Study of signal process of gas sensor array with nonlinear principal component analysis

Complex-valued neural networks for nonlinear complex principal component analysis

This paper presents a nonlinear principal component analysis (PCA) that identifies underlying sources causing the expression of spatial modes or patterns of activity in neuroimaging time-series. The critical aspect of this technique is that, in relation to conventional PCA, the sources can interact to produce (second-order) spatial modes that represent the modulation of one (first-order) spatial mode by another. This nonlinear PCA uses a simple neural network architecture that embodies a specific form for the nonlinear mixing of sources that cause observed data. This form is motivated by a second-order approximation to any general nonlinear mixing and emphasizes interactions among pairs of sources. By introducing these nonlinearities principal components obtain with a unique rotation and scaling that does not depend on the biologically implausible constraints adopted by conventional PCA. The technique is illustrated by application to functional (positron emission tomography and functional magnetic resonance imaging) imaging data where the ensuing first- and second-order modes can be interpreted in terms of distributed brain systems. The interactions among sources render the expression of any one mode context-sensitive, where that context is established by the expression of other modes. The examples considered include interactions between cognitive states and time (i.e. adaptation or plasticity in PET data) and among functionally specialized brain systems (using a fMRI study of colour and motion processing).

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.

Nonlinear principal component analysis (NLPCA) is known as a nonlinear generalization of the standard principal component analysis (PCA). Since nonlinear PCA is a non-unique concept, it is discussed, how nonlinear PCA can be defined as a nonlinear feature extraction technique most similar to linear PCA. The nonlinear reduction of a data set from its original dimension to the intrinsic dimension of the data is one aspect, but we also request that the nonlinear features spanning this intrinsic data space are hierarchically arranged similar to the linear features of PCA. Thus, such nonlinear PCA is a powerful pre-processing step. It can be used as nonlinear sphering (whitening) or it can be considered as a smoothing method which removes nonlinear correlations between variables. Nonlinear PCA can be performed by minimizing a hierarchical error function. This error function is applied to the autoencoder which is a multi-layer perceptron used in auto-associative mode to perform the identity mapping.

An SVM-like framework provides a novel way to learn linear principal component analysis (PCA). Actually it is a weighted PCA and leads to a semi-definite optimization problem (SDP). In this paper, we learn linear and nonlinear PCA with linear programming problems, which are easy to be solved and can obtain the unique global solution. Moreover, two algorithms for learning linear and nonlinear PCA are constructed, and all principal components can be obtained. To verify the performance of the proposed method, a series of experiments on artificial datasets and UCI benchmark datasets are accomplished. Simulation results demonstrate that the proposed method can compete with or outperform the standard PCA and kernel PCA (KPCA) in generalization ability but with much less memory and time consuming.

This research uses eigenvalue characteristics of nonlinear principal component analysis (NLPCA) and principal component analysis (PCA) to investigate total electron content (TEC) anomalies associated with Taiwan’s Chi-Chi earthquake of 21 September 1999 (LT) (M w=7.6). The transforms are used for ionospheric TEC from 01 August to 20 September 1999 (local time) using data from 13 GPS receivers. The data were collected at 22°N–26°N Lat. and 120°E–122°E Long.. Applying the NLPCA to the multi-channel total electron content records of GPS receivers, the earthquake-associated TEC anomalies were represented by large principal eigenvalues of NLPCA (>0.5 in a normalized set) on 14 August and 17, 18, and 20 September, with allowance given for the Dst index, which was quiet for the study period. Comparisons were then made with other researchers who also found TEC anomalies on September 17, 18, and 19 associated with the Chi-Chi earthquake, which cannot be detected by PCA. Consideration is also given for reported ground level geomagnetic field activity that occurred between mid-August and late October, leading up to and including the Chi-Chi and Chia-Yi earthquakes, which are associated with the same series of faults. It is possible that Aug. 14 is representative of an earthquake-associated TEC anomaly. This is an interesting result given how much earlier than the earthquake it occurred.

