Local Structure Of Data Research Articles

Investigating robustness dynamics of shallow machine learning techniques: beyond basic natural variations in image classification

Despite the widespread adoption of deep learning models, shallow machine learning (SML) algorithms are still used for image classification due to simplicity, interpretability and efficiency. This study aims to bridge this gap by investigating the robustness dynamics of SML techniques under more complex scenarios, such as adversarial perturbations and geometric transformation. Five popular classification algorithms, including k-nearest neighbour and support vector machines, were employed to build classification models. Methodology involves investigating the robustness of proposed methods, first, on original and corrupted data by utilising benchmark datasets across several image domains. To strengthen the investigation, the models were trained using a new low-rank representation (LRR) strategy. This hybrid model simultaneously addresses two key limitations in classical LRR models: overcoming the sequential learning process and effectively capturing both local and global data structures. By introducing a dual regularisation mechanism, it integrates a k-nearest neighbour graph to preserve local consistency, while a global low-rank constraint ensures coherent data representation. Experimental results reveal significant drops in accuracy of most SML methods, especially under adversarial attacks and geometric transformations, but LRR approach mitigates these effects to a notable extent, boosting performance across data variations. The results also show that the proposed method outperforms state-of-the-art LRR techniques in most experiments.

ADM: adaptive graph diffusion for meta-dimension reduction.

Dimension reduction is essential for analyzing high-dimensional data, with various techniques developed to address diverse data characteristics. However, individual methods often struggle to capture all intricate patterns and complex structures simultaneously. To overcome this limitation, we introduce ADM (Adaptive graph Diffusion for Meta-dimension reduction), a novel meta-dimension reduction method grounded in graph diffusion theory. ADM integrates results from multiple dimension reduction techniques, leveraging their individual strengths while mitigating their specific weaknesses.ADM utilizes dynamic Markov processes to transform Euclidean space results into an information space, revealing intrinsic nonlinear manifold structures that are hard to capture by conventional methods. A critical advancement in ADM is its adaptive diffusion mechanism, which dynamically selects optimal diffusion time scales for each sample, enabling effective representation of multi-scale structures. This approach generates robust, high-quality low-dimensional representations that capture both local and global data structures while reducing noise and technique-specific distortions. We demonstrate ADM's efficacy on simulated and real-world datasets, including various omics data types. Results show that ADM provides clearer separation between biological groups and reveals more meaningful patterns compared to existing methods, advancing the analysis and visualization of complex biological data.

Topological organization for hybrid rice growth stages Phenotype based on Contrastive clustering

Hybrid-rice seed production technology is a significant contributor to the high yield. The way to improve seed production’s yield and quality is purification. With the functional requirements of the intelligent Undesired-rice removal process, the environmental elements of field operation and the morphological parameters of Desired-rice and Undesired-rice are collected and measured. This study presents a comprehensive analysis of the topological organization of hybrid rice growth stages using a deep clustering algorithm, t-SimCLR. The algorithm was rigorously tested and compared with existing methods, demonstrating superior performance in clustering accuracy and the ability to capture semantic relationships within the dataset. It elucidated expert prior knowledge of abnormal mature varieties for hybrid rice and explored the growth stages of hybrid rice and panicles. Expert knowledge on identifying abnormal mature varieties within hybrid rice was incorporated to ensure accuracy in variety purification. The study utilized three different datasets to reveal underlying structures and patterns, providing insights into the growth dynamics of hybrid rice. The t-SimCLR algorithm, which employs Contrastive Learning and neighbor embeddings, outperformed traditional methods such as UMAP, t-SNE, and SimCLR, particularly in maintaining the local structure of data and offering more meaningful two-dimensional embeddings. The parametric mapping is trained from the high-dimensional pixel space into two dimensions and achieves classification accuracy by the t-SimCLR algorithm. This study contributes to the advancement of hybrid rice purification techniques and sets the stage for developing more sophisticated intelligent systems for agricultural applications.

