Dimensional Data Research Articles

Least angle sparse principal component analysis for ultrahigh dimensional data

AbstractPrincipal component analysis (PCA) has been a widely used technique for dimension reduction while retaining essential information. However, the ordinary PCA lacks interpretability, especially when dealing with large scale data. To address this limitation, sparse PCA (SPCA) has emerged as an interpretable variant of ordinary PCA. However, the ordinary SPCA relies on solving a challenging non-convex discrete optimization problem, which maximizes explained variance while constraining the number of non-zero elements in each principal component. In this paper, we propose an innovative least angle SPCA technique to address the computational complexity associated with SPCA, particularly in ultrahigh dimensional data, by sequentially identifying sparse principal components with minimal angles to their corresponding components extracted through ordinary PCA. This sequential identification enables solving the optimization problem in polynomial time, significantly reducing computational challenges. Despite its efficiency gains, our proposed method also preserves the main attributes of SPCA. Through comprehensive experimental results, we demonstrate advantages of our approach as a viable alternative for dealing with the computational difficulties inherent in ordinary SPCA. Notably, our method emerges as an efficient and effective solution for conducting ultrahigh dimensional data analysis, enabling researchers to extract meaningful insights and streamline data interpretation.

MinLinMo: a minimalist approach to variable selection and linear model prediction

Generating prediction models from high dimensional data often result in large models with many predictors. Causal inference for such models can therefore be difficult or even impossible in practice. The stand-alone software package MinLinMo emphasizes small linear prediction models over highest possible predictability with a particular focus on including variables correlated with the outcome, minimal memory usage and speed. MinLinMo is demonstrated on large epigenetic datasets with prediction models for chronological age, gestational age, and birth weight comprising, respectively, 15, 14 and 10 predictors. The parsimonious MinLinMo models perform comparably to established prediction models requiring hundreds of predictors.

A study on identifying representative trips for mobility service design

AbstractRecently, with growing interest in urban mobility patterns, the demand for collecting and analysing origin‐destination (OD) data is increasing. Due to the large scale and dimensionality of OD data, there are two issues in analysing the data: big‐data storage and major pattern extraction. To deal with two issues at the same time, this study suggests a principal control analysis‐based major demand identification method to improve the usability of microscopic OD data. Especially, this study focuses on finding principal components that preserve major patterns from OD data with small random noise so that the data can be effectively used for mobility service design. The proposed method is applied to smart card data of Seoul and Sejong and extracted major demand patterns from peak‐ and non‐peak hour data of these cities. The degree of daily regularity, reconstruction accuracy, and compression rate of the reconstructed data is analysed varying sets of principal components. The obtained results show that the major demands contain a low volume and a large volume of demand and with lower‐order principal components, major demands can be efficiently extracted by removing randomly appearing small‐volume demand. In addition, the trade‐off behaviour is observed between the degree of daily regularity and reconstruction accuracy depending on the compression rate. Based on the observations, it can be found that the loss of major demand patterns could be prevented when targeting a reconstruction accuracy of 90–95% and the proposed method can reduce the data size while preserving major mobility patterns.

Quantum Distance Approximation for Persistence Diagrams

Abstract Topological Data Analysis methods can be useful for classification and clustering
tasks in many different fields as they can provide two dimensional persistence dia-
grams that summarize important information about the shape of potentially complex
and high dimensional data sets. The space of persistence diagrams can be endowed
with various metrics, which admit a statistical structure and allow to use these summaries for machine learning algorithms, e.g. the Wasserstein distance.

However, computing the distance between two persistence diagrams involves finding an opti-
mal way to match the points of the two diagrams and may not always be an easy
task for classical computers. Recently, quantum algorithms have shown the po-
tential to speedup the process of obtaining the persistence information displayed on
persistence diagrams by estimating the spectra of persistent Dirac operators. So,
in this work we explore the potential of quantum computers to estimate the distance
between persistence diagrams as the next step in the design of a fully quantum frame-
work for TDA. In particular we propose variational quantum algorithms for the
Wasserstein distance as well as the dcp distance. Our implementation is a weighted
version of the Quantum Approximate Optimization Algorithm that relies on control
clauses to encode the constraints of the optimization problem.

