Unsupervised Dimensionality Reduction Techniques Research Articles

UMAP for Geospatial Data Visualization

In this paper, we examine the efficacy of unsupervised learning approaches, particularly clustering and dimensionality reduction techniques, in practical applications such as image compression and geospatial data visualization. Initially, we scrutinize the applicability of the elbow rule in determining the optimal number of clusters within synthetic datasets of varying structures using the k-means algorithm. Subsequently, we evaluate the potency of density-based (DBSCAN) and hierarchical clustering algorithms in unearthing intrinsic patterns within these datasets. Shifting our focus towards practical applications, we leverage the k-means clustering for image compression, demonstrating a notable reduction in storage requirements without a significant compromise in visual quality. Our findings articulate that a strategic selection of cluster numbers can yield substantial compression rates. In the final segment of our investigation, we delve into the utility of dimensionality reduction techniques, specifically t-SNE and UMAP, in the realm of geospatial data visualization. Utilizing a dataset comprising distances between Spanish provinces, we gauge the proficiency of these techniques in preserving relative distances upon projection onto a two-dimensional plane. Our observations denote that both t-SNE and UMAP can generate precise visual representations of the original geographic layouţ with UMAP exhibiting exceptional performance in comparison with alternative methodologies. On a broader scale, our study underscores the versatility and practical utility of unsupervised learning techniques across an array of applications, ranging from image compression to geospatial data visualization. It emphasizes the significance of comprehending their foundational mechanisms and fine-tuning their hyperparameters to achieve optimal performance.

Cyber-Attack Detection Using Principal Component Analysis and Noisy Clustering Algorithms: A Collaborative Machine Learning-Based Framework

This paper proposes a collaborative machine learning-based framework to detect cyber-attacks in a power system, leading to deviation in the state variable behavior. Based on the proposed architecture, three different machine learning-based methods, i.e., visualization, classification, and clustering, are employed and compared to find the best one in the FDIA detection process. To this end, pre-processing is employed in the first stage. In the second stage, the patterns of the state vectors are transferred into features. Hence, 24 statistical features, including measures of central tendency, variability, measures of shape, and position, are extracted to find various properties. Then, in the third stage, a supervised algorithm is employed to rank and find the most crucial features in FDIA. In the fourth stage, an unsupervised dimensionality reduction technique (PCA) is applied to reduce the feature space. In the fifth and last stage, visualization, classification, and clustering-based methods are developed to detect FDIA. To simulate an attack, it is assumed that an intruder decreases or increases the state vectors at different buses with various attack parameters (i.e., 0.90, 0.95, 0.96, 0.97, 0.98, 1, 1.02, 1.03, 1.04, 1.05, and 1.10). The proposed method effectiveness is assessed on the New York Independent System Operator (NYISO) data applied to the IEEE 14-bus system. The results presented in the paper from different scenarios (i.e., phase angle ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta $ </tex-math></inline-formula> ), voltage magnitude ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V_{m}$ </tex-math></inline-formula> ), measurements, and multiple attacks) on a real-world dataset demonstrate that the collaborative optimized PCA-Density-based machine learning technique can detect most of the attack samples with good performance scores (i.e., recall, precision, F1) and outperforms the other investigated methods. Moreover, it is general and adaptable enough to cover the situation where either the system characteristics or the attack behavior changes.

Feature Clustering of Noisy Data and Application in the Currency Market

With the increase in high-dimensional data, researchers pay more attention to dimensionality reduction techniques because there are many noisy, redundant and irrelevant features in high-dimensional data. The existence of noisy features leads to decrease performance when analyzing high-dimensional data. Also, unsupervised dimensionality reduction techniques are widely used due to the lack of available labels. Feature clustering is an unsupervised dimensionality reduction technique to partition features into clusters in which features are strongly related. In addition, the Pearson correlation coefficient is widely used as a similarity tool for feature clustering. However, the Pearson correlation coefficient is easily influenced by outliers and noises, thus leading to misleading results. This paper focuses on the influence of dissimilarity measures on the clustering of noisy features. Heavy-tailed distributions are used for modeling data with outliers and noises. Therefore, we introduce a new dissimilarity measure based on a new dependence coefficient of heavy-tailed distributions. The performance of feature clustering using the proposed dissimilarity is evaluated using ARI and internal criteria on artificial and real currency market datasets. Experiment results have demonstrated the effectiveness of the proposed feature clustering method.

