Principal Component Dimensions Research Articles

Main influencing factors of soil particle distribution in the karst basin

Soil particle distribution is an important soil property that is widely studied. However, more attention has been focused on specific environmental factors. As soil and environmental factors of nature are related, what is the relationship between soil particle distribution and environmental factors? What are the most important factors affecting soil particle distribution at the watershed scale? The principal component dimension reduction analysis showed that the important factors affecting soil particle distribution included and ranked as parent material, slope and slope position. The karst soil in the Houzhaihe Basin, Guizhou Province, China, is taken as the research object. A grid of 150 m·150 m is used for sampling, and the total number of sample collection points is 2755. The effects of seven environmental factors (soil parent material, land use type, slope direction, slope, soil type, slope position and altitude) on soil particle distribution were studied. The results showed that the seven factors all significantly affected the soil particle distribution in the basin, but the significance of different factors was distinct, and some factors had no significant effect on the specific particle type. The principal component dimension reduction analysis showed that the important factors included parent material, slope and slope position, which were ranked as parent material, slope and slope position. On the one hand, the change in soil particle distribution is affected by the factors of the soil formation process (parent material) and by the transport and transportation of dynamic factors such as water and gravity (slope and slope position) in the basin. The change in soil particle distribution is driven by the coupling of these two factors. The redundancy analysis shows that the contribution rates of environmental factors to the content of three kinds of soil particle sizes are arranged in the order of soil parent material, land use type, slope direction, slope, soil type, slope position and altitude and explained 14.2 %, 8.9 %, 3.4 %, 3.0 %, 1.9 %, 1.5 % and 0.9 %, respectively, and only three of them reach the level of P < 0.05. The results of high-density sampling analysis at the karst basin scale show that the parent material is the most important factor affecting the soil particle distribution.

Retracted] PCA and Binary K‐Means Clustering Based Collaborative Filtering Recommendation

Aiming at the problem of similarity calculation error caused by the extremely sparse data in collaborative filtering recommendation algorithm, a collaborative filtering recommendation algorithm based on slope one matrix prefilling model, principal component dimension reduction, and binary K‐means clustering is proposed in this paper. Firstly, the algorithm uses the slope one model based on item similarity to prefill the original scoring matrix. Secondly, principal component analysis is used to reduce the dimension of the filled matrix, retain the most representative dimension of user characteristics, and remove the dimension with less information. Finally, in order to solve the time‐consuming problem of similarity calculation of collaborative filtering algorithm in the case of large‐scale system, binary K‐means clustering is carried out in the reduced dimension vector space to reduce the search range of the nearest neighbour of the target user. The algorithm ensures the efficiency and accuracy of recommendation while the scale of users is expanded. The experimental results on movielens dataset show that the algorithm proposed in this paper is superior to the traditional collaborative filtering algorithm and the collaborative filtering recommendation algorithm based on PCA (principal component analysis) and binary K‐means clustering in recall rate, accuracy rate, average error, and running time.

The Sentinel 2 MSI Spectral Mixing Space

A composite spectral feature space is used to characterize the spectral mixing properties of Sentinel 2 Multispectral Instrument (MSI) spectra over a wide diversity of landscapes. Characterizing the linearity of spectral mixing and identifying bounding spectral endmembers allows the Substrate Vegetation Dark (SVD) spectral mixture model previously developed for the Landsat and MODIS sensors to be extended to the Sentinel 2 MSI sensors. The utility of the SVD model is its ability to represent a wide variety of landscapes in terms of the areal abundance of their most spectrally and physically distinct components. Combining the benefits of location-specific spectral mixture models with standardized spectral indices, the physically based SVD model offers simplicity, consistency, inclusivity and applicability for a wide variety of land cover mapping applications. In this study, a set of 110 image tiles compiled from spectral diversity hotspots worldwide provide a basis for this characterization, and for identification of spectral endmembers that span the feature space. The resulting spectral mixing space of these 13,000,000,000 spectra is effectively 3D, with 99% of variance in 3 low order principal component dimensions. Four physically distinct spectral mixing continua are identified: Snow:Firn:Ice, Reef:Water, Evaporite:Water and Substrate:Vegetation:Dark (water or shadow). The first 3 continua exhibit complex nonlinearities, but the geographically dominant Substrate:Vegetation:Dark (SVD) continuum is conspicuous in the linearity of its spectral mixing. Bounding endmember spectra are identified for the SVD continuum. In a subset of 80 landscapes, excluding the 3 nonlinear mixing continua (reefs, evaporites, cryosphere), a 3 endmember (SVD) linear mixture model produces endmember fraction estimates that represent 99% of modeled spectra with &lt;6% RMS misfit. Two sets of SVD endmembers are identified for the Sentinel 2 MSI sensors, allowing Sentinel 2 spectra to be unmixed globally and compared across time and space. In light of the apparent disparity between the 11D spectral feature space and the statistically 3D spectral mixing space, the relative contribution of 11 Sentinel 2 MSI spectral bands to the information content of this space is quantified using both parametric (Pearson Correlation) and nonparametric (Mutual Information) metrics. Comparison of linear (principal component) and nonlinear (Uniform Manifold Approximation and Projection) projections of the SVD mixing space reveal both physically interpretable spectral mixing continua and geographically distinct spectral properties not resolved in the linear projection.