Intelligent aerodynamic modelling method for steady/unsteady flow fields of airfoils driven by flow field images based on modified U-Net neural network

An intelligent modelling method driven by flow field images for predicting steady and unsteady flow filed around aerofoils has been developed. Signed Distance Field (SDF) images achieve dimensionality enhancement of aerofoil geometric information, and ‘synthesised images’ achieve dimensionality enhancement of the angle of attack of the aerofoil and Mach number. An intelligent aerodynamic model for steady flow field of aerofoils is constructed based on the U-Net neural network architecture, and further incorporating a long short-term memory (LSTM) module to construct a U-Net-LSTM neural network architecture to extract the temporal features. Typical NACA aerofoils results show that, the prediction error for steady flow is less than 1.98%, while the prediction error for unsteady flow is less than 2.56%. Additionally, the model demonstrates good generalization capability, with a generalization error for steady flow less than 2.45% and a generalization error for unsteady flow less than 3.34%. This research provides a new method for intelligent aerodynamic modelling based on physical representations. Compared to existing methods, this method avoids the need for extracting aerofoil geometry information and eliminates the necessity of predicting the flow field point by point, making it more concise and efficient. Highlights 1. An aerodynamic model was constructed using U-Net to rapidly predict the steady flow field around airfoils. 2. A Long Short-Term Memory (LSTM) module was incorporated to capture temporal information, enabling the rapid prediction of the unsteady flow field around airfoils. To address the problem of ‘dimension loss’ in the modelling datasets, effective data dimensionality enhancement was achieved using SDF images and ‘synthesized images’.

A Storm Frame Optimization Method for Predicting and Warning the Safety Status of a Shearer

ABSTRACTReal‐time monitoring, prediction, and early warning of operating status during intelligent mining are the key to ensuring stable production. To solve the problem of lag in determining the operating status of a shearer, this study proposes a new method for predicting and warning the real‐time operating status of the shearer involving the Storm framework, based on parallel optimization of data processing and the gated recurrent unit (GRU) model based on hyperparameter optimization. First, the GRU model is optimized through hyperparameter optimization to achieve adaptive and accurate prediction and early warning of multidimensional state parameters of the shearer. Second, a virtual machine is constructed to host the Storm framework, parallel optimized real‐time processing of data is performed on the Storm framework, and real‐time data flow patterns are constructed to speed up data processing and retrieval, ensuring each tuple is fully processed through the topology structure. Finally, the optimized GRU model is embedded into the optimized Storm framework to achieve real‐time prediction and early warning of different dimensional data of the shearer. The prediction accuracy, early warning accuracy, and processing efficiency of the Storm platform are used as evaluation indicators to analyze and evaluate the model, verifying the efficiency and applicability of the proposed model. Experimental results show that the model has a prediction accuracy of 93%, an early warning accuracy of 93.05%, and consumes 10 s. It can achieve high performance, low latency, and high precision in predicting and providing early warnings for the shearer's state parameters, greatly improving the efficiency of predicting and early warning the operating status parameters of the shearer. This model realizes real‐time prediction and early warning of the shearer's operating status, providing technical support for intelligent mining in coal mines.

Research on a Passenger Flow Prediction Model Based on BWO-TCLS-Self-Attention

In recent years, with the rapid development of the global demand and scale for deep underground space utilization, deep space has gradually transitioned from single-purpose uses such as underground transportation, civil defense, and commerce to a comprehensive, livable, and disaster-resistant underground ecosystem. This shift has brought increasing attention to the safety of personnel flow in deep spaces. In addressing challenges in deep space passenger flow prediction, such as irregular flow patterns, surges in extreme conditions, large data dimensions, and redundant features complicating the model, this paper proposes a deep space passenger flow prediction model that integrates a Temporal Convolutional Network (TCN) and Long Short-Term Memory (LSTM) network. The model first employs a dual-layer LSTM network structure with a Dropout layer to capture complex temporal dynamics while preventing overfitting. Then, a Self-Attention mechanism and TCN network are introduced to reduce redundant feature data and enhance the model’s performance and speed. Finally, the Beluga Whale Optimization (BWO) algorithm is used to optimize hyperparameters, further improving the prediction accuracy of the network. Experimental results demonstrate that the BWO-TCLS-Self-Attention model proposed in this paper achieves an R2 value of 96.94%, with MAE and RMSE values of 118.464 and 218.118, respectively. Compared with some mainstream prediction models, the R2 value has increased, while both MAE and RMSE values have decreased, indicating its ability to accurately predict passenger flow in deep underground spaces.

