Dimensionality Reduction Method Research Articles

Dimensionality reduction beyond neural subspaces with slice tensor component analysis.

Recent work has argued that large-scale neural recordings are often well described by patterns of coactivation across neurons. Yet the view that neural variability is constrained to a fixed, low-dimensional subspace may overlook higher-dimensional structure, including stereotyped neural sequences or slowly evolving latent spaces. Here we argue that task-relevant variability in neural data can also cofluctuate over trials or time, defining distinct 'covariability classes' that may co-occur within the same dataset. To demix these covariability classes, we develop sliceTCA (slice tensor component analysis), a new unsupervised dimensionality reduction method for neural data tensors. In three example datasets, including motor cortical activity during a classic reaching task in primates and recent multiregion recordings in mice, we show that sliceTCA can capture more task-relevant structure in neural data using fewer components than traditional methods. Overall, our theoretical framework extends the classic view of low-dimensional population activity by incorporating additional classes of latent variables capturing higher-dimensional structure.

The associations of IGF2, IGF2R and IGF2BP2 gene polymorphisms with gestational diabetes mellitus: A case-control study.

To investigate the associations of Insulin-like growth factor-II (IGF2) gene, Insulin-like growth factor-II receptor (IGF2R) gene and Insulin-like growth factor-II binding protein 2 (IGF2BP2) gene polymorphisms with the susceptibility to gestational diabetes mellitus (GDM) in Chinese population. A total of 1703 pregnant women (835 GDM and 868 Non-GDM) were recruited in this case-control study. All participants underwent prenatal 75 g oral glucose tolerance test (OGTT) examinations during 24-28 gestational weeks at the Maternal and Child Health Hospital of Hubei Province from January 15, 2018 to March 31, 2019. Genotyping of candidate SNPs (IGF2 rs680, IGF2R rs416572, IGF2BP2 rs4402960, rs1470579, rs1374910, rs11705701, rs6777038, rs16860234, rs7651090) was performed on Sequenom MassARRAY platform. Logistic regression analysis was conducted to investigate the associations between candidate SNPs and risk of GDM. In addition, multifactor dimensionality reduction (MDR) method was applied to explore the effects of gene-gene interactions on GDM risk. There were significant distribution differences between GDM group and non-GDM group in age, pre-pregnancy BMI, education level and family history of diabetes (P < 0.05). After adjusted for age, pre-pregnancy BMI, education level and family history of diabetes, there were no significant associations of the candidate SNPs polymorphisms and GDM risk (P > 0.05). Furthermore, there were no gene-gene interactions on the GDM risk among the candidate SNPs (P > 0.05). However, the fasting blood glucose (FBG) levels of rs6777038 CT carriers were significantly lower than TT carriers (4.69±0.69 vs. 5.03±1.57 mmol/L, P < 0.01), and the OGTT-2h levels of rs6777038 CC and CT genotype carriers were significantly lower than TT genotype carriers (8.10±1.91 and 8.08±1.87 vs. 8.99±2.90 mmol/L, P < 0.01). IGF2 rs680, IGF2R rs416572, IGF2BP2 rs4402960, rs1470579, rs11705701, rs6777038, rs16860234, rs7651090 polymorphisms were not significantly associated with GDM risk in Wuhan, China. Further lager multicenter researches are needed to confirm these results.

