Linear Principal Component Analysis Research Articles

Quantitative morphological analysis framework of infant cranial sutures and fontanelles based on CT images.

Characterizing the suture morphological variation is a crucial step to investigate the influence of sutures on infant head biomechanics. This study aimed to establish a comprehensive quantitative framework for accurately capturing the cranial suture and fontanelle morphologies in infants. A total of 69 CT scans of 2-4 month-old infant heads were segmented to identify semilandmarks at the borders of cranial sutures and fontanelles. Morphological characteristics, including length, width, sinuosity index (SI), and surface area, were measured. For this, an automatic method was developed to determine the junction points between sutures and fontanelles, and thin-plate-spline (TPS) was utilized for area calculation. Different dimensionality reduction methods were compared, including nonlinear and linear principal component analysis (PCA), as well as deep-learning-based variational autoencoder (VAE). Finally, the significance of various covariates was analyzed, and regression analysis was performed to establish a statistical model relating morphological parameters with global parameters. This study successfully developed a quantitative morphological framework and demonstrate its application in quantifying morphologies of infant sutures and fontanelles, which were shown to significantly relate to global parameters of cranial size, suture SI, and surface area for infants aged 2-4 months. The developed framework proved to be reliable and applicable in extracting infant suture morphology features from CT scans. The demonstrated application highlighted its potential to provide valuable insights into the morphologies of infant cranial sutures and fontanelles, aiding in the diagnosis of suture-related skull fractures. Infant suture, Infant fontanelle, Morphological variation, Morphology analysis framework, Statistical model.

Predicting anomalies in computer networks using autoencoder-based representation learning

<span>Recent improvements in the internet of things (IoT), cloud services, and network data variety have increased the demand for complex anomaly detection algorithms in network intrusion detection systems (IDSs) capable of dealing with sophisticated network threats. Academics are interested in deep and machine learning (ML) breakthroughs because they have the potential to address complex challenges such as zero-day attacks. In comparison to firewalls, IDS are the initial line of network security. This study suggests merging supervised and unsupervised learning in identification systems IDS. Support vector machine (SVM) is an anomaly-based classification classifier. Deep autoencoder (DAE) lowers dimensionality. DAE are compared to principal component analysis (PCA) in this study, and hyper-parameters for F-1 micro score and balanced accuracy are specified. We have an uneven set of data classes. precision-recall curves, average precision (AP) score, train-test times, t-SNE, grid search, and L1/L2 regularization methods are used. KDDTrain+ and KDDTest+ datasets will be used in our model. For classification and performance, the DAE+SVM neural network technique is successful. Autoencoders outperformed linear PCA in terms of capturing valuable input attributes using t-SNE to embed high dimensional inputs on a two-dimensional plane. Our neural system outperforms solo SVM and PCA encoded SVM in multi-class scenarios.</span>

Mapping multi-decadal wetland loss: Comparative analysis of linear and nonlinear spatiotemporal characterization

Wetlands provide critical habitat for birds and endangered species, and can be influenced by shifts in water availability and land use. The Landsat image archive can help both document historical wetland change and monitor current dynamics, but multi-decadal retrospective studies face two important challenges: 1) many important ecohydrological processes occur at scales finer than the field of view of a 30 m Landsat pixel, and 2) ecologically meaningful wetland response units frequently exhibit spatiotemporal complexity in both vegetation and surface water which may not be well-represented by a simple study area spatial mean. Here we explore a novel method for contending with these challenges with application to the rapidly changing Andrade Mesa wetlands along the US-Mexico border. Using a 26-year (1995–2021) Landsat image time series, we track changes in surface water and vegetation using green vegetation (V) and dark (D) fractions estimated from spectral mixture analysis (SMA). Spatiotemporal dynamics in both V and D fractions were characterized using two techniques: linear Principal Component Analysis (PCA) and nonlinear manifold learning (via Uniform Manifold Approximation and Projection; UMAP). Bounding temporal endmembers were identified from PCA and used to construct a temporal mixture model which quantified total area of surface water and vegetation loss, including an uncertainty estimate. UMAP clearly distinguished areas with differing onset of vegetation and water loss which were not identifiable using PCA. Change maps were then associated with different mechanisms and outcomes, including possible mechanical clearing of vegetation and unexpected greening of woody vegetation. The overall timing of surface water and vegetation decline follows the lining of the All-American Canal, suggesting a potential cross-border hydrologic association between loss of a wetland in Mexico and water efficiency measures implemented in the United States.