Identifying Abnormal CFRP Holes Using Both Unsupervised and Supervised Learning Techniques on In-Process Force, Current, and Vibration Signals

This study aims to conduct abnormality detection by applying machine learning algorithms when drilling a carbon fiber reinforced plastic laminate. In-process signals including current, thrust force, and vibration were captured during the dry drilling experiments using a 6 mm physical vapor deposit diamond-coated drill at the consistent spindle speed of 6500 RPM and 0.05 mm/rev. Across measurements from out-of-process variables, including hole diameter, roundness, surface roughness, entry/exit delamination, and entry/exit uncut fiber area, in-process measurements were most able to find outliers with respect to diameter. Both Principal Component Analysis, an unsupervised dimensionality reduction technique, and Linear Discriminant Analysis, a supervised dimensionality reduction technique, could separate oversize or undersize holes from average-sized holes when using fast Fourier transformation data of in-process vibration. Predictive performance with k-Nearest Neighbors shows that our machine learning pipeline can predict oversized vs. non-oversized holes with over 85% accuracy in this dataset. Peak prediction performance is obtained when in-process measurement data is viewed from the frequency domain, and predictions are weighted based on the relative distances of the nearest neighbors.

Association of Infarct Topography and Outcome After Endovascular Thrombectomy in Patients With Acute Ischemic Stroke.

The care of patients with large vessel occlusion (LVO) stroke has been revolutionized by endovascular thrombectomy (EVT). While EVT has a large effect size, most patients treated with EVT remain disabled or die within 90 days. A better understanding of outcomes may influence EVT selection criteria, novel therapies, and prognostication. We sought to identify associations between outcomes and brain regions involved in ischemic lesions. For this cohort study, consecutive patients with LVO who were treated with EVT and underwent post-EVT MRI were identified from a tertiary referral center (2011-2019). Acute ischemic lesions were manually segmented from diffusion-weighted imaging and spatially normalized. Individual lesions were parcellated (atlas-defined 94 cortical regions, 14 subcortical nuclei, 20 white matter tracts) and reduced to 10 essential lesion patterns with the use of unsupervised dimensionality reduction techniques. Ninety-day modified Rankin Scale (mRS) score (>2) was modeled via bayesian regression, taking the 10 lesion patterns as inputs and controlling for lesion size, age, sex, acute NIH Stroke Scale (NIHSS) score, alteplase, prior stroke, intracerebral hemorrhage, and good reperfusion (Thrombolysis in Cerebral Infarction 2b-3). In comparative analyses, 90-day mRS score was modeled considering covariates only, and compartment-wise relevances for acute stroke severity and 90-day mRS score were evaluated. There were 151 patients with LVO identified (age 68 ± 15 years, 52% female). The median NIHSS score was 16 (interquartile range 13-20); 56% had mRS score >2. Lesion locations predictive of 90-day mRS score involved bilateral but left hemispherically more pronounced precentral and postcentral gyri, insular and opercular cortex, and left putamen and caudate (area under the curve 0.91, highest probability density interval [HPDI] covering 90% certainty 0.90-0.92). The lesion location model outperformed the simpler model relying on covariates only (bayesian model comparison of 97% weight to the model with vs 3% weight to the model without lesion location). While lesions affecting subcortical nuclei had the highest relevance for stroke severity (posterior distribution mean 0.75, 90% HPDI 0.256-1.31), lesions affecting white matter tracts had the highest relevance for 90-day mRS score (0.656, 90% HPDI 0.0864-1.12). These data describe the significance for outcomes of specific brain regions involved in ischemic lesions on MRI after EVT. Future work in additional datasets is needed to confirm these granular findings.

A Convolutional Autoencoder Topology for Classification in High-Dimensional Noisy Image Datasets.

Deep convolutional neural networks have shown remarkable performance in the image classification domain. However, Deep Learning models are vulnerable to noise and redundant information encapsulated into the high-dimensional raw input images, leading to unstable and unreliable predictions. Autoencoders constitute an unsupervised dimensionality reduction technique, proven to filter out noise and redundant information and create robust and stable feature representations. In this work, in order to resolve the problem of DL models’ vulnerability, we propose a convolutional autoencoder topological model for compressing and filtering out noise and redundant information from initial high dimensionality input images and then feeding this compressed output into convolutional neural networks. Our results reveal the efficiency of the proposed approach, leading to a significant performance improvement compared to Deep Learning models trained with the initial raw images.