A novel dimension reduction algorithm based on weighted kernel principal analysis for gene expression data.

Gene expression data has the characteristics of high dimensionality and a small sample size and contains a large number of redundant genes unrelated to a disease. The direct application of machine learning to classify this type of data will not only incur a great time cost but will also sometimes fail to improved classification performance. To counter this problem, this paper proposes a dimension-reduction algorithm based on weighted kernel principal component analysis (WKPCA), constructs kernel function weights according to kernel matrix eigenvalues, and combines multiple kernel functions to reduce the feature dimensions. To further improve the dimensional reduction efficiency of WKPCA, t-class kernel functions are constructed, and corresponding theoretical proofs are given. Moreover, the cumulative optimal performance rate is constructed to measure the overall performance of WKPCA combined with machine learning algorithms. Naive Bayes, K-nearest neighbour, random forest, iterative random forest and support vector machine approaches are used in classifiers to analyse 6 real gene expression dataset. Compared with the all-variable model, linear principal component dimension reduction and single kernel function dimension reduction, the results show that the classification performance of the 5 machine learning methods mentioned above can be improved effectively by WKPCA dimension reduction.

An Improved High-Dimensional Kriging Surrogate Modeling Method through Principal Component Dimension Reduction

The Kriging surrogate model in complex simulation problems uses as few expensive objectives as possible to establish a global or local approximate interpolation. However, due to the inversion of the covariance correlation matrix and the solving of Kriging-related parameters, the Kriging approximation process for high-dimensional problems is time consuming and even impossible to construct. For this reason, a high-dimensional Kriging modeling method through principal component dimension reduction (HDKM-PCDR) is proposed by considering the correlation parameters and the design variables of a Kriging model. It uses PCDR to transform a high-dimensional correlation parameter vector in Kriging into low-dimensional one, which is used to reconstruct a new correlation function. In this way, time consumption of correlation parameter optimization and correlation function matrix construction in the Kriging modeling process is greatly reduced. Compared with the original Kriging method and the high-dimensional Kriging modeling method based on partial least squares, the proposed method can achieve faster modeling efficiency under the premise of meeting certain accuracy requirements.

Examining the macro-level factors affecting vehicle breakdown duration

A substantial part of traffic congestion is triggered by unplanned incidents such as crashes, breakdowns and hazards, reducing road capacity and increasing the delays, pollution, and productivity losses. Previous studies on incident duration have focussed on individual incidents and the influencing factors that could be obtained directly from the incident description. Consequently, the explanatory variables were more localized, and the impacts of broader macro-level factors were not explored. This contrasts with the studies on incident frequency, where the influencing factors are typically collected at a macro-level. Therefore, this study aims to explore the impact of various factors associated with reported vehicle breakdown duration at a macro-level. Street network characteristics such as connectivity, density, and hierarchy were included as covariates, in addition to the demographic, vehicle utilization, and environmental variables. The dataset contains over 72,000 vehicle breakdowns records within 4.5 years (January 2012 to June 2016) in Greater Sydney, Australia involving 44 SA3s (Statistical Area Level 3). After a principal component dimension reduction of independent variables, a fixed-parameters accelerated failure time (AFT) hazard-based model with underlying log-logistic, log-normal and Weibull distributions were used in this analysis. Weibull hazard distribution with gamma frailty and the latent class models were also considered to account for unobserved heterogeneity. The latent class model provides the best fit where road network connectivity, hierarchy, and familiarity factors are considered to have both positive and negative impact on duration; higher road network density, mixed land-use, and spatial disorientation of roads are associated with longer duration; and higher income and exposure (vehicle kilometres travelled) are associated with shorter duration. The results will help incident management agencies to better allocate current response resources and predict the resources required in the future. Besides, the results associated with network structure measures can provide valuable insights to community planning authorities to manage unplanned congestion.