Temporal Trends and Spatial Relationships of Radioactive Isotopes (I-131, Cs-134, and Cs-137) in Response to Nuclear Events: A Comprehensive Analysis Using Time Series Graphs, Regression, and Multivariate Techniques

This research aims to comprehend the evolution of radioactive isotopes Iodine-131 (I-131), Cesium-134 (Cs-134), and Cesium-137 (Cs-137) over time in diverse locations and analyze their relationships with the independent variables Longitude and Latitude using Linear Regression, Principal Component Analysis (PCA), and Canonical Correlation Analysis (CCA). The data used in this study were processed from the "DE.xlsx" file, including the imputation of missing values with 0 and column transformation into factors. The results of the Linear Regression analysis indicate a significant association between these isotopes and Longitude and Latitude. Additionally, PCA and CCA analyses reveal complex relationships between the isotopes and independent variables. This research provides valuable insights into the historical trends of radioactive isotopes Iodine-131 (I-131), Cesium-134 (Cs-134), and Cesium-137 (Cs-137) in various locations. The novel aspect and uniqueness of this study lie in the utilization of a comprehensive analytical approach, combining Linear Regression, PCA, and CCA to comprehend the relationships between isotopes and specific environmental factors. Moreover, this study significantly contributes to understanding the phenomena of radioactive isotopes and can serve as a foundation for further research in this field. The findings of this research are expected to support efforts in preventing and managing potential environmental and human health impacts of radioactive isotopes in the future.

The Effect of Different Vegetation Restoration Types on Soil Quality in Mountainous Areas of Beijing

Soil quality is a very important indicator used to assess ecosystem restoration states in terms of vegetation recovery and establishment. Evaluating the soil quality of different vegetation restoration types in mountainous areas of Beijing and identifying their influencing factors would provide a scientific basis and be helpful for vegetation restoration in the future. Six vegetation types (or communities), including Platycladus orientalis (L.) Franco pure forest (POP), Pinus tabulaeformis Carr. pure forest (PTP), Platycladus orientalis–Pinus tabulaeformis mixed forest (PPM), Platycladus orientalis coniferous and broadleaved mixed forest (POCB), Pinus tabulaeformis coniferous and broadleaved mixed forest (PTCB), deciduous broadleaved mixed forest (DBMF), and one area of non-afforested land (NF), with similar stand conditions were selected and fourteen factors of soil physical and chemical characteristics were measured and used to establish a total data set (TDS), while a minimum data set (MDS) was obtained by using the principal component analysis (PCA) and Pearson correlation analysis methods. Two scoring methods, linear (L) and non-linear (NL), were used to calculate the soil quality index (SQI), and the key factors influencing soil quality by vegetation were identified by a general linear model (GLM), PCA, and correlation analysis. The results showed that: (1) The screened MDS indicators which showed good relationships with the SQIs in the study areas were total nitrogen (TN), sand content, total potassium (TK), pH, and available water capacity (AWC). The SQI–NLM method has better applicability. (2) The contribution rates of vegetation to different soil factors accounted for 28.644% (TN), 21.398% (sand content), 24.551% (TK), 16.075% (pH), and 9.332% (AWC). (3) TN showed a positive relationship with all vegetation types; the content of TN in PTCB and DBMF was obviously larger than in the other types in the 0–10 cm layer; PPM, PTCB, and POCB affected the sand content, which showed negative correlativity; and DBMF showed positive correlativity with AWC. The mechanism of how different species affect TN, sand content, and AWC should be focused on and taken into consideration in further studies.