The (im)possibility of strong chemical tagging

Context.The possibility of identifying co-natal stars that have dispersed into the Galactic disc based on chemistry alone is called strong chemical tagging. It has been debated for a long time whether this is indeed feasible; it holds the promise of reconstructing the detailed star formation history of a large fraction of stars in the Galactic disc.Aims.We investigate the feasibility of strong chemical tagging using known member stars of open clusters.Methods.We analysed the largest sample of cluster members that have been homogeneously characterised with high-resolution differential abundances for 16 different elements. We also investigated the possibility of finding the known clusters in the APOGEE DR16 red clump sample with 18 chemical species. For both purposes, we used a clustering algorithm and an unsupervised dimensionality reduction technique to blindly search for groups of stars in chemical space.Results.Even if the internal coherence of the stellar abundances in the same cluster is high, typically 0.03 dex, the overlap in the chemical signatures of the clusters is large. In the sample with the highest precision and no field stars, we only recover 9 out of the 31 analysed clusters at a 40% threshold of homogeneity and precision. This ratio slightly increases when we only use clusters with 7 or more members. In the APOGEE sample, field stars are present along with four populated clusters. In this case, only one of the open clusters was moderately recovered.Conclusions.In our best-case scenario, more than 70% of the groups of stars are in fact statistical groups that contain stars belonging to different real clusters. This indicates that the chances of recovering the majority of birth clusters dissolved in the field are slim, even with the most advanced clustering techniques. We show that different stellar birth sites can have overlapping chemical signatures, even when high-resolution abundances of many different nucleosynthesis channels are used. This is substantial evidence against the possibility of strong chemical tagging. However, we can hope to recover some particular birth clusters that stand out at the edges of the chemical distribution.

Unique Clusters of Sudden Unexpected Infant Death (SUID) Descendants Revealed Through Machine Learning Epidemiological Analyses

Sudden unexpected infant death (SUID) rates have substantially declined due to public health prevention efforts as well as mechanistic research over the past thirty years. Following an extensive medico-legal investigation, the decedent under one year of age is assigned as the cause of death: sudden infant death syndrome (SIDS), accidental suffocation and strangulation, or other ill-defined or unspecified cause of mortality. However, the extent to which these diseases manifest with an underlying neuropathological mechanism is highly controversial due to the heterogeneity of findings. In addition, substantial disparities are present when comparing SUID rates amongst race/ethnicity in the United States (US). The intersection of an underlying unknown biological abnormality and health disparities in the role of SUID is not well understood. Cluster analysis within heterogenous diseases has been highly instructive in neuropathology by identifying unique patient subtypes. Using maternal and infantile characteristics, we sought to identify unique groups of SUID decedents indicating distinct risk factors and neurodevelopmental causes. Using the US Period Linked Birth/Infant Mortality Files from 1990-2017 (excluding 1992-1994), we performed unsupervised machine learning dimensionality reduction techniques. Following identification of unique groups, we analyzed SUID rates in these clusters at the state level. We were able to identify three groups of SIDS decedents, each with a unique mean age at death when adjusting for length of gestation and performed similar analysis with the remaining SUID causes. We found that the implementation of clinical guidelines has had a distinct impact in decreasing the SUID rate in the unique clusters across geographical regions, however not all are experiencing a rapid reduction. The unexpected death of a previously seemingly healthy infant places a hard emotional burden on families. Through identifying unique risk factors and developmental timepoints of distinct SUID clusters, our findings can assist with public health infant mortality prevention policies and aid basic mechanistic research.