Optimal Multitask Linear Regression and Contextual Bandits under Sparse Heterogeneity

Large and complex datasets are often collected from several, possibly heterogeneous sources. Multitask learning methods improve efficiency by leveraging commonalities across datasets while accounting for possible differences among them. Here, we study multitask linear regression and contextual bandits under sparse heterogeneity, where the source/task-associated parameters are equal to a global parameter plus a sparse task-specific term. We propose a novel two-stage estimator called MOLAR that leverages this structure by first constructing a covariate-wise weighted median of the task-wise linear regression estimates and then shrinking the task-wise estimates towards the weighted median. Compared to task-wise least squares estimates, MOLAR improves the dependence of the estimation error on the data dimension. Extensions of MOLAR to generalized linear models and constructing confidence intervals are discussed in the paper. We then apply MOLAR to develop methods for sparsely heterogeneous multitask contextual bandits, obtaining improved regret guarantees over single-task bandit methods. We further show that our methods are minimax optimal by providing a number of lower bounds. Finally, we support the efficiency of our methods by performing experiments on both synthetic data and the PISA dataset on student educational outcomes from heterogeneous countries.

Automatic extraction of fine structural information in angle-resolved photoemission spectroscopy by multi-stage clustering algorithm

Unsupervised clustering method has shown strong capabilities in automatically categorizing the ARPES (ARPES: angle-resolved photoemission spectroscopy) spatial mapping dataset. However, there is still room for improvement in distinguishing subtle differences caused by different layers and substrates. Here, we propose a method called Multi-Stage Clustering Algorithm (MSCA). Using the K-means clustering results/metrics for real space in different energy-momentum windows as the input of the second round K-means clustering for momentum space, the energy-momentum windows that exhibit subtle inhomogeneity in real space will be highlighted. It recognizes different types of electronic structures both in real space and momentum space in spatially resolved ARPES dataset. This method can be used to capture the areas of interest, and is especially suitable for samples with complex band dispersions, and can be a practical tool to any high dimensional scientific data analysis.

Image Processing Technique for Enhanced Combustion Efficiency of Wood Pellets

The combustion efficiency of wood pellets is partly affected by their average length. The ISO 17829 standard defines the methodology for assessing the average length of sample pellets, but the method does not always lead to representative data. Furthermore, a standard analysis is time-consuming as it requires manual measurement of the pellets using a caliper. This paper, whilst evaluating the effect of pellet length on combustion efficiency, proposes a pending-patented dimensional image processing method (DIP) for assessing pellet length. DIP allows the dimensional data of grouped and stacked pellets to be obtained by exploiting the shadows produced by pellets when exposed to a light source, assuming that different-sized pellets produce different shadows. Thus, the proposed method allows for the extraction of dimensional information from non-distinct objects, overcoming the reliance of classical image processing methods on object distance for effective segmentation. Combustion tests, carried out using pellets varying only in length, confirmed the influence of length on combustion efficiency. Shorter pellets, compared to longer ones, significantly reduced CO emissions by up to 94% (mg/MJ). However, they exhibited a higher fuel mass consumption rate (kg/h), with an increase of up to 22.8% compared to the longest sample. In addition, longer pellets produced fewer but larger shadows than shorter ones. Further studies are needed to correlate the number and size of shadows with samples’ average length so that DIP could be implemented in stoves and programmed to communicate with the control unit and automatically optimize the setting in order to improve combustion efficiency.

Big Data and Oral Health Disparities: A Critical Appraisal.

Big data has emerged as a pivotal asset in addressing oral health disparities in recent years. Big data encompasses the vast pool of health care-related biomedical information sourced from diverse channels, such as claims data, patient registries, and electronic health records (EHRs). This study is a critical review that synthesizes the evidence, identifies gaps in knowledge, and discusses future implications regarding big data analytics and oral health disparities. Published reports from 2014 to 2023 that studied associations between big data, social determinants of oral health, and oral health disparities, published in English and available in electronic databases, were included. Search engines were MEDLINE via PubMed, Google Scholar, and Web of Science. A total of 23 studies were included in the review, and all were retrospective data analytics. Studies have used a variety of big data sources, including EHRs, claims, and national or regional registries. This study used a framework of data quality dimensions with intrinsic (data attributes) and contextual values (information provided by the data, in this case, oral health disparities) to critically appraise the included studies. Big data revealed disparities in oral health outcomes and dental care utilization based on race, ethnicity, socioeconomic status, geographical location, insurance category, access to care, and other barriers to care. For the intrinsic data dimension, none of the studies addressed or reported data missingness or consistency of the data. The studies clearly provided contextual data dimensions. From a value-added perspective, several studies provided novel and new information related to racial oral health inequities. Several studies used more than one oral health disparities variable or a composite variable. However, the conclusions from several studies were based on association-based analytics, and few studies used artificial intelligence approaches to understand the population's oral health inequities-gaps were seen in the study designs and causal analytics.