Resource-efficient quantum principal component analysis

Abstract Principal component analysis (PCA) is an important dimensionality reduction method in machine learning and data analysis. Recently, the quantum version of PCA has been established to diagonalize quantum states. Although these quantum algorithms promise quantum advantages, they require substantial resources beyond the reach of state-of-the-art quantum technologies. This work aims to reduce resource requirements and improve the efficiency of quantum principal component analysis. &amp;#xD;Assuming that the quantum state is accessed through a purified quantum query model and a sampling model, we propose quantum algorithms that use minimal resource requirements for ancillary qubits to reveal properties of eigenvectors and eigenvalues of a state. In particular, we show that estimating eigenvalue $\lambda$ with error $\epsilon$ and success probability larger than $\lambda(1-\eta)$ requests a query complexity {$\mathcal{\widetilde{O}}(\epsilon^{-1})$} and a sample complexity {$\mathcal{\widetilde{O}}(\epsilon^{-2}\eta^{-1})$}, respectively. To our knowledge, our result is the first quantum speedup that achieves asymptotic linear scaling in $1/\epsilon$ for quantum PCA. As applications, we discuss estimating the minimum relative entropy of entanglement of bipartite pure-states and performing quantum state discrimination tasks. We show that quantum speedups are maintained when the pure state has a low Schmidt number and states of discrimination have a low rank. This study opens up a new quantum principal component analysis method for high-dimensional quantum data analysis and discusses its application in quantum information processing tasks.

Hydroacoustic optimization with using Noise-GAN

In recent years, noise pollution has a significant impact on marine organisms, hence requiring some restrictions and safety protocols. The primary objective of these restrictions is to minimize the noise generated by human-driven vehicles in aquatic environments. As a result, hydroacoustical studies are becoming increasingly integrated into design studies. The objective of this study is to provide an innovative approach to the design of hydrofoils, are considered a crucial component in the field of hydroacoustic engineering. The objective of this approach is to create a cutting-edge optimization tool through the integration of machine learning and hydroacoustic performance calculations. This article presents the development of a novel method called Noise-GAN, combines Generative Adversarial Networks (GAN) algorithms with hydroacoustic optimization capabilities. The GAN algorithm is used as a dimensionality reduction method in the optimization process, allowing for quick exploration of the design space and obtaining unique profile geometries during optimization. This method is used to generate optimal hydrofoil geometry for various conditions. The hydroacoustic and hydrodynamic performances of the generated geometry are analyzed to determine the applicability and performance of the method. The results are compared to two existing dimensionality reduction method to enhance comprehension of the performance. In order to gain insight into the performance of generated geometries compared to traditional geometries, the results are also compared to the performance data of the profiles available in the literature. This article also includes comparing the performance results of the NACA0009 profile, which is typically employed in hydrofoil research, with the optimal geometries to evaluate of the method and the performance of the generated geometries. In order to determine the real-life applicability of the hydrofoil geometries generated by the method, optimization studies were performed at the five different Angle of Attack (AoA) conditions within the range of 0o - 15o. In this way, the feasibility of the method at different AoA values was also examined. The results of all these comparisons demonstrate that the Noise-GAN method, which was developed to generate hydroacoustically optimized hydrofoil geometry, is highly effective in a variety of respects. The optimization tool developed in this study generates hydrodynamically efficient and unique hydrofoil profiles while optimizing for hydroacoustical performance. The results of this study are presented in this paper.

Using noise filtering and sufficient dimension reduction method on unstructured economic data

Using noise filtering and sufficient dimension reduction method on unstructured economic data

Quantitative condition assessment method for rotating machinery using fuzzy neural network

Abstract Health condition assessment of rotating machinery has been a persistent challenge. Traditional condition assessment methods often rely on single features, limiting their application to comprehensively measure the health condition of rotating machinery. This study introduced a quantitative condition assessment method for rotating machinery using fuzzy neural network (FNN). Initially, multi-domain features of signals from rotating machinery are extracted to achieve comprehensive representation of signals in the feature space. To eliminate redundant information of various features, a feature dimensionality reduction method is explored based on variance variation and stacked auto-encoder (SAE). Afterward, a normalized health indicator is constructed by integrating the optimized features through FNN, and it can indicate the current conditions of rotating machinery. Furthermore, an early anomaly alarm strategy based on 3σ criterion is designed for rotating machinery. The abnormal signal will be recognized automatically when it exceeds the predetermined thresholds. Last, the effectiveness of the proposed method is validated on IMS bearing dataset and XJTU-SY bearing dataset. The results show that the proposed method can effectively obtain the quantitative indicators that reflect the operation conditions of rotating machinery and can accurately detect the early abnormal signals.