Abstract P474: Functional Outcomes and Regional Significance of Ischemic Lesions After Thrombectomy for Large Vessel Occlusion Stroke

Introduction: Endovascular thrombectomy (EVT) has revolutionized large vessel occlusion (LVO) stroke care. However, over half remain functionally disabled or die despite treatment. Understanding outcomes may influence EVT selection, novel therapies, and prognostication. We sought to identify associations between outcomes and brain regions involved in ischemic lesions. Methods: For consecutive LVO patients with post-EVT MRI, acute ischemic lesions were manually segmented from DWI and spatially normalized. Individual lesion volumes were automatically parcellated (atlas-defined 94 cortical regions, 14 subcortical nuclei, 20 white matter tracts) and then reduced to ten anatomically plausible lesion patterns using unsupervised dimensionality reduction techniques. Ninety-day modified Rankin Scale (mRS) was modeled via Bayesian regression, taking the ten lesion patterns as inputs and controlling for lesion size, age, sex, acute NIH Stroke Scale, alteplase, and TICI 2b-3 reperfusion. Results: We identified 153 LVO patients with mean age 68±15 years and 51% female. Median NIHSS was 16 (IQR 13-20), 56% received alteplase, and 84% achieved TICI2b-3. The lesion patterns predictive of 90-day mRS involved bilateral subcortical nuclei, pre- and postcentral gyri, insular and opercular cortex, as well as left-sided inferior frontal and angular gyri ( Figure 1A ). Lesions affecting white matter tracts had the highest relevance predicting 90-day mRS ( Figure 1B ). Conclusions: These data describe the significance for outcomes of specific brain regions involved in ischemic lesions on MRI after EVT. Future work in additional datasets is needed to confirm these granular findings.

Self-generated persistent random forces drive phase separation in growing tumors.

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Dynamics of cells in the core is glass-like, whereas those in the periphery undergoes diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of the core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves the way toward understanding the origins of intratumor heterogeneity using experimental imaging data.

Unsupervised damage clustering in complex aeronautical composite structures monitored by Lamb waves: An inductive approach

Structural Health Monitoring (SHM), i.e. the action of monitoring structures in real-time and in an automated manner, is a major challenge in several industrial fields such as aeronautic. SHM is by nature a very high dimensional data-driven problem that possesses several specificities when addressed as a machine learning problem. First of all data in damaged cases are rare and very costly as the generation of damaged data is not always possible and simulations are not reliable especially when dealing with complex structures. SHM is thus by nature an unsupervised problem. Furthermore, any incoming sample should be instantaneously clustered and handcrafted damage indexes are commonly used as a first dimension reduction step due to large datasets to be processed. As a consequence, unsupervised dimensionality reduction (DR) techniques that project very high dimensional data into a two or three-dimensional space (such as t-SNE or UMAP) are very appealing in such a context. However, these methods suffer from one major drawback which is that they are unable to cluster any unknown incoming sample. To solve this we propose to add inductive abilities to these well know methods by associating their projection bases with Deep Neural Networks (DNNs). The resulting DNNs are then able to cluster any incoming unknown samples. Based on those tools, a SHM methodology allowing for unsupervised damage clustering with dimensionality reduction is presented here. To demonstrate the effectiveness of the method, results of damage classification on large experimental data sets coming from complex aeronautical composite structures monitored through Lamb waves are shown. Furthermore, several DR techniques have been benchmarked and recommendations are derived. It is demonstrated that the use of raw Lamb wave signals instead of the associated damage indexes is more effective. This non-intuitive result helps to reduce the gap between laboratory research and the actual start-up of SHM activities in industrial applications.

Robust unsupervised dimensionality reduction based on feature clustering for single-cell imaging data

Biological data, and in particular imaging data, have experienced an exponential growth in terms of volume and complexity in the last few years, raising new challenges in the field of machine learning. Unsupervised problems are of particular relevance, as the generation of labels for the data is often labor-intensive, expensive or simply not possible. However, interpretability of the data and the results is key to extract new valuable knowledge from the large-scale datasets that are studied. This highlights the necessity of adequate unsupervised dimensionality reduction techniques that can lower the computational workload necessary to process the dataset, while at the same time providing information on its structure. This paper describes a framework that brings together previous proposals on unsupervised feature clustering, with the goal of providing a scalable, interpretable and robust dimensionality reduction on single-cell imaging data. The framework integrates several inter-feature dissimilarity measures, clustering algorithms, quality criteria to select the best feature clustering, and dimensionality reduction methods that are built on the clustering. For each of these components, several approaches proposed in previous works have been tested and evaluated on three use cases coming from two different imaging datasets, highlighting the best-performing components. Affinity clustering is applied for feature clustering for the first time. The results were validated using statistical tests, showing that many of the combinations tested lowered the complexity of the datasets while maintaining or improving the accuracy yielded by classifiers applied on them. The analysis highlighted affinity clustering as the best algorithm for feature clustering, with median differences of up to 8.9% and 0.9% in accuracy with respect to FSFS and hierarchical clustering. Representation entropy obtained a median difference of 13.0% and 0.8% with respect to class separability and silhouette index, respectively, as a robust unsupervised criterion to select the cluster set. Dissimilarities based on Pearson’s correlation performed slightly better than the alternatives, with a median improvement of 2.8% with respect to the cosine distance.