Performance evaluation of KPCA pre-imaging methods for speech signal denoising

<p class="Abstract">Kernel principal component analysis (KPCA) has gained wider interest amongst the researchers in nonlinear dimensionality reduction, data compression, feature extraction, and denoising applications. In KPCA, data from low dimensional input space implicitly mapped to higher dimensional feature space where linear PCA is enforced. However, for denoising application data need to invert back to input space, which is impossible and known as pre-imaging problems. Over recent years, several pre-imaging methods have proposed each with its benefits and disadvantages. In this paper, we evaluated the performance for selected pre-imaging methods for denoising speech signal, whose intelligibility and quality degraded by background noises. Further, we extend our work by comparing the performance of these pre-imaging methods by objective evaluation of denoised speech signal on generated toy examples and NOIZUES database.</p>

Canonical Response Parameterization: Quantifying the structure of responses to single-pulse intracranial electrical brain stimulation.

Single-pulse electrical stimulation in the nervous system, often called cortico-cortical evoked potential (CCEP) measurement, is an important technique to understand how brain regions interact with one another. Voltages are measured from implanted electrodes in one brain area while stimulating another with brief current impulses separated by several seconds. Historically, researchers have tried to understand the significance of evoked voltage polyphasic deflections by visual inspection, but no general-purpose tool has emerged to understand their shapes or describe them mathematically. We describe and illustrate a new technique to parameterize brain stimulation data, where voltage response traces are projected into one another using a semi-normalized dot product. The length of timepoints from stimulation included in the dot product is varied to obtain a temporal profile of structural significance, and the peak of the profile uniquely identifies the duration of the response. Using linear kernel PCA, a canonical response shape is obtained over this duration, and then single-trial traces are parameterized as a projection of this canonical shape with a residual term. Such parameterization allows for dissimilar trace shapes from different brain areas to be directly compared by quantifying cross-projection magnitudes, response duration, canonical shape projection amplitudes, signal-to-noise ratios, explained variance, and statistical significance. Artifactual trials are automatically identified by outliers in sub-distributions of cross-projection magnitude, and rejected. This technique, which we call "Canonical Response Parameterization" (CRP) dramatically simplifies the study of CCEP shapes, and may also be applied in a wide range of other settings involving event-triggered data.

An Improved Genetic-XGBoost Classifier for Customer Consumption Behavior Prediction

Abstract In an increasingly competitive market, predicting the customer’s consumption behavior has a vital role in customer relationship management. In this study, a new classifier for customer consumption behavior prediction is proposed. The proposed methods are as follows: (i) A feature selection method based on least absolute shrinkage and selection operator (Lasso) and Principal Component Analysis (PCA), to achieve efficient feature selection and eliminate correlations between variables. (ii) An improved genetic-eXtreme Gradient Boosting (XGBoost) for customer consumption behavior prediction, to improve the accuracy of prediction. Furthermore, the global search ability and flexibility of the genetic mechanism are used to optimize the XGBoost parameters, which avoids inaccurate parameter settings by manual experience. The adaptive crossover and mutation probabilities are designed to prevent the population from falling into the local extremum. Moreover, the grape-customer consumption behavior dataset is employed to compare the six Lasso-based models from the original, normalized and standardized data sources with the Isometric Mapping, Locally Linear Embedding, Multidimensional Scaling, PCA and Kernel Principal Component Analysis methods. The improved genetic-XGBoost is compared with several well-known parameter optimization algorithms and state-of-the-art classification approaches. Furthermore, experiments are conducted on the University of California Irvine datasets to verify the improved genetic-XGBoost algorithm. All results show that the proposed methods outperform the existing ones. The prediction results provide the decision-making basis for enterprises to formulate better marketing strategies.

