PCA Decomposition Research Articles

Design, Synthesis, Antitumor Activity Evaluation, and Molecular Dynamics Simulation of Some 2-Aminopyrazine Derivatives.

Cancer poses a great threat to human health, and effective drugs to treat it are always needed. Several compounds containing a 2-aminopyrazine framework have been identified as antitumor agents with SHP2 inhibition activities. This current work aimed to search for more potent novel compounds possessing a 2-aminopyrazine moiety with antitumor activities. A series of 12 novel 2-aminopyrazine derivatives was synthesized, and their structures were confirmed by spectroscopic techniques. The inhibitory activities of all the synthesized compounds against MDA-MB-231 and H1975 cancer cell lines were evaluated by an MTT assay. The most potent compound 3e was analyzed by flow cytometry. Subsequently, computational studies were performed to investigate the possible antitumor mechanisms of compound 3e. The results indicated that compound 3e exhibited potent antitumor activities with IC50 values of 11.84±0.83μM against H1975 cells and 5.66±2.39μM against MDA-MB-231 cells, which were more potent than the SHP2 inhibitor GS493 (IC50 = 19.08±1.01 μM against H1975 cells and IC50 = 25.02±1.47 μM against MDA-MB-231 cells). Further analysis by flow cytometry demonstrated that compound 3e induced cell apoptosis in H1975 cells. The results of the molecular docking and MD simulations, including RMSD, RMSF, PCA, DCCM and binding energy and decomposition analyses, revealed that compound 3e probably selectively inhibited SHP2. A new compound having a 2-aminopyrazine substructure with potent inhibitory activities against the H1975 and MDA-MB-231 cancer cells was obtained, meriting further investigation as an antitumor drug.

An Ensemble Method for EEG-based Texture Discrimination during Open Eyes Active Touch

Touch sensation is a key modality that allows humans to understand and interact with their environment. More often than not, touch sensation depends on vision to accumulate and validate the received information. The ability to distinguish between materials and surfaces through active touch consists of a complex of neurophysiological operations. To unveil the functionality of these operations, neuroimaging and neurophysiological research tools are employed, with electroencephalography being the most used. In this paper, we attempt to distinguish between brain states when touching different natural textures (smooth, rough, and liquid). Recordings were obtained with a commercially available EEG wearable device. Time and frequency-based features were extracted, transformed with PCA decomposition, and an ensemble classifier combining Random Forest, Support Vector Machine, and Neural Network was utilized. High accuracy scores of 79.64% for the four-class problem and 89.34% for the three-class problem (Null-Rough-Water) were accordingly achieved. Thus, the methodology's robustness indicates its ability to classify different brain states under haptic stimuli.

Accuracy Enhancement and Feature Extraction for GNSS Daily Time Series Using Adaptive CEEMD-Multi-PCA-Based Filter

Global navigation satellite system (GNSS) positions include various useful signals and some unmodeled errors. In order to enhance the accuracy and extract the features of the GNSS daily time sequence, an improved method of complete ensemble empirical mode decomposition (CEEMD) and multi-PCA (MPCA) based on correlation coefficients and block spatial filtering was proposed. The results showed that the mean standard deviations of the raw residual time sequence were 1.09, 1.20 and 4.79 mm, while those of the newly proposed method were 0.15, 0.20 and 2.86 mm in north, east and up directions, respectively. The proposed method outperforms wavelet decomposition (WD)-PCA and empirical mode decomposition (EMD)-PCA in effectively eliminating low- and high-frequency noise, and is suitable for denoising nonlinear and nonstationary GNSS position sequences. Furthermore, feature extraction of the denoised GNSS daily time series was based on CEEMD, which is superior to WD and EMD. Results of noise analysis suggested that the noise components in the original and denoised GNSS time sequence are complex. The advantages of the proposed method are the following: (i) it fully exploits the merits of CEEMD and WD, where CEEMD is first used to obtain the limited intrinsic modal functions (IMFs) and then to extract seasonal and trend features; (ii) it has good adaptive processing ability via WD for noise-dominant IMFs; and (iii) it fully considers the correlation between the different components of each station and the non-uniform behavior of common mode error on a spatial scale.