LN-SNE: Log-Normal Distributed Stochastic Neighbor Embedding for Anomaly Detection

We present a new unsupervised dimensionality reduction technique, called LN-SNE, for anomaly detection. LN-SNE generates a parametric embedding by means of Restricted Boltzmann Machines and uses a heavy-tail distribution to project data to a lower dimensional space such that dissimilarities between normal data and anomalies are preserved or strengthened. We compare LN-SNE to several benchmark dimensionality reduction methods on real datasets. The results suggest that LN-SNE for anomaly detection is less sensitive to the dimension of the latent space than the other methods and outperforms them in terms of accuracy. We empirically show that our technique scales near-linearly with respect to the number of dimensions and data size.

Visualization of Single Cell RNA-Seq Data Using t-SNE in R.

Single cell RNA sequencing (scRNA-seq) is a powerful tool to analyze cellular heterogeneity, identify new cell types, and infer developmental trajectories, which has greatly facilitated studies on development, immunity, cancer, neuroscience, and so on. Visualizing of scRNA-Seq data is fundamental and essential because it is critical to biological interpretation. Although principal component analysis (PCA) is used for visualizing scRNA-seq at early studies, t-Distributed Stochastic Neighbor embedding (t-SNE), an unsupervised nonlinear dimensionality reduction technique, is widely used nowadays due to its advantage in visualization of scRNA-seq data. Here, we detailed the process of visualization of single-cell RNA-seq data using t-SNE via Seurat, an R toolkit for single cell genomics.

Semi-supervised discriminant Isomap with application to visualization, image retrieval and classification

As one of the most promising nonlinear unsupervised dimensionality reduction (DR) technique, the Isomap reveals the intrinsic geometric structure of manifold by preserving geodesic distance of all data pairs. Recently, some supervised versions of Isomap have been presented to guide the manifold learning and increase the discriminating capability. However, the performance may deteriorate when there is no sufficient prior information available. Hence, a novel semi-supervised discriminant Isomap (SSD-Isomap) is proposed in the paper. First, two pairwise constraints including must-link and likely-link (LL) are used to depict the neighborhoods of data points. Then, two graphs are constructed based on the two constraints, and distances between points belonging to the LL constraint are modified by a scale parameter. Finally, the geodesic distance metric is obtained based on the graphs, and the corresponding optimal nonlinear subspace is sought. The performance of SSD-Isomap is evaluated by extensive experiments of data visualization, image retrieval and classification. Compared with other state-of-the-art DR methods, SSD-Isomap presents more accurate and robust results.

Evaluation of effect of unsupervised dimensionality reduction techniques on automated arrhythmia classification

Abstract Automation in cardiac arrhythmia classification helps medical professionals to make accurate decisions upon the patient’s health. The aim of this work is to evaluate the performance of five different linear and nonlinear unsupervised dimensionality reduction (DR) techniques namely principal component analysis (PCA), fast independent component analysis (fastICA) with tangential, kurtosis and Gaussian contrast functions, kernel PCA (KPCA) with polynomial kernel, hierarchical nonlinear PCA (hNLPCA) and principal polynomial analysis (PPA) on classification of cardiac arrhythmias using probabilistic neural network classifier (PNN). The design phase of the classification model comprises of the following stages: preprocessing of the cardiac signal by eliminating detail coefficients that contain noise, feature extraction through Daubechies wavelet transform, dimensionality reduction through unsupervised DR techniques, and arrhythmia classification using PNN. PCA is a widely used DR technique for mapping high dimensional data to its low dimensional representation. But real world data like electrocardiogram (ECG) signals are complex and nonlinear in nature. This work concentrates on performance analysis of four nonlinear DR techniques and conventional linear PCA technique on classification of cardiac arrhythmias. Entire MIT-BIH arrhythmia database is used for experimentation. The experimental results demonstrate that the combination of PNN classifier (at spread parameter, σ = 0.4) and fastICA DR technique with tangential contrast function exhibit highest F score of 99.83% with a minimum of 10 dimensions. hNLPCA and KPCA requires more computation time for low dimensional mapping. PPA performs about 10% better than PCA and serves intermediate between linear and nonlinear techniques.