Data Analysis of MYO Signals during Upper Limb Movements of Enhanced Exoskeleton

Equipped with enhanced exoskeleton in the individual combat system can effectively enhance the soldiers’long-term load-bearing capacity and enhance the combat effectiveness of the army. In the exoskeleton control system, accurate recognition of human movement intentions plays an important role as upper-level control. This paper uses MYO armband as a sEMG sensor to collect 8 channels sEMG signals. Neural network method is applied to estimate the joint angles during arm movement. Motion capture system is used to verify the estimation accuracy. PCA (Principle Component Analysis) method is performed on the 8 channels data collected by MYO and processed dimensions were selected by experiments to make the estimation accuracy the highest. The results show that when the principal component dimension is selected as 8, which makes the estimation accuracy of the joint angles the highest.

Comparisons between USDA soil taxonomy and the Australian Soil Classification system II: Comparison of order, suborder and great group taxa

Soil taxonomies over the world are incongruent- based on different tiers and different sets of properties. This second paper is concerned with understanding the relationships of each tier (Order, Suborder and Great Group) in both Soil Taxonomy (ST) and the Australian Soil Classification system (ASC) using mean nearest neighbour distances and convex hull areas in two principal component dimensions. It is determined that in most instances, convex hull comparisons using only two principal components, representing 30% of the variation in the data describe much of the variability between and within the orders, suborders and great groups of each classification system. These are useful for visual comparisons of taxa at various levels. Mean nearest-neighbour distances can include all 414 variables if necessary, which is more rigorous but complex. Both distance calculations and convex hulls highlight the same associations between taxa from ASC and ST. Both these methods demonstrate the robust soil classification capability of the ST and the ASC, but with convex hull sizes and nearest-neighbour distances that are smaller, the ASC proves to be slightly more coherent. The two systems occupy somewhat different areas in PC space, and ST covers a larger overall area, demonstrating that ASC is a purpose-built classification for Australian conditions while ST Is a more general system that can cover a wider variety of soils and management issues. We also show that great groups in ST are at about the same level of taxonomic generalization as great groups of the ASC. Combining the best elements and taxa of both these systems would be a positive step in the creation of a comprehensive system.

A new unsupervised clustering algorithm applied to genome-wide profiles of breast cancers in The Cancer Genome Atlas proper subsets triple-negative samples.

e23195 Background: Clustering algorithms have identified subtypes of major cancers from analysis of genome-wide gene expression (GE) and somatic mutation (SM) profiles. These algorithms almost never discover a proper subset cluster, a recovered cluster that includes all the samples of a specific subtype. For breast cancer (BC), clustering of genome-wide profiles has been unable to proper subset triple negatives (TNs), TN subtypes, or other major subtypes. Methods: To search for a proper subset cluster for TNs, we applied a new clustering algorithm to the public domain GE and SM data of BC samples in The Cancer Genome Atlas (TCGA). A module of Medidata’s Clinical Trial Genomics (CTG) platform for automated clinical and genomic data integration and analysis, it uses a hierarchical component with tree learned cut points applied to a principal component dimension reduced similarity matrix calculated from a genome-wide data profile. Results: Our analysis of 540 TCGA BC samples run without human supervision produced a proper subset cluster that included all 55 TN samples and only 74 non-TN samples. GE data have previously indicated TN status, but this is the first demonstration that these TCGA BC data contain enough information to proper subset TNs, implying that this broad BC subtype has a strong, quantifiable impact on GE. We show that the genome-wide SMs of TCGA BC samples can be used to proper subset 4 novel subtypes distinguished as classes “TP53 mutated”, “PIK3CA mutated”, “both TP53 and PIK3CA mutated”, and “neither mutated”, signifying an important role for these known driver mutations in producing the subtypes’ genome-wide mutation profiles. We find that most ( &gt; 80%) TN BCs are in “TP53 mutated” but only 1 TN sample ( &lt; 2%) is in “PIK3CA mutated”, indicating distinct biology for these TNs with potential implications for TN therapy. Conclusions: CTG clustering achieves proper subset cancer subtype clustering of TCGA BC samples. These results illustrate the therapeutic discovery potential possible from genomic data of the high quality present in TCGA if combined with detailed clinical data with the Medidata CTG integration and annotation platform.