Single-trial-based temporal principal component analysis on extracting event-related potentials of interest for an individual subject

Background:Temporal principal component analysis (tPCA) has been widely used to extract event-related potentials (ERPs) at group level of multiple subjects ERP data and it assumes that the underlying factor loading is fixed across participants. However, such assumption may fail to work if latency and phase for one ERP vary considerably across participants. Furthermore, effect of number of trials on tPCA decomposition has not been systematically examined as well, especially for within-subject PCA. New method:We reanalyzed a real ERP data of an emotional experiment using tPCA to extract N2 and P2 from single-trial EEG of an individual. We also explored influence of the number of trials (consecutively increased from 10 to 42 trials) on PCA decomposition by comparing temporal correlation, the statistical result, Cronbach’s alpha, spatial correlation of both N2 and P2 for the proposed method with the conventional time-domain analysis, trial-averaged group PCA, and single-trial-based group PCA. Results:The results of the proposed method can enhance spatial and temporal consistency. We could obtain stable N2 with few trials (about 20) for the proposed method, but, for P2, approximately 30 trials were needed for all methods. Comparison with Existing Method(s):About 30 trials for N2 were required and the reconstructed P2 and N2 were poor correlated across participants for the other three methods. Conclusion:The proposed approach may efficiently capture variability of one ERP from an individual that cannot be extracted by group PCA analysis.

A new model for simultaneous dimensionality reduction and time-varying functional connectivity estimation.

An important question in neuroscience is whether or not we can interpret spontaneous variations in the pattern of correlation between brain areas, which we refer to as functional connectivity or FC, as an index of dynamic neuronal communication in fMRI. That is, can we measure time-varying FC reliably? And, if so, can FC reflect information transfer between brain regions at relatively fast-time scales? Answering these questions in practice requires dealing with the statistical challenge of having high-dimensional data and a comparatively lower number of time points or volumes. A common strategy is to use PCA to reduce the dimensionality of the data, and then apply some model, such as the hidden Markov model (HMM) or a mixture model of Gaussian distributions, to find a set of distinct FC patterns or states. The distinct spatial properties of these FC states together with the time-resolved switching between them offer a flexible description of time-varying FC. In this work, I show that in this context PCA can suffer from systematic biases and loss of sensitivity for the purposes of finding time-varying FC. To get around these issues, I propose a novel variety of the HMM, named HMM-PCA, where the states are themselves PCA decompositions. Since PCA is based on the data covariance, the state-specific PCA decompositions reflect distinct patterns of FC. I show, theoretically and empirically, that fusing dimensionality reduction and time-varying FC estimation in one single step can avoid these problems and outperform alternative approaches, facilitating the quantification of transient communication in the brain.

Speeded-up Convolution Neural Network for classification tasks using multiscale 2-dimensional decomposition

In this paper, we propose a strategy for network simplification and acceleration. First, we propose to generate a suitable resized image using multiscale patching in the first convolutional layer, which can then be used for the rest of the network. We use p convolutional filters that operate on patches of size m × n, and we first select all the possible non-superposed m × n patches from the available images. If the number of such patches is not sufficient, the remaining ones are collected using scales a × b or c × d such that ab = cd = mn or a = 2 m or b = 2n. Patches generated from the former condition are directly extracted from the images, while the downsampled results are used in the latter case.We also introduce a 2-dimensional decomposition for patch compression, by stacking all the available image patches along the columns and applying a 2D PCA decomposition. Finally, a layer weight decomposition technique followed by module-based finetuning is adopted, for a new fast module-based CNN model.Extensive evaluations using public data sets like MNIST, Pascal VOC, and WebCASIA, and with different state-of-the art CNN architectures like Open-Face, VGG and DarkNet verify that our proposed model is able to accelerate the training process and even to provide higher classification accuracies for small-sized datasets. We obtain 8% increase in Top-1 and Top-5 recognition rates, and 5% increase in F1 score over general interpolation-based resizing.