Classification model for blast furnace status based on multi-source information

The blast furnace (BF) is the key equipment for smelting, which has a significant impact on the sustainable development of global environment and energy. Therefore, it will be helpful for the operators if accurate evaluation to the status of the BF is realized. The classification model based on multi-source information is proposed in this paper, where the kernel fisher (KF) algorithm is enhanced to simplify the complexity both in algorithm and data dimensionality. The proposed model can realize the classification of both the distribution of gas flow (GF) and the geometric information of the burden surface (BS), and this paper also proposes a dynamic process adaptive kernel fisher (DPAKF) algorithm to enhance the adaptive ability of the classifier, where the online algorithm updating mechanism is designed. The experimental results demonstrate that the classification accuracy was increased from 90% to 95%, and the time expense of DPAKF was 236 s, which is prior compared with the existing support vector machine (SVM), k-nearest neighbor (KNN) and genetic algorithm (GA) models. The results of the student's t-distribution show that the statistics between DPAKF and KF, SVM, KNN and GA were 1.25, 2.81, 2.84 and 2.96, respectively, which demonstrate that there are significant statistical differences between DPAKF and SVM, KNN, and GA. This research provides a potential solution to the classification problem of the BF.

Data-driven approach for the classification of gas turbine faults

Gas turbines (GTs) play a crucial role in the production of electricity. Extreme working conditions can lead to deterioration in GTs' performance, resulting in the occurrence of various issues. This study proposes an approach to deal with this issue by combining a layered recurrent neural network (LRNN) with principal component analysis (PCA). This approach aims to reduce the dimensionality of data and computational complexity effectively while enhancing the accuracy of gas turbine fault classification. The methodology outlined consists of two steps. The first step is to apply PCA to the dataset that was collected from the gas turbine. By transforming the data into a lower-dimensional space, PCA helps to eliminate redundant information and improve computational efficiency. Next, LRNN is employed to detect and classify faults in the gas turbine. The LRNN’s structure enables it to capture complex patterns and relationships in the data, which enhances the accuracy of fault classification. This study is based on historical data collected from a gas turbine power station, consisting of 8200 samples of 34 measured variables. The operating parameters contain data such as temperature and pressure. Each data point's relationship to a specific turbine scenario reveals if it is healthy or one of the four faulty scenarios. The results showed that by combining the LRNN with PCA, the gas turbine fault classification achieved good performance in terms of accuracy, precision and neural network model performances, while also showcasing the faster convergence speed of the LRNN when trained on PCA instead of the original dataset.

Revisiting the Endoscopic Third Ventriculostomy Success Score using machine learning: can we do better?

The Endoscopic Third Ventriculostomy Success Score (ETVSS) is a useful decision-making heuristic when considering the probability of surgical success, defined traditionally as no repeat cerebrospinal fluid diversion surgery needed within 6 months. Nonetheless, the performance of the logistic regression (LR) model in the original 2009 study was modest, with an area under the receiver operating characteristic curve (AUROC) of 0.68. The authors sought to use a larger dataset to develop more accurate machine learning (ML) models to predict endoscopic third ventriculostomy (ETV) success and also to perform the largest validation of the ETVSS to date. The authors queried the MarketScan national database for the years 2005-2022 to identify patients < 18 years of age who underwent first-time ETV and subsequently had at least 6 months of continuous enrollment in the database. The authors collected data on predictors matching the original ETVSS: age, etiology of hydrocephalus, and history of any previous shunt placement. Next, they used 6 ML algorithms-LR, support vector classifier, random forest, k-nearest neighbors, Extreme Gradient Boosted Regression (XGBoost), and naive Bayes-to develop predictive models. Finally, the authors used nested cross-validation to assess the models' comparative performances on unseen data. The authors identified 2047 patients who met inclusion criteria, and 1261 (61.6%) underwent successful ETV. The performances of most ML models were similar to that of the original ETVSS, which had an AUROC of 0.693 on the validation set and 0.661 (95% CI 0.600-0.722) on the test set. The authors' new LR model performed comparably with AUROCs of 0.693 on both the validation and test sets, with 95% CI 0.633-0.754 on the test set. Among the more complex ML algorithms, XGBoost performed best, with AUROCs of 0.683 and 0.672 (95% CI 0.609-0.734) on the validation and test sets, respectively. This is the largest external validation of the ETVSS, and it confirms modest performance. More sophisticated ML algorithms do not meaningfully improve predictive performance compared to ETVSS; this underscores the need for higher utility, novelty, and dimensionality of input data rather than changes in modeling strategies.

