A DOA estimation method for area array based on dimensionality reduction processing

Local appearance-based methods have been proposed recently for face recognition. We analyze the effects of different dimension reduction and normalization methods on local appearance-based face recognition in this paper. Each image is divided into equal sized blocks and six different dimension reduction methods are implemented for each block separately to create local visual feature vectors. On these local features, several normalization methods are applied in an attempt to eliminate the changes in lighting conditions and contrast differences among blocks of different face images. The experimental results show the improvements in recognition rates due to the effects of dimension reduction and normalization for three different classifiers. Usage of trainable dimension reduction methods instead of DCT and a new normalization method in our work (within-block normalization as referred in this paper) are two factors that makes difference from previous works in literature. The best performance is achieved using a block size of 16times16, performing dimension reduction using approximate pairwise accuracy criterion (aPAC) and applying within-block mean and variance normalization.

Graph-based dimensionality reduction (DR) methods have been applied successfully in many practical problems, such as face recognition, where graphs play a crucial role in modeling the data distribution or structure. However, the ideal graph is, in practice, difficult to discover. Usually, one needs to construct graph empirically according to various motivations, priors, or assumptions; this is independent of the subsequent DR mapping calculation. Different from the previous works, in this paper, we attempt to learn a graph closely linked with the DR process, and propose an algorithm called dimensionality reduction with adaptive graph (DRAG), whose idea is to, during seeking projection matrix, simultaneously learn a graph in the neighborhood of a prespecified one. Moreover, the pre-specified graph is treated as a noisy observation of the ideal one, and the square Frobenius divergence is used to measure their difference in the objective function. As a result, we achieve an elegant graph update formula which naturally fuses the original and transformed data information. In particular, the optimal graph is shown to be a weighted sum of the pre-defined graph in the original space and a new graph depending on transformed space. Empirical results on several face datasets demonstrate the effectiveness of the proposed algorithm.

This work presents a new interactive data visualization approach based on mixture of the outcomes of dimensionality reduction (DR) methods. Such a mixture is a weighted sum, whose weighting factors are defined by the user through a visual and intuitive interface. Additionally, the low-dimensional representation space produced by DR methods are graphically depicted using scatter plots powered via an interactive data-driven visualization. To do so, pairwise similarities are calculated and employed to define the graph to be drawn on the scatter plot. Our visualization approach enables the user to interactively combine DR methods while provided information about the structure of original data, making then the selection of a DR scheme more intuitive.

During the COVID-19 pandemic, researchers have made efforts to detect COVID-19 through various methods. In the dataset used for this study, COVID-19 patients were identified using chest computed tomography (CT) images. High dimensionality is frequently an issue in machine learning image classification. Accordingly, this study implemented three dimensionality reduction methods in combination with various machine learning algorithms for improved classification. Principal component analysis (PCA), uniform manifold approximation and projection (UMAP), and diffusion maps were applied to the dataset to extract the most important features of the chest CT images. The extracted features were given as input either to logistic regression or the extreme gradient boosting (XGBoost) algorithm to perform classification. The strongest model identified from this study was diffusion maps in combination with logistic regression. This model, evaluated against existing models from similar studies in recent years, yielded strong performance for detecting COVID-19 cases using chest CT images. Our proposed model achieved 97.35% accuracy, 92.16% sensitivity, and 98.59% specificity on the held-out test set in differentiating between COVID-19-positive cases and healthy, non-COVID-19 cases. This study aimed to detect COVID-19 without the use of viral testing. Importantly, this method could assist clinicians in making an initial diagnosis, especially when viral testing is not available or timely enough for the patient’s case. This study also provides deeper insight into various dimensionality reduction methods and how compatible they are with biomedical imaging data. Models were trained using stratified cross-validation on the training set, with final performance evaluated on a held-out test set at the patient level to prevent data leakage. Additional imbalance-aware metrics were used to assess robustness given class distribution differences.