Joint Classification of Hyperspectral and LiDAR Data via Multiprobability Decision Fusion Method

With the development of sensor technology, the sources of remotely sensed image data for the same region are becoming increasingly diverse. Unlike single-source remote sensing image data, multisource remote sensing image data can provide complementary information for the same feature, promoting its recognition. The effective utilization of remote sensing image data from various sources can enhance the extraction of image features and improve the accuracy of feature recognition. Hyperspectral remote sensing (HSI) data and light detection and ranging (LiDAR) data can provide complementary information from different perspectives and are frequently combined in feature identification tasks. However, the process of joint use suffers from data redundancy, low classification accuracy and high time complexity. To address the aforementioned issues and improve feature recognition in classification tasks, this paper introduces a multiprobability decision fusion (PRDRMF) method for the combined classification of HSI and LiDAR data. First, the original HSI data and LiDAR data are downscaled via the principal component–relative total variation (PRTV) method to remove redundant information. In the multifeature extraction module, the local texture features and spatial features of the image are extracted to consider the local texture and spatial structure of the image data. This is achieved by utilizing the local binary pattern (LBP) and extended multiattribute profile (EMAP) for the two types of data after dimensionality reduction. The four extracted features are subsequently input into the corresponding kernel–extreme learning machine (KELM), which has a simple structure and good classification performance, to obtain four classification probability matrices (CPMs). Finally, the four CPMs are fused via a multiprobability decision fusion method to obtain the optimal classification results. Comparison experiments on four classical HSI and LiDAR datasets demonstrate that the method proposed in this paper achieves high classification performance while reducing the overall time complexity of the method.

Graph regularized discriminative nonnegative matrix factorization

It is well known that both the label information and the local geometry structure information are very important for image data clustering and classification. However, nonnegative matrix factorization (NMF) and its variants do not fully utilize the information or only use one of them. This paper presents a graph regularized discriminative nonnegative matrix factorization (GDNMF) for image data clustering, in which the local geometrical structure and label information of the observed samples are thoroughly considered. In the objective function of NMF, two constraint terms are added to preserve the above information. One is a sparse graph, which is adaptively constructed to obtain the local geometrical structure information. The other is data label information, which is used to capture discriminative information of the original data. By using local and label information, the proposed regularized discriminative nonnegative matrix factorization indeed improves the discrimination power of matrix decomposition. In addition, the F-norm formulation based cost function of regularized discriminative nonnegative matrix factorization is given, and the update rules for the optimization function of regularized discriminative nonnegative matrix factorization are proved. The experiment results on several public image datasets demonstrate the effectiveness of GDNMF algorithm. The innovation of this paper lies in extending unsupervised NMF to semi-supervised case and adaptively capturing the local structure of data based on sparse graph. However, the proposed method does not take into account the challenges of multiview data processing.

Enhancing ID-based Recommendation with Large Language Models

Large Language Models (LLMs) have recently garnered significant attention in various domains, including recommendation systems. Recent research leverages the capabilities of LLMs to improve the performance and user modeling aspects of recommender systems. These studies primarily focus on utilizing LLMs to interpret textual data in recommendation tasks. However, it's worth noting that in ID-based recommendations, textual data is absent, and only ID data is available. The untapped potential of LLMs for ID data within the ID-based recommendation paradigm remains relatively unexplored. To this end, we introduce a pioneering approach called “LLM for ID-based Recommendation” (LLM4IDRec). This innovative approach integrates the capabilities of LLMs while exclusively relying on ID data, thus diverging from the previous reliance on textual data. The basic idea of LLM4IDRec is that by employing LLM to augment ID data, if augmented ID data can improve recommendation performance, it demonstrates the ability of LLM to interpret ID data effectively, exploring an innovative way for the integration of LLM in ID-based recommendation. Specifically, we first define a prompt template to enhance LLM's ability to comprehend ID data and the ID-based recommendation task. Next, during the process of generating training data using this prompt template, we develop two efficient methods to capture both the local and global structure of ID data. We feed this generated training data into the LLM and employ LoRA for fine-tuning LLM. Following the fine-tuning phase, we utilize the fine-tuned LLM to generate ID data that aligns with users’ preferences. We design two filtering strategies to eliminate invalid generated data. Thirdly, we can merge the original ID data with the generated ID data, creating augmented data. Finally, we input this augmented data into the existing ID-based recommendation models without any modifications to the recommendation model itself. We evaluate the effectiveness of our LLM4IDRec approach using three widely-used datasets. Our results demonstrate a notable improvement in recommendation performance, with our approach consistently outperforming existing methods in ID-based recommendation by solely augmenting input data.