Aiming at the radiated electromagnetic interference (EMI) noise of electronic equipment, a novel method of radiated EMI noise analysis based on non-linear principal component analysis (NLPCA) algorithm is proposed in this paper. In order to obtain multiple independent common-mode / differential-mode radiated sources, and to find the sources that cause the radiated noises that exceed the limit of standard, NLPCA algorithm is used to process the near-field radiated signals superimposed by multiple radiated sources. The simulation results show that NLPCA can successfully screen out the radiated EMI noises which exceed the limit of standard. Moreover, the experiments are carried out with three models: double-common-mode hybrid sources, double-differential-mode hybrid sources and common-differential-mode hybrid sources. Compared with the traditional independent component algorithm (ICA), the method proposed in this paper can separate the radiated EMI noise sources more accurately and quickly. It can be concluded that the accuracy of NLPCA algorithm is 10% higher than ICA algorithm. This work will contribute to trace the radiated EMI noise sources, and to provide the theoretical basis for the future suppression.

In order to improve the operation and management level of thermal power units, and to achieve the goal of saving energy and reducing consumption, the nonlinear principal component analysis (PCA) was proposed to assess the operating condition of fossil-fired power plants comprehensively, which can resolve the problem on the evaluation of multiple indicators. This method improves the traditional PCA by eliminating the relativity. Moreover, this paper applies the nonlinear PCA to evaluate the operating state of power plants, which can reduce the dimensions of the indicators and abstract the principal components. It can provide the high reference value for the power generation group on how to implement saving energy, optimal operation, indicators evaluation and competition in thermal power units. The practical example shows that the proposed method is effective.

The design of the step-size is crucial to the convergence rate of the Nonlinear Principle Component Analysis(NPCA) algorithm.However,the commonly used fixed step-size algorithm can hardly satisfy the convergence speed and estimation precision requirements simultaneously.To address this issue,the gradient-based adaptive step-size NPCA algorithm and optimal step-size NPCA algorithm were proposed to speed up the convergence rate and improve tracking ability.In particular,the optimal step-size NPCA algorithm linearly approximated the contrast function and figured out the optimal step-size currently.The optimal step-size NPCA algorithm utilized an adaptive step-size whose value was adjusted in sympathy with the value of the contrast function and free from any manual parameters.The simulation results show that the proposed adaptive step-size NPCA algorithms have faster convergence rate or better tracking ability in comparison with the fixed step-size NPCA algorithm when the estimation precisions are same.The convergence performance of the optimal step-size NPCA algorithm is superior to that of the gradient-based adaptive NPCA algorithm.

This paper aims to study how to use gas sensor array detection system to realize the remote contactless identification of drug-producing chemicals in the external environment. The dynamic temperature modulation method of semiconductor sensor array is used to prove the feasibility and practicality of the method. In this paper, the influence of heating period on sensor stability under rectangular wave heating condition is studied. The hardware system of gas sensor array is established, and the data is collected by the data acquisition system. In the simulated external environment, acetone, toluene, ether and 2-butanone are qualitative analysis and identification. The data are dimensionally reduced by principal component analysis (PCA) algorithm and combined with decision tree algorithm to identify the data dynamic temperature modulation and array, which provides a research direction for more accurate qualitative identification and quantitative analysis of drug-producing chemicals.

Machine learning algorithms play an important role in fault detection and fault diagnosis of gas sensor arrays. Because the gas sensor array will see stability degradation and a shift in output signal amplitude under long-term operation, it is very important to detect the abnormal output signal of the gas sensor array in time and achieve accurate fault location. In order to solve the problem of low detection accuracy of micro-faults in gas sensor arrays, this paper adopts the serial principal component analysis (SPCA) method, which combines the advantages of principal component analysis (PCA) in the linear part and the advantages of kernel principal component analysis (KPCA) in the nonlinear part. The experimental results show that this method is more sensitive to micro-faults and has better fault detection accuracy than the fault detection methods of PCA and KPCA. In addition, in order to solve the current problem of low accuracy of multiple-fault isolation, a SPCA-based reconstruction contribution fault isolation method is proposed in this paper. The experimental results show that this method has higher fault isolation accuracy than the method based on contribution graph.