Learning rates for partially linear functional models with high dimensional scalar covariates

This paper is concerned with learning rates for partial linear functional models (PLFM) within reproducing kernel Hilbert spaces (RKHS), where all the covariates consist of two parts: functional-type covariates and scalar ones. As opposed to frequently used functional principal component analysis for functional models, the finite number of basis functions in the proposed approach can be generated automatically by taking advantage of reproducing property of RKHS. This avoids additional computational costs on PCA decomposition and the choice of the number of principal components. Moreover, the coefficient estimators with bounded covariates converge to the true coefficients with linear rates, as if the functional term in PLFM has no effect on the linear part. In contrast, the prediction error for the functional estimator is significantly affected by the ambient dimension of the scalar covariates. Finally, we develop the proposed numerical algorithm for the proposed penalized approach, and some simulated experiments are implemented to support our theoretical results.

高维数据降维中的PCA与CUR分解对比分析

高维数据降维中的PCA与CUR分解对比分析

Neural Networks Based Dynamic Implied Volatility Surface

A pricing model is tied to its ability of capturing the dynamics of the spot price process. Its misspecification will lead to pricing and hedging errors. Parametric pricing formula depends on the particular form of the dynamics of the underlying asset. For tractability reasons, some assumptions are made which are not consistent with the multifractal properties of market returns. On the other hand, non-parametric models such as neural networks use market data to estimate the implicit stochastic process driving the spot price and its relationship with contingent claims. We propose to use neural networks for learning the dynamics of the implied volatility surface. Rather than learning the dynamics of the whole volatility surface, we perform a dimensionality reduction and choose to learn that of the main volatility risk factors from the data. These risk factors form a vector basis for the implied volatility surface. They can be the first three eigenmodes of a PCA decomposition, the parameters of a polynomial model, or any other model parameters from a stochastic volatility model. We assume that these factors are driven by explanatory variables, such as spot price, volume, estimated volatility, and financial indicators like the VIX and options from the main indices. We use neural networks to capture the relation between the volatility risk factors and their explanatory variables. We model the dynamics of the IV surfaces by letting the parameters of a polynomial model, or a stochastic volatility model with an explicit expression for the smile such as the SVI and the SABR model, be statistically evolved, by considering one neural network per parameter. The smile is reconstructed by using the polynomial model, or the parametric smile representation, where each parameter is replaced by a trained network. That is, not only do we learn the model parameters at a fixed time, but we use the fact that the networks are universal interpolators to learn about the dynamics of their term-structures. We can then reconstruct the volatility surface and use it for pricing and hedging options as well as for risk analysis, forecasting, and volatility trading. We also describe how to use the model for pricing forward starting contracts such as cliquet options.

Channelized reservoir estimation using a low-dimensional parameterization based on high-order singular value decomposition

Prior to the estimation process of channelized reservoirs, in the context of any Assisted History Matching method, the parameterization of facies field is a necessary task. The parameterization of the facies field consists of defining a numerical field (parameter field) on the reservoir domain so that, using a projection function, we are able to recover the facies field from the values of parameter field. One of the most important issues encountered is the loss of the multipoint geostatistical properties in the updates (channel continuity). In this study, we start from an initial (global) parameterization of the channelized field and infer from it a low-dimensional parameterization obtained after a high-order singular value decomposition of a tensor built with the parameter fields. We decompose the parameter field as a linear combination of some basis functions with coefficients. The decomposition is followed by a truncation so that we keep the relevant information from the channel continuity perspective, but with a small number of coefficients. The coefficients will represent the low-dimensional parameterization and are further introduced in the estimation process of facies field, using the Ensemble Smoother with Multiple Data Assimilations (ES-MDA). For a fair assessment of the parameterization, we perform a comparison of the results with those obtained by applying the traditional truncated singular value decomposition and the global parameterization. In addition, we compare the parameterization with a low-dimensional parameterization defined with the PCA decomposition. The comparison is done from the perspective of multipoint geostatistical characteristics of the updates and predictions. We show that the new parameterization is able to better keep the multipoint geostatistical structure in the updates than the other parameterizations, while the prediction capabilities are the same.