Sparse discriminant manifold projections for automatic depression recognition

In recent years, depression has become an increasingly serious problem globally. Previous research have shown that EEG-based depression recognition is a promising technique to serve as auxiliary diagnosis methods that provide assistance to clinicians. Typically, in clinical studies, due to the multichannel nature of EEG, the extracted features usually are high-dimensional and contain many redundant information. Therefore, it is necessary to perform dimensionality reduction before classification to improve the performance of machine learning algorithms. However,existing dimensionality reduction techniques do not design the objective function based on the characteristics of EEG signal and the goal of depression recognition, so they are less suitable for dimensionality reduction of EEG features. To solve this problem, in this paper we propose a novel dimensionality reduction technique called sparse discriminant manifold projections(SDMP) for depression recognition. Specifically, the use of the ℓ2-norm instead of the squared ℓ2-norm as a similarity measure in the objective function reduces sensitivity to noise and outliers. Moreover, the local geometric structure and global discriminative properties of data are integrated, which makes the extracted features more discriminative. Finally, the ℓ2,1-norm regularization is introduced to achieve feature selection. Furthermore, The formulation is extended to the ℓ2,p-norm regularization case, which is more likely to offer better sparsity when 0<p<1. Extensive experiments on EEG data show that the SDMP achieves the competitive performance compared with other state-of-the-art dimensionality reduction methods. It also shows the practical application value of our method in detecting depression.

HDCCT: Hybrid Densely Connected CNN and Transformer for Infrared and Visible Image Fusion

Multi-modal image fusion is a methodology that combines image features from multiple types of sensors, effectively improving the quality and content of fused images. However, most existing deep learning fusion methods need to integrate global or local features, restricting the representation of feature information. To address this issue, a hybrid densely connected CNN and transformer (HDCCT) fusion framework is proposed. In the proposed HDCCT framework, the network of the CNN-based blocks obtain the local structure of the input data, and the transformer-based blocks obtain the global structure of the original data, significantly improving the feature representation. In the fused image, the proposed encoder–decoder architecture is designed for both the CNN and transformer blocks to reduce feature loss while preserving the characterization of all-level features. In addition, the cross-coupled framework facilitates the flow of feature structures, retains the uniqueness of information, and makes the transform model long-range dependencies based on the local features already extracted by the CNN. Meanwhile, to retain the information in the source images, the hybrid structural similarity (SSIM) and mean square error (MSE) loss functions are introduced. The qualitative and quantitative comparisons of grayscale images with infrared and visible image fusion indicate that the suggested method outperforms related works.

Improved diffusion mapping combined with procrustes analysis for capturing local-global data structures in industrial process monitoring

BackgroundProcess monitoring, by providing early warnings of abnormal operating states resulting from process faults, facilitates the maintenance of normal production and ensures process safety. In the domain of industrial process monitoring, capturing the local-global structural features of data and acquiring an explicit mapping relationship for dimensionality reduction projection holds significant importance for online fault detection in industrial processes. MethodsThis study introduces an Improved Diffusion Mapping and Procrustes analysis (IDM-P) method for this purpose. Initially, considering the multiscale and correlation among industrial data features, the Mahalanobis distance is incorporated to improve the diffusion mapping algorithm. Utilizing this method allows for the concurrent capture of both local and global data structures, leading to a more efficient extraction of data-representative features, which enhances the accuracy of fault detection. Procrustes analysis is then used to obtain an explicit mapping matrix between high-dimensional data and low-dimensional manifolds, improving the efficiency of the key feature extraction of the new samples. Finally, this matrix is utilized to construct process monitoring statistics for fault detection. Significant FindingsThe method's effectiveness was validated through experiments on the TEP dataset and actual industrial data, demonstrating that IDM-P maintains higher accuracy and achieves optimal fault detection compared to other methods.

Supervised spectral feature selection with neighborhood rough set

Spectral feature selection, an excellent dimensionality reduction method, is extensively used in knowledge mining and protein sequence analysis. However, the graph representation derived from data with potential noises significantly impacts feature selection performance. Similarly, its performance deteriorates when label information is ignored, as the selected features have poor discrimination ability. To overcome these drawbacks, this article optimizes neighborhood structure and further constructs the conditional entropy based on neighborhood purity to generate a precise graph representation incorporating label information to enhance the compactness of intra-class samples and increase the dispersion between inter-class samples. Then this article proposes a novel spectral feature selection method. Specifically, the method dynamically learns the precise graph representation from low-dimension space, which can effectively preserve the local structure of data, and the global structure is preserved by introducing a constraint term that maintains the graph representation before and after dimension reduction. Additionally, ℓ2,1-norm is introduced to ensure row sparsity and select the valuable features. The alternative optimization algorithm is employed to solve the optimization problem and its convergence is theoretically analyzed. Finally, to assess the performance of the proposed method, a series of comprehensive experiments are performed on several real-world datasets.