Exploring combinations of dimensionality reduction, transfer learning, and regularization methods for predicting binary phenotypes with transcriptomic data

BackgroundNumerous transcriptomic-based models have been developed to predict or understand the fundamental mechanisms driving biological phenotypes. However, few models have successfully transitioned into clinical practice due to challenges associated with generalizability and interpretability. To address these issues, researchers have turned to dimensionality reduction methods and have begun implementing transfer learning approaches.MethodsIn this study, we aimed to determine the optimal combination of dimensionality reduction and regularization methods for predictive modeling. We applied seven dimensionality reduction methods to various datasets, including two supervised methods (linear optimal low-rank projection and low-rank canonical correlation analysis), two unsupervised methods [principal component analysis and consensus independent component analysis (c-ICA)], and three methods [autoencoder (AE), adversarial variational autoencoder, and c-ICA] within a transfer learning framework, trained on > 140,000 transcriptomic profiles. To assess the performance of the different combinations, we used a cross-validation setup encapsulated within a permutation testing framework, analyzing 30 different transcriptomic datasets with binary phenotypes. Furthermore, we included datasets with small sample sizes and phenotypes of varying degrees of predictability, and we employed independent datasets for validation.ResultsOur findings revealed that regularized models without dimensionality reduction achieved the highest predictive performance, challenging the necessity of dimensionality reduction when the primary goal is to achieve optimal predictive performance. However, models using AE and c-ICA with transfer learning for dimensionality reduction showed comparable performance, with enhanced interpretability and robustness of predictors, compared to models using non-dimensionality-reduced data.ConclusionThese findings offer valuable insights into the optimal combination of strategies for enhancing the predictive performance, interpretability, and generalizability of transcriptomic-based models.

Cluster-based multidimensional scaling embedding tool for data visualization

Abstract We present a new technique for visualizing high-dimensional data called cluster MDS (cl-MDS), which addresses a common difficulty of dimensionality reduction methods: preserving both local and global structures of the original sample in a single 2-dimensional visualization. Its algorithm combines the well-known multidimensional scaling (MDS) tool with the k-medoids data clustering technique, and enables hierarchical embedding, sparsification and estimation of 2-dimensional coordinates for additional points. While cl-MDS is a generally applicable tool, we also include specific recipes for atomic structure applications. We apply this method to non-linear data of increasing complexity where different layers of locality are relevant, showing a clear improvement in their retrieval and visualization quality.

Minimax estimation of functional principal components from noisy discretized functional data

AbstractFunctional Principal Component Analysis is a reference method for dimension reduction of curve data. Its theoretical properties are now well understood in the simplified case where the sample curves are fully observed without noise. However, functional data are noisy and necessarily observed on a finite discretization grid. Common practice consists in smoothing the data and then to compute the functional estimates, but the impact of this denoising step on the procedure's statistical performance are rarely considered. Here we prove new convergence rates for functional principal component estimators. We introduce a double asymptotic framework: one corresponding to the sampling size and a second to the size of the grid. We prove that estimates based on projection onto histograms show optimal rates in a minimax sense. Theoretical results are illustrated on simulated data and the method is applied to the visualization of genomic data.