Assessing cross-modal target transition effects with a visual-auditory oddball

Prior research has shown contextual manipulations involving temporal and sequence related factors significantly moderate attention-related responses, as indexed by the P3b event-related-potential, towards infrequent (i.e., deviant) target oddball stimuli. However, significantly less research has looked at the influence of cross-modal switching on P3b responding, with the impact of target-to-target cross-modal transitions being virtually unstudied. To address this gap, this study recorded high-density (256 electrodes) EEG data from twenty-five participants as they completed a cross-modal visual-auditory oddball task. This task was comprised of unimodal visual (70% Nontargets: 30% Deviant-targets) and auditory (70% Nontargets: 30% Deviant-targets) oddballs presented in fixed alternating order (i.e., visual-auditory-visual-auditory, etc.) with participants being tasked with detecting deviant-targets in both modalities. Differences in the P3b response towards deviant-targets as a function of preceding deviant-target's presentation modality was analyzed using temporal-spatial PCA decomposition. In line with predictions, the results indicate that the ERP response to auditory deviant-targets preceded by visual deviant-targets exhibits an elevated P3b, relative to the processing of auditory deviant-targets preceded by auditory deviant-targets. However, the processing of visual deviant-targets preceded by auditory deviant-targets exhibited a reduced P3b response, relative to the P3b response towards visual deviant-targets preceded by visual deviant-targets. These findings provide the first demonstration of temporally and perceptually decoupled target-to-target cross-modal transitions moderating P3b responses on the oddball paradigm, generally providing support for the context-updating interpretation of the P3b response.

Photosynthesis, growth, and decay traits in Sphagnum - a multispecies comparison.

Peat mosses (Sphagnum) largely govern carbon sequestration in Northern Hemisphere peatlands. We investigated functional traits related to growth and decomposition in Sphagnum species. We tested the importance of environment and phylogeny in driving species traits and investigated trade‐offs among them. We selected 15 globally important Sphagnum species, representing four sections (subgenera) and a range of peatland habitats. We measured rates of photosynthesis and decomposition in standard laboratory conditions as measures of innate growth and decay potential, and related this to realized growth, production, and decomposition in their natural habitats. In general, we found support for a trade‐off between measures of growth and decomposition. However, the relationships are not strong, with r ranging between 0.24 and 0.45 for different measures of growth versus decomposition. Using photosynthetic rate to predict decomposition in standard conditions yielded R 2 = 0.20. Habitat and section (phylogeny) affected the traits and the trade‐offs. In a wet year, species from sections Cuspidata and Sphagnum had the highest production, but in a dry year, differences among species, sections, and habitats evened out. Cuspidata species in general produced easily decomposable litter, but their decay in the field was hampered, probably due to near‐surface anoxia in their wet habitats. In a principal components analysis, PCA, photosynthetic capacity, production, and laboratory decomposition acted in the same direction. The species were imperfectly clustered according to vegetation type and phylogeny, so that some species clustered with others in the same section, whereas others clustered more clearly with others from similar vegetation types. Our study includes a wider range of species and habitats than previous trait analyses in Sphagnum and shows that while the previously described growth–decay trade‐off exists, it is far from perfect. We therefore suggest that our species‐specific trait measures offer opportunities for improvements of peatland ecosystem models. Innate qualities measured in laboratory conditions translate differently to field responses. Most dramatically, fast‐growing species could only realize their potential in a wet year. The same species decompose fast in laboratory, but their decomposition was more retarded in the field than that of other species. These relationships are crucial for understanding the long‐term dynamics of peatland communities.

Sparsity Preserving Discriminant Projections with Applications to Face Recognition

Dimensionality reduction is extremely important for understanding the intrinsic structure hidden in high-dimensional data. In recent years, sparse representation models have been widely used in dimensionality reduction. In this paper, a novel supervised learning method, called Sparsity Preserving Discriminant Projections (SPDP), is proposed. SPDP, which attempts to preserve the sparse representation structure of the data and maximize the between-class separability simultaneously, can be regarded as a combiner of manifold learning and sparse representation. Specifically, SPDP first creates a concatenated dictionary by classwise PCA decompositions and learns the sparse representation structure of each sample under the constructed dictionary using the least square method. Secondly, a local between-class separability function is defined to characterize the scatter of the samples in the different submanifolds. Then, SPDP integrates the learned sparse representation information with the local between-class relationship to construct a discriminant function. Finally, the proposed method is transformed into a generalized eigenvalue problem. Extensive experimental results on several popular face databases demonstrate the feasibility and effectiveness of the proposed approach.