Robust Principal Component Analysis Based on Fuzzy Local Information Reservation.

Principal Component Analysis (PCA) aims to acquire the principal component space containing the essential structure of data, instead of being used for mining and extracting the essential structure of data. In other words, the principal component space contains not only information related to the essential structure of data but also some unrelated information. This frequently occurs when the intrinsic dimensionality of data is unknown or when it has complex distribution characteristics such as multi-modalities, manifolds, etc. Therefore, it is unreasonable to identify noise and useful information based solely on reconstruction error. For this reason, PCA is unsuitable as a preprocessing technique for most applications, especially in noisy environment. To solve this problem, this paper proposes robust PCA based on fuzzy local information reservation (FLIPCA). By analyzing the impact of reconstruction error on sample discriminability, FLIPCA provides a theoretical basis for noise identification and processing. This not only greatly improves its robustness but also extends its applicability and effectiveness as a data preprocessing technique. Meanwhile, FLIPCA maintains consistent mathematical descriptions with traditional PCA while having few adjustable hyperparameters and low algorithmic complexity. Finally, we conducted comprehensive experiments on synthetic and real-world datasets, which substantiated the superiority of our proposed algorithm.

HMS-TENet: A hierarchical multi-scale topological enhanced network based on EEG and EOG for driver vigilance estimation

Driving vigilance estimation is an important task for traffic safety. Nowadays, electroencephalography (EEG) and electrooculography (EOG) have made some achievements in vigilance estimation, but there are still some challenges: 1) The traditional approachs with direct multimodal fusion may face the problems of information redundancy and data dimensionality mismatch; 2) Capture key discriminative features during multimodal fusion without losing specific patterns to each modality. In order to solve the above problems, this paper proposes a approach with fusion of EEG and EOG features in split bands, which not only preserves the information about brain activities in different bands of EEG, but also effectively integrates the relevant information of EOG. On this basis, we further propose a hierarchical multi-scale topological enhanced network (HMS-TENet). This network first introduces a pyramid pooling structure (PPS) to capture contextual relationships from different discriminative perspectives. And then we design a selective convolutional structure (SCS) for adaptive sense-field selection, which enables us to mine the desired discriminative information in small-size features. In addition, we design a topology self-aware attention to enhance the learning of representations of complex topological relationships among EEG channels. Finally, the output of the model can be selected for both regression and classification tasks, providing higher flexibility and adaptability. We demonstrate the robustness, generalizability, and utility of the proposed method based on intra-subject and cross-subject experiments on the SEED-VIG public dataset. Codes are available at https://github.com/tangmeng28/HMS-TENet.

Evaluation of grounding grid corrosion extent based on laser-induced breakdown spectroscopy (LIBS) combined with machine learning

As one of the most widely used forms of energy, the safety and stability of power systems are crucial to modern society. Grounding grids dissipate current and reduce touch and pace voltage during lightning strikes or fault currents, ensuring the safety of personnel and equipment. However, prolonged submersion in soil causes inevitable corrosion, compromising grounding efficacy by increasing resistance and reducing current dissipation. This deterioration can result in unsafe local potential differences. This study uses Laser-Induced Breakdown Spectroscopy (LIBS) to measure corrosion degrees in grounding grids. Spectral data from samples with varying corrosion extent were collected, with outliers removed using the Local Outlier Factor (LOF) algorithm. Principal Component Analysis (PCA) reduced data dimensionality, revealing clustering in spectral data corresponding to corrosion extent. Three machine learning models were compared: Adaptive Boosting - Backpropagation Neural Network (Adaboost-BP), Support Vector Machine (SVM), and Random Forest (RF). The RF model showed the highest accuracy in predicting corrosion degree (R²=0.9845, MSE=0.0296), outperforming Adaboost-BP and SVM, especially for intermediate corrosion extent. These findings validate the effectiveness and reliability of combining LIBS with machine learning for predicting grounding grid corrosion, providing a theoretical foundation for the safe operation of power systems.