A scalable framework for NBA player and team comparisons using player tracking data

The release of NBA player tracking data greatly enhances the granularity and dimensionality of basketball statistics used to evaluate and compare player performance. However, the high dimensionality of this new data source can be troublesome as it demands more computational resources and reduces the ability to easily interpret findings. Therefore, we must find a way to reduce the dimensionality of the data while retaining the ability to differentiate and compare player performance. In this paper, Principal Component Analysis (PCA) is used to identify four principal components that account for 68% of the variation in player tracking data from the 2013-2014 regular season and intuitive interpretations of these new dimensions are developed by examining the statistics that influence them the most. In this new high variance, low dimensional space, you can easily compare statistical profiles across any or all of the principal component dimensions to evaluate characteristics that make certain players and teams similar or unique. A simple measure of similarity between two player or team statistical profiles based on the four principal component scores is also constructed. The Statistical Diversity Index (SDI) allows for quick and intuitive comparisons using the entirety of the player tracking data. As new statistics emerge, this framework is scalable as it can incorporate existing and new data sources by reconstructing the principal component dimensions and SDI for improved comparisons. Using principal component scores and SDI, several use cases are presented for improved personnel management.

EPIG-Seq: extracting patterns and identifying co-expressed genes from RNA-Seq data.

BackgroundRNA sequencing (RNA-Seq) measures genome-wide gene expression. RNA-Seq data is count-based rendering normal distribution models for analysis inappropriate. Normalization of RNA-Seq data to transform the data has limitations which can adversely impact the analysis. Furthermore, there are a few count-based methods for analysis of RNA-Seq data but they are essentially for pairwise analysis of treatment groups or multiclasses but not pattern-based to identify co-expressed genes.ResultsWe adapted our extracting patterns and identifying genes methodology for RNA-Seq (EPIG-Seq) count data. The software uses count-based correlation to measure similarity between genes, quasi-Poisson modelling to estimate dispersion in the data and a location parameter to indicate magnitude of differential expression. EPIG-Seq is different than any other software currently available for pattern analysis of RNA-Seq data in that EPIG-Seq 1) uses count level data and supports cases of inflated zeros, 2) identifies statistically significant clusters of genes that are co-expressed across experimental conditions, 3) takes into account dispersion in the replicate data and 4) provides reliable results even with small sample sizes. EPIG-Seq operates in two steps: 1) extract the pattern profiles from data as seeds for clustering co-expressed genes and 2) cluster the genes to the pattern seeds and compute statistical significance of the pattern of co-expressed genes. EPIG-Seq provides a table of the genes with bootstrapped p-values and profile plots of the patterns of co-expressed genes. In addition, EPIG-Seq provides a heat map and principal component dimension reduction plot of the clustered genes as visual aids. We demonstrate the utility of EPIG-Seq through the analysis of toxicogenomics and cancer data sets to identify biologically relevant co-expressed genes. EPIG-Seq is available at: sourceforge.net/projects/epig-seq.ConclusionsEPIG-Seq is unlike any other software currently available for pattern analysis of RNA-Seq count level data across experimental groups. Using the EPIG-Seq software to analyze RNA-Seq count data across biological conditions permits the ability to extract biologically meaningful co-expressed genes associated with coordinated regulation.Electronic supplementary materialThe online version of this article (doi:10.1186/s12864-016-2584-7) contains supplementary material, which is available to authorized users.

