image data is correlated in time and space, it is retained as principal component, while the noise is considered to be uncorrelated in both time and space and be removed as minor component. Then some LLL images is used in the experiment to confirm the proposed method. The sampling number of LLL image which can lead to the best de-noising effects is given. Some performance parameters are calculated and the results are analyzed in detail. To compare with the proposed method, some traditional de-noising algorithm are utilized to suppress noise of LLL images. Judging from the results, the proposed method has more significant effects of de-noising than the traditional algorithm. Theoretical analysis and experimental results show that the proposed method is reasonable and efficient.

Multitemporal Landsat TM imagery were classified to extract land cover information using principal component analysis (PCA) and backpropagation (BP) algorithm of artificial neural network. Data used are two Landsat TM data of in Jan. 1, 1991 (Data I) and May 9, 1994 (Data II). Twelve bands data were compressed to 4 bands data by the first and second PCA. Approximately 95 percent of the total variance of each Landsat TM data was included resulting from the first and second component analysis. Analyzed data through the PCA were classified by the BP training algorithm of artificial neural network. As a result of classification, it is concluded that this approach will become an attractive and effective method in extracting land cover or land use information using multitemporal Landsat TM data.

The principal components, i.e. the eigenvectors corresponding to the largest eigenvalues of an autocorrelation matrix, contain the desired information of the considered signal. The principal component analysis (PCA) algorithms have a widespread application field in signal and image processing. We propose an invariant-norm algorithm with complex values. The solutions of the corresponding averaging differential equations converge to the principal eigenvectors of the autocorrelation matrix. This PCA algorithm is suitable for complex values of the input and the weight vectors. In addition, we consider a possibility to reduce the computational complexity of the proposed algorithm.