Optimized data driven fault detection and diagnosis in chemical processes

Fault detection and diagnosis (FDD) is crucial for ensuring process safety and product quality in the chemical industry. Despite the large amounts of process data recorded and stored in chemical plants, most of them are not well-labeled, and their conditions are not adequately specified. In this study, an optimized data-driven FDD model was developed for a chemical process based on automatic clustering algorithms. Due to data preprocessing importance, feature selection was performed by a non-dominated sorting genetic algorithm (NSGAII) based on k-means clustering. The optimal subset of features is selected by comparing clustering results for each subset. The performance of the proposed feature selection method was compared with the Fisher discriminant ratio (FDR), and XGBoost methods. The t-distributed stochastic neighbor embedding (t-SNE), Isomap, and KPCA dimension reduction methods were also employed for feature extraction. Finally, automatic clustering was performed based on metaheuristic algorithms for fault detection and diagnosis. Results were compared with non-automatic clustering methods. The performance of the proposed method was evaluated by examining the Tennessee Eastman and four water tank processes as case studies. The results showed that the proposed method is reliable and capable of online and offline chemical process fault detection and diagnosis. As a result, the findings of this study can be used to stabilize the operation of chemical processes.

Prediction and optimization method for welding quality of components in ship construction

Welding process, as one of the crucial industrial technologies in ship construction, accounts for approximately 70% of the workload and costs account for approximately 40% of the total cost. The existing welding quality prediction methods have hypothetical premises and subjective factors, which cannot meet the dynamic control requirements of intelligent welding for processing quality. Aiming at the low efficiency of quality prediction problems poor timeliness and unpredictability of quality control in ship assembly-welding process, a data and model driven welding quality prediction method is proposed. Firstly, the influence factors of welding quality are analyzed and the correlation mechanism between process parameters and quality is determined. According to the analysis results, a stable and reliable data collection architecture is established. The elements of welding process monitoring are also determined based on the feature dimensionality reduction method. To improve the accuracy of welding quality prediction, the prediction model is constructed by fusing the adaptive simulated annealing, the particle swarm optimization, and the back propagation neural network algorithms. Finally, the effectiveness of the prediction method is verified through 74 sets of plate welding experiments, the prediction accuracy reaches over 90%.

Dimensionality Reduction problem: a Comprehensive Exploration of Disjoint Principal Component Analysis (DPCA) and Disjoint Multiple Correspondence Analysis (DMCA)

This paper delves into the realm of advanced data analysis, focusing on two powerful dimensionality reduction methods: Disjoint Principal Component Analysis (DPCA) and Disjoint Multiple Correspondence Analysis (DMCA). Methodological marvels in their own right, these approaches are scrutinized for their unique properties and applications across diverse domains. We navigate through the intricacies of their algorithms and explore how they unveil patterns within complex datasets. The comparative analysis highlights the strengths and weaknesses of DPCA and DMCA, shedding light on their distinct contributions to the analytical landscape. This paper serves as a comprehensive guide for researchers and analysts seeking deeper insights into these cutting-edge techniques for dimensional reduction.

An effective ensemble classification framework for intrusion detection system using LSTM autoencoder

In intrusion detection, the curse of dimensionality and the trade-off between maintaining a low false alarm rate and achieving a high detection rate are significant challenges. This research suggests a unique strategy based on dimensionality reduction methods to improve the performance of network intrusion detection systems (NIDS). Compressing high-dimensional network traffic data using a Long Short-Term Memory Autoencoder (LSTMAE) allows the reduced characteristics to be submitted to a classifier to identify anomalies that may indicate an attack. Using standard datasets, including Network Security Laboratory - Knowledge Discovery in Datasets (NSL-KDD), UNSW-NB15, and Canadian Institute for Cyber Security - Intrusion Detection Systems (CICIDS2017), the proposed model is tested with classifiers like Random Forest (RF) and LightGBM (Light Gradient Boosting Machines). It is hoped that by adopting this method, NIDS response times may be improved while costs associated with storing and processing data are minimized. Precision, recall, F-score, accuracy, detection rate (DR), and false alarm rate (FAR) are only a few of the performance measures used to assess the quality of the suggested models. The experimental findings show that the proposed LSTMAE model reduces prediction errors more effectively than classic machine learning techniques such as Random Forest (RF), Gradient Boosting (GB), Support Vector Machines (SVM), Deep Belief Networks (DBN), Deep Neural Networks (DNN), Autoencoder (AE), and Long Short-Term Memory (LSTM). The results also show that the proposed solution outperforms the state-of-the-art methods of detection accuracy and computing complexity using accuracy, precision, recall, F1_Score, detection rate, and FAR.