Physicochemical and sensory characterization of Cheddar cheese with variable NaCl levels and equal moisture content

The present study investigated the effect of salt (NaCl) on the flavor and texture of Cheddar cheese with the particular aim to elucidate consequences of, and strategies for, reducing the salt concentration. Descriptive sensory analysis and physicochemical mapping of 9-mo-old Cheddar cheeses containing 0.9, 1.3, 1.7, and 2.3% salt and an equal level of moisture (37.6±0.1%) were undertaken. Moisture regulation during manufacture resulted in slightly higher calcium retention (158 to 169mmol/kg) with decreasing NaCl concentration. Lactose was depleted only at 0.9 and 1.3% salt, resulting in concomitantly higher levels of lactate. Lower levels of casein components and free amino acids were observed with decreasing NaCl concentration, whereas levels of pH 4.6-soluble peptides were higher. Key taste-active compounds, including small hydrophobic peptides, lactose, lactate, and free amino acids, covaried positively with bitter, sweet, sour, and umami flavor intensities, respectively. An additional direct effect of salt due to taste–taste enhancement and suppression was noted. Sensory flavor profiles spanned a principal component dimension of palatability projecting true flavor compensation of salt into the space between cheeses containing 1.7 and 2.3% salt. This space was characterized by salt, umami, sweet, and a range of sapid flavors, and was contrasted by bitter and other off-flavors. Rheological and sensory measurements of texture were highly correlated. Cheeses made with 2.3% salt had a longer and slightly softer texture than cheeses containing 0.9, 1.3, and 1.7% salt, which all shared similar textural properties. Moisture regulation contributed to restoring the textural properties upon a 50% reduction in salt, but other factors were also important. On the other hand, significant flavor deterioration occurred inevitably. We discuss the potential of engineering a favorable basic taste profile to restore full palatability of Cheddar with a 50% reduction in salt.

Applicability analysis of the model for remotely estimating total suspended matter concentration based on principal component dimension reduction

Total suspended matter concentration(C TSM) is an important parameter for water quality evaluation.In this study,to improve the estimation accuracy of C TSM in inland type II water,principal component analysis(PCA) was used to reduce the dimensions of hyperspectral data measured in Lake Taihu in April,2009.Different multiple linear regression models of TSM were subsequently constructed using several principle components(PCs),and the optimal model was determined by comparing the performance of these models with each other.Finally,the applicability of the model to image data of the several current hyperspectral sensors was evaluated.The results show:① The first 3 PCs(PC 1,PC 2,PC 3) could explain the most of TSM variation information and the correlation coefficients between the first 3 PCs and ln(C TSM) are 0.728,0.401 and 0.403,respectively;② The optimal model could be developed when the number of PCs selected to be six.The performance of the model proposed in this study is better than that of the four traditional empirical models;③ Image data of the hyperspectral sensor that has more than 45 bands between 400 and 850 nm could be used to build a stable and accurate model for estimating TSM using PCA.In addition,data from frequently used sensors such as MERIS,HJ1-HSI,Hyperion and CHRIS could be also used to build this type model.

Unsupervised feature selection using weighted principal components

Feature selection has received considerable attention in various areas as a way to select informative features and to simplify the statistical model through dimensional reduction. One of the most widely used methods for dimensional reduction includes principal component analysis (PCA). Despite its popularity, PCA suffers from a lack of interpretability of the original feature because the reduced dimensions are linear combinations of a large number of original features. Traditionally, two or three dimensional loading plots provide information to identify important original features in the first few principal component dimensions. However, the interpretation of what constitutes a loading plot is frequently subjective, particularly when large numbers of features are involved. In this study, we propose an unsupervised feature selection method that combines weighted principal components (PCs) with a thresholding algorithm. The weighted PC is obtained by the weighted sum of the first k PCs of interest. Each of the k loading values in the weighted PC reflects the contribution of each individual feature. We also propose a thresholding algorithm that identifies the significant features. Our experimental results with both the simulated and real datasets demonstrated the effectiveness of the proposed unsupervised feature selection method.

Dynamical analysis of neuromuscular transmission jitter

Utilizing prolonged axonal stimulation single fiber EMG, neuromuscular transmission becomes a time-series of interpotential intervals (IPIs). In this form, the underlying processes of neuromuscular transmission can be studied using standard numerical techniques to determine whether these processes can be described by a simple mathematical model. In particular, neuromuscular transmission jitter can be examined in this way. In this article, we attempt to determine whether healthy jitter is noise or deterministic chaos. The presence of deterministic chaos was assessed by analysis of the IPI time-series using visual inspection of both phase-space plots and their principal component dimensions, and using the Grassberger-Procaccia algorithm to determine the correlation dimension of the time-series dynamics. These graphical and mathematical techniques provided little evidence for the existence of deterministic chaos. Linear autoregression time-series prediction also failed to account for the variability of the data and IPI histograms exhibited simple gaussian distributions. These results suggest normal neuromuscular transmission jitter is the result of intrinsic noise.