Extracting the nonlinear features of motor imagery EEG using parametric t-SNE

When performing studies on brain computer interface based rehabilitation problems, researchers frequently encounter difficulty due to the curse of dimensionality and the nonlinear nature of Motor Imagery Electroencephalography (MI-EEG). Though many approaches have been proposed recently to address the feature extraction problem and have shown surprising performance, unfortunately, most of them are non-parametric or linear dimension reduction techniques, which are limited in utility for out-of-sample extension for MI-EEG classification. To address the problem and obtain accurate MI-EEG features, a new unsupervised nonlinear dimensionality reduction technique termed parametric t-Distributed Stochastic Neighbor Embedding (P. t-SNE) is employed to extract the nonlinear features from MI-EEG. Considering that MI-EEG is a kind of non-stationary signal with remarkable time-frequency rhythmic distribution characteristics, Discrete Wavelet Transform (DWT) is used to extract the time-frequency features of MI-EEG. Furthermore, P. t-SNE is applied to selected wavelet components to get the nonlinear features. They are then combined serially to construct the feature vector. Experiments are conducted on a publicly available dataset, and the experimental results show that the nonlinear features have great visualization performance with obvious clustering distribution, and the feature extraction method indicates excellent classification performance as evaluated by a support vector machine classifier. This paper suggests a manifold based technique for further analysis and classification research of MI-EEG.

Learning-based text classifiers using the Mahalanobis distance for correlated datasets

We present a novel approach to text categorisation with the aid of the Mahalanobis distance measure for classification. For correlated datasets, classification using the Euclidean distance is not very accurate. The use of the Mahalanobis distance exploits the correlation in data for the purpose of classification. For achieving this on large datasets, an unsupervised dimensionality reduction technique, principal component analysis (PCA) is used prior to classification using the k-nearest neighbours (kNN) classifier. As kNN does not work well for high-dimensional data, and moreover computing correlations for huge and sparse data is inefficient, we use PCA to obtain a reduced dataset for the training phase. Experimental results show improvement in classification accuracy and a significant reduction in error percentage by using the proposed algorithm on huge datasets, in comparison with classifiers using the Euclidean distance.

Principal component analysis - a tutorial

Dimensionality reduction is one of the preprocessing steps in many machine learning applications and it is used to transform the features into a lower dimension space. Principal component analysis (PCA) technique is one of the most famous unsupervised dimensionality reduction techniques. The goal of the technique is to find the PCA space, which represents the direction of the maximum variance of the given data. This paper highlights the basic background needed to understand and implement the PCA technique. This paper starts with basic definitions of the PCA technique and the algorithms of two methods of calculating PCA, namely, the covariance matrix and singular value decomposition (SVD) methods. Moreover, a number of numerical examples are illustrated to show how the PCA space is calculated in easy steps. Three experiments are conducted to show how to apply PCA in the real applications including biometrics, image compression, and visualisation of high-dimensional datasets.

Nonlocal structure constrained neighborhood preserving embedding model and its application for fault detection

In this paper, an unsupervised dimensionality reduction technique named nonlocal structure constrained neighborhood preserving embedding (NSC-NPE) is developed and applied for fault detection. To exploit the underlying geometrical structure, NSC-NPE constructs a global information-based dual-objective optimization function for modeling the process data. Besides the local variance information refined by the neighborhood preserving embedding algorithm, NSC-NPE also considers to utilize the meaningful nonlocal variance information via maximizing the Euclidean distance between the points outside the neighbors. The objective that having the local and nonlocal characteristics preserved in the low-dimensional space is achieved by minimizing the local scatter and maximizing the nonlocal scatter simultaneously. The proposed method is applied to fault detection based on the Hotelling’s T2 and squared prediction error (SPE) statistics. Three case studies are provided to demonstrate the efficiency of the proposed method.