Interaction of physico-chemical parameters with Shannon-Weaver Diversity Index based on phytoplankton diversity in coastal water of Diu, India

Phytoplankton acts as carbon sinks due to photosynthetic efficacy and their diversity is expressed by SWDI (Shannon-Weaver Diversity Index), which depends on water quality parameters. The coastal water of Diu was studied for three seasons, and the relationship between different parameters and SWDI was established. Subsequently, an attempt was made to build up a prediction model of SWDI based on multilayer perceptron Artificial neural network (ANN) using the R programme. Analysis shows interrelationship between the water quality parameters and phytoplankton diversity is same in linear principal component analysis (PCA) and neural network model. Variations of different parameters depend on seasonal changes. The ANN model shows that ammonia and phosphate are key parameters that influence the SWDI of phytoplankton. Seasonal variation in SWDI is related to variation in water quality parameters, as explained by both ANN and PCA. Hence, the ANN model can be an important tool for coastal environmental interaction study.

Natural Lipid Extracts as an Artificial Membrane for Drug Permeability Assay: In Vitro and In Silico Characterization

In vitro non-cellular permeability models such as the parallel artificial membrane permeability assay (PAMPA) are widely applied tools for early-phase drug candidate screening. In addition to the commonly used porcine brain polar lipid extract for modeling the blood-brain barrier's permeability, the total and polar fractions of bovine heart and liver lipid extracts were investigated in the PAMPA model by measuring the permeability of 32 diverse drugs. The zeta potential of the lipid extracts and the net charge of their glycerophospholipid components were also determined. Physicochemical parameters of the 32 compounds were calculated using three independent forms of software (Marvin Sketch, RDKit, and ACD/Percepta). The relationship between the lipid-specific permeabilities and the physicochemical descriptors of the compounds was investigated using linear correlation, Spearman correlation, and PCA analysis. While the results showed only subtle differences between total and polar lipids, permeability through liver lipids highly differed from that of the heart or brain lipid-based models. Correlations between the in silico descriptors (e.g., number of amide bonds, heteroatoms, and aromatic heterocycles, accessible surface area, and H-bond acceptor-donor balance) of drug molecules and permeability values were also found, which provides support for understanding tissue-specific permeability.

Complexity vs linearity: relations between functional traits in a heterotrophic protist

BackgroundFunctional traits are phenotypic traits that affect an organism’s performance and shape ecosystem-level processes. The main challenge when using functional traits to quantify biodiversity is to choose which ones to measure since effort and money are limited. As one way of dealing with this, Hodgson et al. (Oikos 85:282, 1999) introduced the idea of two types of traits, with soft traits that are easy and quick to quantify, and hard traits that are directly linked to ecosystem functioning but difficult to measure. If a link exists between the two types of traits, then one could use soft traits as a proxy for hard traits for a quick but meaningful assessment of biodiversity. However, this framework is based on two assumptions: (1) hard and soft traits must be tightly connected to allow reliable prediction of one using the other; (2) the relationship between traits must be monotonic and linear to be detected by the most common statistical techniques (e.g. linear model, PCA).ResultsHere we addressed those two assumptions by focusing on six functional traits of the protist species Tetrahymena thermophila, which vary both in their measurement difficulty and functional meaningfulness. They were classified as: easy traits (morphological traits), intermediate traits (movement traits) and hard traits (oxygen consumption and population growth rate). We detected a high number (> 60%) of non-linear relations between the traits, which can explain the low number of significant relations found using linear models and PCA analysis. Overall, these analyses did not detect any relationship strong enough to predict one trait using another, but that does not imply there are none.ConclusionsOur results highlighted the need to critically assess the relations among the functional traits used as proxies and those functional traits which they aim to reflect. A thorough assessment of whether such relations exist across species and communities is a necessary next step to evaluate whether it is possible to take a shortcut in quantifying functional diversity by collecting the data on easily measurable traits.