Complete canonical correlation analysis with application to multi-view gait recognition

Canonical correlation analysis (CCA) is a well-known multivariate analysis method for quantifying the correlations between two sets of multidimensional variables. However, for multi-view gait recognition, it is difficult to directly apply CCA to deal with two sets of high-dimensional vectors because of computational complexity. Moreover, in such situation, the eigenmatrix of CCA is usually singular which makes the direct implementation of the CCA algorithm almost impossible. In practice, PCA or singular value decomposition is employed as a preprocessing step to solve these problems. Nevertheless, this strategy may discard dimensions that contain important discriminative information and correlation information. To overcome the shortcomings of CCA when dealing with two sets of high-dimensional vectors, we develop a novel method, named complete canonical correlation analysis (C3A). In our method, we first reformulate the traditional CCA so that we can avoid the computing of the inverse of a high-dimensional matrix. With the help of this reformulation, C3A further transforms the singular generalized eigensystem computation of CCA into two stable eigenvalue decomposition problems. Moreover, a feasible and effective method is proposed to alleviate the computational burden of high dimensional matrix for typical gait image data. Experimental results on two benchmark gait databases, CASIA gait database and the challenge USF gait database, demonstrate the effectiveness of the proposed method.

Short-Term Electric Load Forecasting Using Echo State Networks and PCA Decomposition

In this paper, we approach the problem of forecasting a time series (TS) of an electrical load measured on the Azienda Comunale Energia e Ambiente (ACEA) power grid, the company managing the electricity distribution in Rome, Italy, with an echo state network (ESN) considering two different leading times of 10 min and 1 day. We use a standard approach for predicting the load in the next 10 min, while, for a forecast horizon of one day, we represent the data with a high-dimensional multi-variate TS, where the number of variables is equivalent to the quantity of measurements registered in a day. Through the orthogonal transformation returned by PCA decomposition, we reduce the dimensionality of the TS to a lower number $k$ of distinct variables; this allows us to cast the original prediction problem in $k$ different one-step ahead predictions. The overall forecast can be effectively managed by $k$ distinct prediction models, whose outputs are combined together to obtain the final result. We employ a genetic algorithm for tuning the parameters of the ESN and compare its prediction accuracy with a standard autoregressive integrated moving average model.

Independent components of neural activity carry information on individual populations.

Local field potential (LFP), the low-frequency part of the potential recorded extracellularly in the brain, reflects neural activity at the population level. The interpretation of LFP is complicated because it can mix activity from remote cells, on the order of millimeters from the electrode. To understand better the relation between the recordings and the local activity of cells we used a large-scale network thalamocortical model to compute simultaneous LFP, transmembrane currents, and spiking activity. We used this model to study the information contained in independent components obtained from the reconstructed Current Source Density (CSD), which smooths transmembrane currents, decomposed further with Independent Component Analysis (ICA). We found that the three most robust components matched well the activity of two dominating cell populations: superior pyramidal cells in layer 2/3 (rhythmic spiking) and tufted pyramids from layer 5 (intrinsically bursting). The pyramidal population from layer 2/3 could not be well described as a product of spatial profile and temporal activation, but by a sum of two such products which we recovered in two of the ICA components in our analysis, which correspond to the two first principal components of PCA decomposition of layer 2/3 population activity. At low noise one more cell population could be discerned but it is unlikely that it could be recovered in experiment given typical noise ranges.