Dynamic sparse PCA: a dimensional reduction method for sensor data in virtual metrology

Virtual metrology (VM) is the ideal technique for predicting the quality of every wafer and reducing overall inspection costs in semiconductor manufacturing. The data from numerous monitoring sensors in semiconductor production poses challenges in terms of data dimensionality. Thus, dimensionality reduction techniques are required before building the prediction model in VM. Additionally, to reduce the sensor cost, it is crucial to determine the sensors that contribute significantly to the output of the prediction model. Therefore, in this paper, we propose a dimensionality reduction technique called dynamic sparse principal component analysis to establish global sparsity in the first few principal components. The proposed method seeks extracted features that involve a limited number of sensors in the VM to reduce sensor cost and increase the interpretability of the features while reasonably capturing data variability. The experimental results demonstrate that the proposed method is not sensitive to the scale of the problem and can solve the large-scale high-dimensional problems that are commonly encountered in semiconductor manufacturing.

Cross-sectional analysis of initially curved composite beams with rectangular and circular sections using an asymptotic meshless method

An analytical meshless cross-sectional dimensional reduction method is developed to perform structural analysis of initially curved composite beams. By introducing the Pascal polynomials in the Cartesian coordinates system for beams with rectangular cross-sections and in the polar coordinates system for the beams with circular cross-sections to the warping field, a three-dimensional beam problem can be split into a two-dimensional cross-sectional analysis and a one-dimensional along the reference line of the beam. The obtained cross-sectional stiffness matrix based on higher-order of the strain energy can be incorporated into a one-dimensional finite element solution for initially curved composite beams, for the purpose of strain and stress analysis. Finally, the three-dimensional strain through the thickness of the beam can be achieved by the recovery analysis. The present method takes advantage of Pascal polynomials so that the solution procedure will be more simplified and computationally more efficient compared to three-dimensional finite element (3D FE) method. The proposed method for different isotropic and anisotropic beams is examined and compared with the literature, 3D FE, and Variational Asymptotic Beam Sectional (VABS) package which is a finite element based cross-sectional analysis tool for composite beams.

Application of texture signatures based on multiparameter-magnetic resonance imaging for predicting microvascular invasion in hepatocellular carcinoma: Retrospective study.

Despite continuous changes in treatment methods, the survival rate for advanced hepatocellular carcinoma (HCC) patients remains low, highlighting the importance of diagnostic methods for HCC. To explore the efficacy of texture analysis based on multi-parametric magnetic resonance (MR) imaging (MRI) in predicting microvascular invasion (MVI) in preoperative HCC. This study included 105 patients with pathologically confirmed HCC, categorized into MVI-positive and MVI-negative groups. We employed Original Data Analysis, Principal Component Analysis, Linear Discriminant Analysis (LDA), and Non-LDA (NDA) for texture analysis using multi-parametric MR images to predict preoperative MVI. The effectiveness of texture analysis was determined using the B11 program of the MaZda4.6 software, with results expressed as the misjudgment rate (MCR). Texture analysis using multi-parametric MRI, particularly the MI + PA + F dimensionality reduction method combined with NDA discrimination, demonstrated the most effective prediction of MVI in HCC. Prediction accuracy in the pulse and equilibrium phases was 83.81%. MCRs for the combination of T2-weighted imaging (T2WI), arterial phase, portal venous phase, and equilibrium phase were 22.86%, 16.19%, 20.95%, and 20.95%, respectively. The area under the curve for predicting MVI positivity was 0.844, with a sensitivity of 77.19% and specificity of 91.67%. Texture analysis of arterial phase images demonstrated superior predictive efficacy for MVI in HCC compared to T2WI, portal venous, and equilibrium phases. This study provides an objective, non-invasive method for preoperative prediction of MVI, offering a theoretical foundation for the selection of clinical therapy.