Bilinear Distance Feature Network for Semantic Segmentation in PowerLine Corridor Point Clouds.

Semantic segmentation of target objects in power transmission line corridor point cloud scenes is a crucial step in powerline tree barrier detection. The massive quantity, disordered distribution, and non-uniformity of point clouds in power transmission line corridor scenes pose significant challenges for feature extraction. Previous studies have often overlooked the core utilization of spatial information, limiting the network's ability to understand complex geometric shapes. To overcome this limitation, this paper focuses on enhancing the deep expression of spatial geometric information in segmentation networks and proposes a method called BDF-Net to improve RandLA-Net. For each input 3D point cloud data, BDF-Net first encodes the relative coordinates and relative distance information into spatial geometric feature representations through the Spatial Information Encoding block to capture the local spatial structure of the point cloud data. Subsequently, the Bilinear Pooling block effectively combines the feature information of the point cloud with the spatial geometric representation by leveraging its bilinear interaction capability thus learning more discriminative local feature descriptors. The Global Feature Extraction block captures the global structure information in the point cloud data by using the ratio between the point position and the relative position, so as to enhance the semantic understanding ability of the network. In order to verify the performance of BDF-Net, this paper constructs a dataset, PPCD, for the point cloud scenario of transmission line corridors and conducts detailed experiments on it. The experimental results show that BDF-Net achieves significant performance improvements in various evaluation metrics, specifically achieving an OA of 97.16%, a mIoU of 77.48%, and a mAcc of 87.6%, which are 3.03%, 16.23%, and 18.44% higher than RandLA-Net, respectively. Moreover, comparisons with other state-of-the-art methods also verify the superiority of BDF-Net in point cloud semantic segmentation tasks.

Efficient Local Coherent Structure Learning via Self-Evolution Bipartite Graph.

Dimensionality reduction (DR) targets to learn low-dimensional representations for improving discriminability of data, which is essential for many downstream machine learning tasks, such as image classification, information clustering, etc. Non-Gaussian issue as a long-standing challenge brings many obstacles to the applications of DR methods that established on Gaussian assumption. The mainstream way to address above issue is to explore the local structure of data via graph learning technique, the methods based on which however suffer from a common weakness, that is, exploring locality through pairwise points causes the optimal graph and subspace are difficult to be found, degrades the performance of downstream tasks, and also increases the computation complexity. In this article, we first propose a novel self-evolution bipartite graph (SEBG) that uses anchor points as the landmark of subclasses, and learns anchor-based rather than pairwise relationships for improving the efficiency of locality exploration. In addition, we develop an efficient local coherent structure learning (ELCS) algorithm based on SEBG, which possesses the ability of updating the edges of graph in learned subspace automatically. Finally, we also provide a multivariable iterative optimization algorithm to solve proposed problem with strict theoretical proofs. Extensive experiments have verified the superiorities of the proposed method compared to related SOTA methods in terms of performance and efficiency on several real-world benchmarks and large-scale image datasets with deep features.

Accurate identification of single-cell types via correntropy-based Sparse PCA combining hypergraph and fusion similarity

ABSTRACT The advent of single-cell RNA sequencing (scRNA-seq) technology enables researchers to gain deep insights into cellular heterogeneity. However, the high dimensionality and noise of scRNA-seq data pose significant challenges to clustering. Therefore, we propose a new single-cell type identification method, called CHLSPCA, to address these challenges. In this model, we innovatively combine correntropy with PCA to address the noise and outliers inherent in scRNA-seq data. Meanwhile, we integrate the hypergraph into the model to extract more valuable information from the local structure of the original data. Subsequently, to capture crucial similarity information not considered by the PCA model, we employ the Gaussian kernel function and the Euclidean metric to mine the similarity information between cells, and incorporate this information into the model as the similarity constraint. Furthermore, the principal components (PCs) of PCA are very dense. A new sparse constraint is introduced into the model to gain sparse PCs. Finally, based on the principal direction matrix learned from CHLSPCA, we conduct extensive downstream analyses on real scRNA-seq datasets. The experimental results show that CHLSPCA performs better than many popular clustering methods and is expected to promote the understanding of cellular heterogeneity in scRNA-seq data analysis and support biomedical research.