Peak Aggregation as an Innovative Strategy for Improving the Predictive Power of LC-MS Metabolomic Profiles

Liquid chromatography-mass spectrometry (LC-MS)-based metabolomic datasets consist of different features including (de)protonated molecules, fragments, adducts, and isotopes that may show high correlation values related to a high level of collinearity. There have been described several sources of these high correlation patterns regarding metabolomic datasets. Among these sources, it should be highlighted the high level of correlation computed between features coming from the same metabolite. It is well-known that soft ionization methods (such as electrospray) produce several mass features from a particular compound (i.e., metabolite spectrum). Typically, the statistical methods used in metabolomics consider spectral peaks as variables. However, it has been reported that a high collinearity between variables might be the responsible for high uncertainty values in the predictors of a regression. In this context, this technical note proposes a new strategy based on the application of the so-called peak aggregation methods (NMF Reduction, PCA Decomposition, Maximum Peak, and Spectrum Mean) to take advantage of the variable collinearity and solve the issue of high variable collinearity. A set of real samples obtained after human nutritional intervention with placebo or polyphenol-rich beverages was used to test this methodology. The results showed that applying any peak aggregation method (especially NMF and PCA) improves the statistical prediction power of class pertinence independently of the nature of the classifier (linear PLS-DA or nonlinear SVM). Overall, the introduction of this new approach resulted in a reduction of the dimensionality of the data and, in addition, in a significant increase in the overall predictive power of the data.

Sparse regularization discriminant analysis for face recognition

Recently the underlying sparse representation structure in high dimensional data has attracted considerable interests in pattern recognition and computer vision. Sparse representation structure means the sparse reconstructive relationship of the data. In this paper, we propose a novel dimensionality reduction method called Sparse Regularization Discriminant Analysis (SRDA), which aims to preserve the sparse representation structure of the data when learning an efficient discriminating subspace. More specifically, SRDA first constructs a concatenated dictionary through class-wise PCA decompositions which conduct PCA on data from each class separately, and learns the sparse representation structure under the constructed dictionary quickly through matrix–vector multiplications. Then SRDA takes into account both the sparse representation structure and the discriminating efficiency by using the learned sparse representation structure as a regularization term of linear discriminant analysis. Finally, the optimal embedding of the data is learned via solving a generalized eigenvalue problem. The extensive and promising experimental results on four publicly available face data sets (Yale, Extended Yale B, ORL and CMU PIE) validate the feasibility and effectiveness of the proposed method.

Facilitating Neuronal Connectivity Analysis of Evoked Responses by Exposing Local Activity with Principal Component Analysis Preprocessing: Simulation of Evoked MEG

When connectivity analysis is carried out for event related EEG and MEG, the presence of strong spatial correlations from spontaneous activity in background may mask the local neuronal evoked activity and lead to spurious connections. In this paper, we hypothesized PCA decomposition could be used to diminish the background activity and further improve the performance of connectivity analysis in event related experiments. The idea was tested using simulation, where we found that for the 306-channel Elekta Neuromag system, the first 4 PCs represent the dominant background activity, and the source connectivity pattern after preprocessing is consistent with the true connectivity pattern designed in the simulation. Improving signal to noise of the evoked responses by discarding the first few PCs demonstrates increased coherences at major physiological frequency bands when removing the first few PCs. Furthermore, the evoked information was maintained after PCA preprocessing. In conclusion, it is demonstrated that the first few PCs represent background activity, and PCA decomposition can be employed to remove it to expose the evoked activity for the channels under investigation. Therefore, PCA can be applied as a preprocessing approach to improve neuronal connectivity analysis for event related data.

Fast Fisher Sparsity Preserving Projections

Recently, there has been a lot of interest in the underlying sparse representation structure in high-dimensional data such as face images. In this paper, we propose two novel efficient dimensionality reduction methods named Fast Sparsity Preserving Projections (FSPP) and Fast Fisher Sparsity Preserving Projections (FFSPP), respectively, which aim to preserve the sparse representation structure in high-dimensional data. Unlike the existing Sparsity Preserving Projections (SPP), where the sparse representation structure is learned through resolving n (the number of samples) time-consuming \( \ell^{ 1} \) norm optimization problems, FSPP constructs a dictionary through classwise PCA decompositions and learns the sparse representation structure under the constructed dictionary through matrix–vector multiplications, which is much more computationally tractable. FFSPP takes into consideration both the sparse representation structure and the discriminating efficiency by adding the Fisher constraint to the FSPP formulation to improve FSPP’s discriminating ability. Both of the proposed methods can boil down to a generalized eigenvalue problem. Experimental results on three publicly available face data sets (Yale, Extended Yale B and ORL), and a standard document collection (Reuters-21578) validate the feasibility and effectiveness of the proposed methods.