Interpretation of autoencoder-learned collective variables using Morse-Smale complex and sublevelset persistent homology: An application on molecular trajectories.

Dimensionality reduction often serves as the first step toward a minimalist understanding of physical systems as well as the accelerated simulations of them. In particular, neural network-based nonlinear dimensionality reduction methods, such as autoencoders, have shown promising outcomes in uncovering collective variables (CVs). However, the physical meaning of these CVs remains largely elusive. In this work, we constructed a framework that (1) determines the optimal number of CVs needed to capture the essential molecular motions using an ensemble of hierarchical autoencoders and (2) provides topology-based interpretations to the autoencoder-learned CVs with Morse-Smale complex and sublevelset persistent homology. This approach was exemplified using a series of n-alkanes and can be regarded as a general, explainable nonlinear dimensionality reduction method.

Enhanced Model Predictions through Principal Components and Average Least Squares-Centered Penalized Regression

We address the estimation of regression parameters for the ill-conditioned predictive linear model in this study. Traditional least squares methods often encounter challenges in yielding reliable results when there is multicollinearity. Therefore, we employ a better shrinkage method, average least squares-centered penalized regression (ALPR), as it offers a more efficient approach for handling multicollinearity than ridge regression. Additionally, we integrate ALPR with the principal component (PC) dimension reduction method for enhanced performance. We compared the proposed PCALPR estimation technique with existing ones for ill-conditioned problems through comprehensive simulations and real-life data analyses using the mean squared error. This integration results in superior model performance compared to other methods, highlighting the potential of combining dimensionality reduction techniques with penalized regression for enhanced model predictions.

An Abnormal Account Identification Method by Topology Feature Analysis for Blockchain-Based Transaction Network

Cryptocurrency, as one of the most successful applications of blockchain technology, has played a vital role in promoting the development of the digital economy. However, its anonymity, large scale of cryptographic transactions, and decentralization have also brought new challenges in identifying abnormal accounts and preventing abnormal transaction behaviors, such as money laundering, extortion, and market manipulation. Recently, some researchers have proposed efficient and accurate abnormal transaction detection based on machine learning. However, in reality, abnormal accounts and transactions are far less common than normal accounts and transactions, so it is difficult for the previous methods to detect abnormal accounts by training with such an imbalance in abnormal/normal accounts. To address the issues, in this paper, we propose a method for identifying abnormal accounts using topology analysis of cryptographic transactions. We consider the accounts and transactions in the blockchain as graph nodes and edges. Since the abnormal accounts may have special topology features, we extract topology features from the transaction graph. By analyzing the topology features of transactions, we discover that the high-dimensional sparse topology features can be compressed by using the singular value decomposition method for feature dimension reduction. Subsequently, we use the generative adversarial network to generate samples like abnormal accounts, which will be sent to the training dataset to produce an equilibrium of abnormal/normal accounts. Finally, we utilize several machine learning techniques to detect abnormal accounts in the blockchain. Our experimental results demonstrate that our method significantly improves the accuracy and recall rate for detecting abnormal accounts in blockchain compared with the state-of-the-art methods.

Spherical random projection

Abstract We propose a new method for dimension reduction of high-dimensional spherical data based on the nonlinear projection of sphere-valued data to a randomly chosen subsphere. The proposed method, spherical random projection, leads to a probabilistic lower-dimensional mapping of spherical data into a subsphere of the original. In this paper, we investigate some properties of spherical random projection, including expectation preservation and distance concentration, from which we derive an analogue of the Johnson–Lindenstrauss Lemma for spherical random projection. Clustering model selection is discussed as an application of spherical random projection, and numerical experiments are conducted using real and simulated data.