Local phase-constrained convolutional autoencoder network for identifying multivariate geochemical anomalies

Autoencoder is a powerful tool for identifying multivariate geochemical anomalies. However, existing autoencoder-based geochemical anomaly detection methods primarily rely on a global reconstruction error (e.g., mean square error) to define the lower limit of geochemical anomalies, neglecting the common, local structure information of geochemical data. This limitation inevitably results in the decreased accuracy of geochemical anomaly identification. This study proposed a local Phase-Constrained Convolutional AutoEncoder network (PC-CAE) for the identification of multivariate geochemical anomalies. Initially, we employed a local Fourier transform to extract phase information from both the original and the reconstructed data. Subsequently, a convolutional autoencoder network was utilized to learn the latent representation of geochemical background, using the local phase difference between the original and reconstructed data to preserve the local data structure related to geology setting. Additionally, an adaptive weighting strategy was employed to mitigate the overfitting issue. The training samples with high reconstruction errors were finally identified as anomalies. We tested the validity of PC-CAE using the stream sediment geochemical dataset collected in the Jiaodong gold province, Eastern China. The results demonstrated that PC-CAE outperforms existing convolutional autoencoder network and spectrum–area multifractal model in identifying multivariate geochemical anomalies associated with Au mineralization.

Riemannian Geodesic Discriminant Analysis–Minimum Riemannian Mean Distance: A Robust and Effective Method Leveraging a Symmetric Positive Definite Manifold and Discriminant Algorithm for Image Set Classification

This study introduces a novel method for classifying sets of images, called Riemannian geodesic discriminant analysis–minimum Riemannian mean distance (RGDA-MRMD). This method first converts image data into symmetric positive definite (SPD) matrices, which capture important features related to the variability within the data. These SPD matrices are then mapped onto simpler, flat spaces (tangent spaces) using a mathematical tool called the logarithm operator, which helps to reduce their complexity and dimensionality. Subsequently, regularized local Fisher discriminant analysis (RLFDA) is employed to refine these simplified data points on the tangent plane, focusing on local data structures to optimize the distances between the points and prevent overfitting. The optimized points are then transformed back into a complex, curved space (SPD manifold) using the exponential operator to enhance robustness. Finally, classification is performed using the minimum Riemannian mean distance (MRMD) algorithm, which assigns each data point to the class with the closest mean in the Riemannian space. Through experiments on the ETH-80 (Eidgenössische Technische Hochschule Zürich-80 object category), AFEW (acted facial expressions in the wild), and FPHA (first-person hand action) datasets, the proposed method demonstrates superior performance, with accuracy scores of 97.50%, 37.27%, and 88.47%, respectively. It outperforms all the comparison methods, effectively preserving the unique topological structure of the SPD matrices and significantly boosting image set classification accuracy.

T-distributed Stochastic Neighbor Network for unsupervised representation learning

Unsupervised representation learning (URL) is still lack of a reasonable operator (e.g. convolution kernel) for exploring meaningful structural information from generic data including vector, image and tabular data. In this paper, we propose a simple end-to-end T-distributed Stochastic Neighbor Network (TsNet) for URL with clustering downstream task. Concretely, our TsNet model has three major components: (1) an adaptive connectivity distribution learning module is presented to construct a pairwise graph for preserving the local structure of generic data; (2) a T-distributed stochastic neighbor embedding based loss function is designed to learn a transformation between embeddings and original data, which improves the discrimination of representations; (3) a nonlinear parametric mapping is learned via our TsNet on an unsupervised generalized manner, which can address the “out-of-sample” issue. By combining these components, our method is able to considerably outperform previous related unsupervised learning approaches on visualization and clustering of generic data. A simple deep neural network equipped on our model respectively achieves 74.90%, 76.56% ACC and NMI, which is 8% relative improvement over previous state-of-the-art on real single-cell RNA-sequencing (scRNA-seq) datasets clustering.

A Delayed Spiking Neural Membrane System for Adaptive Nearest Neighbor-Based Density Peak Clustering.