Emulating Rainfall-Runoff-Inundation Model using Deep Neural Network with Dimensionality Reduction

Abstract Predicting the spatial distribution of maximum inundation depth (depth-MAP) is important for the mitigation of hydrological disasters induced by extreme precipitation. However, physics-based rainfall-runoff-inundation (RRI) models, which are used operationally to predict hydrological disasters in Japan, require massive computational resources for numerical simulations. Here, we aimed at developing a computationally inexpensive deep learning model (Rain2Depth) that emulates an RRI model. Our study focused on the Omono River (Akita Prefecture, Japan) and predicted the depth-MAP from spatial and temporal rainfall data for individual events. Rain2Depth was developed based on a convolutional neural network (CNN), and predicts depth-MAP from 7-day successive hourly rainfall at 13 rain gauge stations in the basin. For training the Rain2Depth, we simulated the depth-MAP by the RRI model forced by 50-ensembles of 30-year data from large-ensemble weather/climate predictions. Instead of using the input and output data directly, we extracted important features from input and output data with two dimensionality reduction techniques (principal component analysis (PCA) and the CNN approach) prior to training the network. This dimensionality reduction aimed to avoid overfitting caused by insufficient training data. The nonlinear CNN approach was superior to the linear PCA for extracting features. Finally, Rain2Depth was architected by connecting the extracted features between input and output data through a neural network. Rain2Depth-based predictions were more accurate than predictions from our previous model (K20), which used ensemble learning of multiple regularized regressions for a specific station. Whereas the K20 can predict maximum inundation depth only at stations, our study achieved depth-MAP prediction by training only the single model Rain2Depth.

Penalized optimal scaling for ordinal variables with an application to international classification of functioning core sets.

Ordinal data occur frequently in the social sciences. When applying principal component analysis (PCA), however, those data are often treated as numeric, implying linear relationships between the variables at hand; alternatively, non-linear PCA is applied where the obtained quantifications are sometimes hard to interpret. Non-linear PCA for categorical data, also called optimal scoring/scaling, constructs new variables by assigning numerical values to categories such that the proportion of variance in those new variables that is explained by a predefined number of principal components (PCs) is maximized. We propose a penalized version of non-linear PCA for ordinal variables that is a smoothed intermediate between standard PCA on category labels and non-linear PCA as used so far. The new approach is by no means limited to monotonic effects and offers both better interpretability of the non-linear transformation of the category labels and better performance on validation data than unpenalized non-linear PCA and/or standard linear PCA. In particular, an application of penalized optimal scaling to ordinal data as given with the International Classification of Functioning, Disability and Health (ICF) is provided.

Protein Interaction Prediction Method Based on Feature Engineering and XGBoost

Human protein interaction prediction studies occupy an important place in systems biology. The understanding of human protein interaction networks and interactome will provide important insights into the regulation of developmental, physiological and pathological processes. In this study, we propose a method based on feature engineering and integrated learning algorithms to construct protein interaction prediction models. Principal Component Analysis (PCA) and Locally Linear Embedding (LLE) dimensionality reduction methods were used to extract sequence features from the 174-dimensional human protein sequence vector after Normalized Difference Sequence Feature (NDSF) encoding, respectively. The classification performance of three integrated learning methods (AdaBoost, Extratrees, XGBoost) applied to PCA and LLE features was compared, and the best combination of parameters was found using cross-validation and grid search methods. The results show that the classification accuracy is significantly higher when using the linear dimensionality reduction method PCA than the nonlinear dimensionality reduction method LLE. the classification with XGBoost achieves a model accuracy of 99.2%, which is the best performance among all models. This study suggests that NDSF combined with PCA and XGBoost may be an effective strategy for classifying different human protein interactions.

Intraspecific variation in growth response to drought stress across geographic locations and genetic groups in Coffea canephora.