Malaysia, Sarawak state in particular produces superior quality black pepper compared to other producing countries. While Sarawak black pepper deserves higher price in the global market, from year 2015 onwards, its price has been plummeting due to global oversupply of pepper. Physical, chemical and biological profiling of Sarawak pepper is conducted to differentiate Sarawak pepper against adulteration and to justify its higher market price. However, the analysis of pepper was performed using time-consuming, non-portable, expensive and invasive laboratory equipment and methodologies. This paper reports an attempt to develop a black pepper geo-tracing system using metal oxide semiconductor (MOS) gas sensors array. The pneumatic system to contain and purge the sample volatile organic compounds (VOCs) is designed, simulated, fabricated and proven to be contain and purge sample VOCs effectively. A total of 200 black pepper samples from Malaysia and India are sampled using non-invasive method for the MOS gas sensors response and the sensors response are analyzed using Principal Component Analysis (PCA). The PCA scatter plots shows that Malaysia and India black pepper can be discriminated based on the MOS gas sensor response towards different VOCs composition in the black pepper samples. The PCA result are then used for geo-tracing of a total of 40 samples (20 from Malaysia; 20 from India), which shows an overall accuracy of 92.5%. The geo-tracing system developed performs rapidly with 260-600 s sampling cycle compared to gas chromatography-mass spectroscopy (GC-MS) equipment which requires at least 30 minutes sampling time, and is portable, cheaper and non-invasive.

This paper introduces a new unsupervised method for dimensionality reduction via regression (DRR). The algorithm belongs to the family of invertible transforms that generalize Principal Component Analysis (PCA) by using curvilinear instead of linear features. DRR identifies the nonlinear features through multivariate regression to ensure the reduction in redundancy between he PCA coefficients, the reduction of the variance of the scores, and the reduction in the reconstruction error. More importantly, unlike other nonlinear dimensionality reduction methods, the invertibility, volume-preservation, and straightforward out-of-sample extension, makes DRR interpretable and easy to apply. The properties of DRR enable learning a more broader class of data manifolds than the recently proposed Non-linear Principal Components Analysis (NLPCA) and Principal Polynomial Analysis (PPA). We illustrate the performance of the representation in reducing the dimensionality of remote sensing data. In particular, we tackle two common problems: processing very high dimensional spectral information such as in hyperspectral image sounding data, and dealing with spatial-spectral image patches of multispectral images. Both settings pose collinearity and ill-determination problems. Evaluation of the expressive power of the features is assessed in terms of truncation error, estimating atmospheric variables, and surface land cover classification error. Results show that DRR outperforms linear PCA and recently proposed invertible extensions based on neural networks (NLPCA) and univariate regressions (PPA).

Aroma essential oils contain ingredients that are beneficial to the human body. A gas sensor array is required to monitor the concentration of these essential oil components to regulate their concentration by air conditioning systems. Therefore, we investigated the discrimination ability and concentration measurement accuracy of 14 effective components, including four aroma essential oils (lavender, melissa, tea tree, and eucalyptus), from a single gas sample and mixtures of two gases using sensor arrays. To obtain our data, we used two sensor arrays comprising commercially available semiconductor sensors and our developed semiconductor sensors. For machine learning, principal component analysis was used to visualize the dataset obtained from the sensor signals, and an artificial neural network was used for a detailed analysis. Our developed sensor array, which included sensors that possessed excellent sensor responses to 14 effective components and combined different semiconductive sensor principles, showed a better discrimination and prediction accuracy than the commercially available sensors investigated in this study.

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.