One of the dimension reduction (DR) methods for data-visualization, t-distributed stochastic neighbor embedding (t-SNE), has drawn increasing attention. t-SNE gives us better visualization than conventional DR methods, by relieving so-called crowding problem. The crowding problem is one of the curses of dimensionality, which is caused by discrepancy between high and low dimensional spaces. However, in t-SNE, it is assumed that the strength of the discrepancy is the same for all samples in all datasets regardless of ununiformity of distributions or the difference in dimensions, and this assumption sometimes ruins visualization. Here we propose a new DR method inhomogeneous t-SNE, in which the strength is estimated for each point and dataset. Experimental results show that such pointwise estimation is important for reasonable visualization and that the proposed method achieves better visualization than the original t-SNE.

Advances in functional magnetic resonance imaging (fMRI) have led to the ability to study the brain across many contexts. However, the large number of features generated by functional connectivity approaches may overfit the data. These problems can be overcome with either feature selection (FS) or dimensionality reduction (DR), which can be applied to less complex models. We utilize two open source datasets to compare the performance of DR/FS methods on cognitive task decoding using a suite of ML classifiers. While FS and DR methods have been used previously in decoding research, no systematic comparison of their performance has been undertaken. Here, we compare available methods using commonly utilized machine learning libraries to establish which methods provide the best predictive performance. We then conduct statistical tests to examine the relative contributions of DR and FS methods and classifiers on decoding accuracy. Neither DR or FS was found to be superior. However, differences were identified across datasets and tasks. In the majority of methods and datasets, a peak in predictive performance was found using a small percentage (005-.10%) of the total number of original features. Some methods perform better than the baseline method of prediction with all available features or selecting features randomly. Decoding performance with some datasets with some method exceeds that of deep learning approaches. These results suggest a "sweet spot" for the tradeoff between the retention of features and predictive accuracy.

This paper carries on research surrounding the influences produced by dimensionality reduction on machine learning classification effect. Firstly, paper constructs the analysis architecture of data dimension reduction classification, combines the two different unsupervised dimension reduction methods, locally linear embedding (LLE) and principal component analysis (PCA) with the five machine learning classification methods: Gradient Boosting Decision Tree (GBDT), Random Forest, Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Logistic Regression. And then uses the handwritten digital identification dataset to analyze the classification performance of these five classification methods on different dimension datasets by different dimensionality reduction methods. The analysis shows that using the appropriate dimensionality reduction method for dimensionality reduction classification can effectively improve the classification accuracy; the dimensionality reduction classification effect of non-linear dimensionality reduction method is generally better than the linear dimensionality reduction method; different machine learning classification algorithms have significant differences in the sensitivity of dimensions.

Dimension reduction has been used to visualise the distribution of multidimensional microbiome data, but the composite variables calculated by the dimension reduction methods have not been widely used to investigate the relationship of the human gut microbiome with lifestyle and disease. In the present study, we applied several dimension reduction methods, including principal component analysis, principal coordinate analysis (PCoA), non-metric multidimensional scaling (NMDS), and non-negative matrix factorization, to a microbiome dataset from 186 subjects with symptoms of allergic rhinitis (AR) and 106 controls. All the dimension reduction methods supported that the distribution of microbial data points appeared to be continuous rather than discrete. Comparison of the composite variables calculated from the different dimension reduction methods showed that the characteristics of the composite variables differed depending on the distance matrices and the dimension reduction methods. The first composite variables calculated from PCoA and NMDS with the UniFrac distance were strongly associated with AR (FDR adjusted P = 2.4 × 10–4 for PCoA and P = 2.8 × 10–4 for NMDS), and also with the relative abundance of Bifidobacterium and Prevotella. The abundance of Bifidobacterium was also linked to intake of several nutrients, including carbohydrate, saturated fat, and alcohol via composite variables. Notably, the association between the composite variables and AR was much stronger than the association between the relative abundance of individual genera and AR. Our results highlight the usefulness of the dimension reduction methods for investigating the association of microbial composition with lifestyle and disease in clinical research.