Uganda lies within the drier end of the natural distribution range of Coffea canephora and contains unexplored genetic material that could be drought-adapted and useful for developing climate-resilient varieties. Using water treatment: (i) ample and (ii) restricted-water, the response of 148 genotypes were studied comprising wild, feral and cultivated C. canephora. Biomass allocation, standing leaf area and leaf area growth data were collected. Linear mixed effect models and PCA were used to the analyze effect of water treatment on genotypes from different: (i) cultivation status, (ii) genetic groups and (iii) locations. We also assessed the relationship between drought tolerance for relative growth rate in leaf area (RGRA), total number of leaves (TNL), total leaf area (TLA) and total leaf dry weight (TLDW) of genotypes at final harvest. Restricted-water reduced RGRA across genetic groups (3.2-32.5%) and locations (7.1-36.7%) but not cultivation status. For TNL, TLA and TLDW, genotypes that performed well in ample-water performed worse under restricted-water, indicating growth-tolerance trade-off. Drought tolerance in RGRA and TNL were negatively correlated with wetness index suggesting some degree of adaptation to local climate. Findings indicate a growth-tolerance trade-off within this tropical tree species and drought tolerance of Uganda's C. canephora is somewhat associated with local climate.

Optimisation of the core subset for the APY approximation of genomic relationships

BackgroundBy entering the era of mega-scale genomics, we are facing many computational issues with standard genomic evaluation models due to their dense data structure and cubic computational complexity. Several scalable approaches have been proposed to address this challenge, such as the Algorithm for Proven and Young (APY). In APY, genotyped animals are partitioned into core and non-core subsets, which induces a sparser inverse of the genomic relationship matrix. This partitioning is often done at random. While APY is a good approximation of the full model, random partitioning can make results unstable, possibly affecting accuracy or even reranking animals. Here we present a stable optimisation of the core subset by choosing animals with the most informative genotype data.MethodsWe derived a novel algorithm for optimising the core subset based on a conditional genomic relationship matrix or a conditional single nucleotide polymorphism (SNP) genotype matrix. We compared the accuracy of genomic predictions with different core subsets for simulated and real pig data sets. The core subsets were constructed (1) at random, (2) based on the diagonal of the genomic relationship matrix, (3) at random with weights from (2), or (4) based on the novel conditional algorithm. To understand the different core subset constructions, we visualise the population structure of the genotyped animals with linear Principal Component Analysis and non-linear Uniform Manifold Approximation and Projection.ResultsAll core subset constructions performed equally well when the number of core animals captured most of the variation in the genomic relationships, both in simulated and real data sets. When the number of core animals was not sufficiently large, there was substantial variability in the results with the random construction but no variability with the conditional construction. Visualisation of the population structure and chosen core animals showed that the conditional construction spreads core animals across the whole domain of genotyped animals in a repeatable manner.ConclusionsOur results confirm that the size of the core subset in APY is critical. Furthermore, the results show that the core subset can be optimised with the conditional algorithm that achieves an optimal and repeatable spread of core animals across the domain of genotyped animals.

A unified multivariate statistical approach for the assessment of deep groundwater quality of rapidly growing city of Maharashtra Province, India, with potential health risk.