Although the density peak clustering (DPC) algorithm can effectively distribute samples and quickly identify noise points, it lacks adaptability and cannot consider the local data structure. In addition, clustering algorithms generally suffer from high time complexity. Prior research suggests that clustering algorithms grounded in P systems can mitigate time complexity concerns. Within the realm of membrane systems (P systems), spiking neural P systems (SN P systems), inspired by biological nervous systems, are third-generation neural networks that possess intricate structures and offer substantial parallelism advantages. Thus, this study first improved the DPC by introducing the maximum nearest neighbor distance and K-nearest neighbors (KNN). Moreover, a method based on delayed spiking neural P systems (DSN P systems) was proposed to improve the performance of the algorithm. Subsequently, the DSNP-ANDPC algorithm was proposed. The effectiveness of DSNP-ANDPC was evaluated through comprehensive evaluations across four synthetic datasets and 10 real-world datasets. The proposed method outperformed the other comparison methods in most cases.

Steady-state simulation of Euler equations by the discontinuous Galerkin method with the hybrid limiter

In the realm of steady-state solutions of Euler equations, the challenge of achieving convergence of residue close to machine zero has long plagued high-order shock-capturing schemes, particularly in the presence of strong shock waves. In response to this issue, this paper presents a hybrid limiter designed specifically for the discontinuous Galerkin (DG) method which incorporates a pseudo-time marching method. This hybrid limiter, initially introduced in DG methods for unsteady problems, preserves the local data structure while enhancing resolution through effective and precise shock capturing. Notably, for the steady problem, the hybridization of the DG solution with the cell average is employed, deviating from the low-order limited DG solution typically used for unsteady problems. This approach seamlessly integrates the previously distinct troubled cell indicator and limiter components resulting in a more cohesive and efficient limiter. It obviates the need for characteristic decomposition and intercell communication, leading to substantial reductions in computational costs and enhancement in parallel efficiency. Numerical experiments are presented to demonstrate the robust performance of the hybrid limiter for steady-state Euler equations both on the structured and unstructured meshes.

Joint Projected Fuzzy Neighborhood Preserving C-means Clustering with Local Adaptive Learning

Graph-based dimensionality reduction approaches are extensively applied for preserving the intrinsic structures of high-dimensional data. To capture discriminative information from data clusters that lack a clear manifold structure, previous studies have combined clustering algorithms with local manifold structure preservation. These methods assume that two neighbor data points share the same cluster label. However, the assumption may not hold for Fuzzy C-Means which may assign two nearby data points to different clusters depending on the distance between data points and cluster centroids. This inconsistency degrades the performance in clustering and dimensionality reduction. To tackle this issue, we propose a novel approach for dimensionality reduction, termed joint Projected Fuzzy Neighborhood Preserving C-means Clustering with Local Adaptive Learning (PFNPCM). PFNPCM learns cluster centroids, sparse membership grades, embedded subspaces, and structured graphs simultaneously and extracts both global and local structures of data. Through clustering data that preserves the local neighborhood structure in a low-dimensional space instead of the original one, PFNPCM can effectively capture both global and local information from the inherent manifold structure and cluster structure. The employment of ℓ2,1-norm as the distance metric in the clustering and the preservation of neighborhood structure further ensure the robustness of clustering results against noise or outliers. To achieve the consistency of the captured global and local discriminative information, PFNPCM adopts a novel fuzzy local similarity measure based on the manifold structure, and the manifold assumption thus holds when partitioning unlabeled samples into subgroups. Massive experiments on diverse well-known datasets demonstrate that PFNPCM is superior to some state-of-the-art methods.

Wasserstein local slow feature analysis and its application to process monitoring

Abstract Complex industrial processes are commonly characterized by dynamics, which results from the fact that there exists compensation of the closed-loop control and complex reflux during process operations. In this work, we propose a new method termed Wasserstein local slow feature analysis approach (WLSFA) used for monitoring the dynamic process, which can learn slowly varying information to capture the trend of process variations and characterize dynamics. Specifically, Wasserstein graph embedding based on optimal transport is proposed to preserve the local geometrical structure of raw data so that the reduced-dimensional representations can more faithfully reveal the underlying information of data, enhancing monitoring performance. Moreover, the l_2 -norm orthogonal constraint is incorporated into the objective function to improve generalization ability and alleviate the false alarm rate. On the basis of WLSFA model, a contribution plot in the sense of reconstruction is developed to locate the fault variables, which is beneficial to regulate abnormal conditions towards normal levels. Finally, the efficiency of the proposed approach is illustrated by a benchmark process and the application to a real-world fractionation process.