Another pipeline in local Partial Least Squares Regression (LPLS) methods: Assessing the impact of wavelet transform integration

This study evaluates the performance of four Partial Least Squares Regression (PLS) methods, focusing on a new Local Partial Least Squares Regression (LPLS) variant integrating wavelet transformation, named WLPLS, for analyzing feed using Near-Infrared (NIR) spectroscopy. While traditional PLS methods are effective for many spectroscopic applications, their global modeling approach often reduces predictive accuracy in large, heterogeneous datasets. In contrast, LPLS adapts models to local data characteristics, which can enhance prediction but also increase computational demands (power and time). WLPLS seeks to mitigate these demands by incorporating wavelet transformation to reduce data dimensionality while effectively managing spectral variances. This research conducts a comparative analysis of WLPLS against traditional PLS, LPLS, and another LPLS pipeline reducing data dimensionality: the LPLS on global PLS scores (LPLS-S). The performances of these methods were evaluated using a large feed database containing 24,644 samples, analyzing five key constituents: ash, crude fibers, fat, moisture, and proteins. The results demonstrate that local approaches outperformed the global PLS method for this dataset and that the performances of the local methods were relatively similar to each other. The selection of the optimal method therefore depends on the specific requirements of the application, such as dataset characteristics and the required prediction speed. Future studies should broaden this comparative framework to additional datasets and contexts to ensure they are adapted for diverse applications.

Sensor attack online classification for UAVs using machine learning

Unmanned Aerial Vehicle (UAV) sensors play a vital role in maintaining flight safety and stability. However, the increasing frequency and complexity of sensor attacks have emerged as a critical threat to UAV systems. The current lack of robust multi-classification methods for detecting sensor attacks limits the effectiveness and completeness of existing defense strategies. This research addresses these challenges by leveraging machine learning (ML) techniques to classify various sensor attacks using heterogeneous sensor data and control parameters, thereby enhancing UAV system security. In this study, we design and implement multiple sensor attack scenarios targeting gyroscopes, accelerometers, barometers, and GPS. Comprehensive datasets are collected during UAV flight, integrating diverse sensor readings, flight states, and control parameters. By analyzing the characteristics of sensor attacks and their impact on position estimation and attitude control, we identify and extract key features. To optimize the classification model, we employ feature importance analysis, correlation analysis, and ablation experiments, significantly reducing data dimensionality and enhancing model training efficiency. The experimental results demonstrate the proposed ML-based multi-classification model’s superior performance, achieving a detection rate of 89.38%, significantly outperforming traditional single-attack detection methods in terms of generalization capability. Our approach efficiently handles complex multi-sensor attack scenarios. Moreover, deploying the optimized model on UAV firmware enables real-time monitoring and classification, achieving an online detection rate of 74% with a response time of approximately 0.495ms per detection. The model’s lightweight design, requiring only 48KB of storage, makes it ideal for resource-constrained UAV environments. These contributions highlight the potential of our approach to enhance real-time anomaly detection and improve UAV system resilience against diverse sensor attacks.

Essential Number of Principal Components and Nearly Training-Free Model for Spectral Analysis.

Learning-enabled spectroscopic analysis, promising for automated real-time analysis of chemicals, is facing several challenges. First, a typical machine learning model requires a large number of training samples that physical systems can not provide. Second, it requires the testing samples to be in range with the training samples, which often is not the case in the real world. Further, a spectroscopy device is limited by its memory size, computing power, and battery capacity. That requires highly efficient learning models for on-site analysis. In this paper, by analyzing multi-gas mixtures and multi-molecule suspensions, we first show that orders of magnitude reduction of data dimension can be achieved as the number of principal components that need to be retained is the same as the independent constituents in the mixture. From this principle, we designed highly compact models in which the essential principal components can be directly extracted from the interrelations between the individual chemical properties and principal components; and only a few training samples are required. Our model can predict the constituent concentrations that have not been seen in the training dataset and provide estimations of measurement noises. This approach can be extended as an effectively standardized method for principle component extraction.