The main aim of this research is to assess the consequences of natural and anthropogenic processes on the groundwater quality of 65 deep aquifers of Nagpur city, Maharashtra Province, India, using a unified multivariate statistical approach. The dominant groundwater type recognized is Ca-HCO3 (recharge waters) in 43.1 and 38.5% of groundwater samples of pre- and post-monsoon seasons, followed by mixed water types. The seasonal distribution of physicochemical parameters shows increase in the concentration of EC, TDS, TH, Mg2+, SO42-, and NO3- signifying the high mineralization and anthropogenic loading from pre- and post-monsoon season respectively. The entropy-weight water quality index categorizes the 84.6% and 75.4% of total samples from pre- and post-monsoon seasons into moderate quality. The multiple linear regression and PCA analysis reveal the masking of rock weathering mechanism by anthropogenic activities. The % of PCA Variance varies from 79 to 83.7% from pre- to post-monsoon season. The high contributions of EC (0.76, 0.72), TDS (0.79, 0.73), TH (0.97, 0.962), Ca2+ (0.84, 0.78), Mg2+ (0.79, 0.83), Cl- (0.73, 0.75), and NO3- (0.78, 0.68) in PC1 components expose high salinity and hardness in urban groundwater that signifies the consequences of urbanization on the groundwater regime. About 55.4 and 70.8% of children population as compared to the adult female (53.8%, 69.2%) and male (32.3%, 46.1%) population in PRM and POM respectively were at high non-carcinogenic health threat of NO3--enriched groundwater. The study is beneficial for understanding the variation in groundwater composition due to unplanned urbanization and is very useful for protecting groundwater resources in urban areas.

A unified framework for analyzing complex systems: Juxtaposing the (Kernel) PCA method and graph theory

In this article, we present a unified framework for the analysis and characterization of a complex system and demonstrate its application in two diverse fields: neuroscience and astrophysics. The framework brings together techniques from graph theory, applied mathematics, and dimensionality reduction through principal component analysis (PCA), separating linear PCA and its extensions. The implementation of the framework maps an abstract multidimensional set of data into reduced representations, which enable the extraction of its most important properties (features) characterizing its complexity. These reduced representations can be sign-posted by known examples to provide meaningful descriptions of the results that can spur explanations of phenomena and support or negate proposed mechanisms in each application. In this work, we focus on the clustering aspects, highlighting relatively fixed stable properties of the system under study. We include examples where clustering leads to semantic maps and representations of dynamic processes within the same display. Although the framework is composed of existing theories and methods, its usefulness is exactly that it brings together seemingly different approaches, into a common framework, revealing their differences/commonalities, advantages/disadvantages, and suitability for a given application. The framework provides a number of different computational paths and techniques to choose from, based on the dimension reduction method to apply, the clustering approaches to be used, as well as the representations (embeddings) of the data in the reduced space. Although here it is applied to just two scientific domains, neuroscience and astrophysics, it can potentially be applied in several other branches of sciences, since it is not based on any specific domain knowledge.

Integrated Evaluation of Financial Risk in Coal Industry Restructuring: A Model of Linear Regression and PCA.

Aiming at the integrated evaluation problem of financial risk in coal industry restructuring, a model of linear regression and PCA is put forward. This paper studies the univariate correlation and multivariable mixed correlation between the main business income and the book value of fixed assets and nonfixed assets in the statements of coal listed companies and gives the correlation function between the variables by using a variety of univariate linear, univariate nonlinear, and binary linear regression methods. It also points out that the coal enterprises in China are basically in the stage of increasing scale income at the present stage and can continue to achieve rapid increase in profits through mergers and acquisitions and other expansion methods. At the same time, it is also concluded that nonfixed assets, namely, intangible assets and human capital, contribute more to the main business income of coal enterprises in China, which objectively proves the correctness of our thinking of developing knowledge economy.

Low-cost assimilation for sound speed fields in the PCA framework

Forecast ocean sound speed fields are often inaccurate and need to be reconciled with observation data. Conventional data-assimilation methods used for this are generally quite computationally intensive. A compressed representation of the forecast sound speed fields can be obtained using principal component analysis (PCA), where the forecast fields are represented by a linear combination fo PCA modes. We develop a low-cost assimilation approach that updates the PCA compressed representation of the background forecast field, based on observation data.The approach uses Bayes‘ rule to obtain the maximum likelihood estimate for the update in the space spanned by the PCA modes. Significant cost savings come from the dimensionality reduction that is provided by PCA. Results are presented for sound speed fields derived from HYCOM ocean forecast data and expendable bathythermograph data obtained from the Scipps Institution of Oceanography.