Existing surface reconstruction methods only work for low-dimensional, mostly 2D or 3D, data. In real applications, high-dimensional data is difficult to interpret as it requires more dimensions to represent. As a dimension reduction method, manifold learning provides an explicit representation for the useful implicit information hidden in the original feature space. But the internal topological and differential structure has disappeared in the dimensionality reduction process. In order to investigate the topological and differential structure of a data set, we introduce boundary compactness, which is used to study the shape of the data set in the original high-dimensional feature space. Beginning with the Delaunay graph (for 3D data) or the complete graph (for data of higher dimensions), we select the edges based on the boundary compactness to make the relevance graph. The relevance graph is then used to reconstruct the surface of the data. Experiments show that the introduced technique based on the boundary compactness works well for data of 3D or higher dimensions.

The majority of the classical dimensionality reduction methods can be unified into a graph-embedding-based framework. A fixed graph constructed in a high-dimensional space has been extensively employed in the graph-embedding-based dimensionality reduction methods. However, a fixed graph often cannot characterize the structure of high-dimensional data owing to the curse of dimensionality. To solve this problem, we combine graph construction and dimensionality reduction into a coherent framework. Thus, the constructed graph can be updated dynamically in dimensionality reduction. In the existing methods based on the coherent framework, graphs are usually constructed by a type of neighborhood relationship and single clustering result. This study proposes an unsupervised dimensionality reduction method guided by fusing multiple clustering results. In the proposed method, multiple clustering results are first obtained by the k-means algorithm, and then a graph is constructed using a weighted co-association matrix of fusing the clustering results to capture data distribution information. Based on the graph, we present an objective function of combining graph construction and dimensionality reduction to implement mutual guidance between them. Numerical experiments on real data sets illustrate that the proposed method achieves significant improvement over some representative and state-of-the-art unsupervised dimensionality reduction methods.

Context. The actual problem of effective intelligent diagnostics of malfunctions of rotating equipment is solved. The object of study is the process of data dimensionality reduction and defect classification based on vibration analysis for maintenance of rotating machines. The subject of study is the methods of dimension reduction and defect classification by vibration analysis.Objective. Development of an approach to data dimensionality reduction and defect classification based on vibration analysis for maintenance of rotating machinesMethod. The comprehensive approach to data dimensionality reduction and defect classification based on vibration analysis is proposed, which solves the problem of data dimensionality reduction for training classifiers and defect classification, and also solves the problem of building a neural network classifier capable of ensuring the speed of fault classification without loss of accuracy on data of reduced dimensionality. The approach differs from the existing ones by the possibility of using optional union and intersection operators when forming a set of significant features, which provides flexibility and allows to adapt to different contexts and data types, ensuring classification efficiency in cases of large-dimensional data.A denoising method allows to preserve important information, avoiding redundancy and improving the quality of data for further analysis. It involves calculating the signal-to-noise ratio, setting thresholds, and applying a fast Fourier transform that separates relevant features from noise. Applying the LIME method to a set of machine learning models allows to identify significant features with greater accuracy and interpretability. This contributes to more reliable results, as LIME helps to understand the influence of each feature on the final model solution, which is especially important when working with large datasets, where the importance of individual features may not be obvious. The implementation of optional operators of union and intersection of significant features provides additional flexibility in choosing an approach to defining important features. This allows the method to be adapted to different contexts and data types, ensuring efficiency even in cases with a large number of features.Results. The developed method was implemented in software and examined when solving the problem of defect classification based on vibration analysis for maintenance of rotating machines.Conclusions. The conducted experimental studies confirmed the high efficiency and workability of the proposed approach forreducing the dimensionality of data and classifying defects based on vibration analysis in the aspect of maintenance of rotating machines. Prospects for further research will be directed to the search for alternative neural network architectures and their training to reduce training time

As one of the most popular dimensionality reduction techniques, locality preserving projections (LPP) has been widely used in computer vision and pattern recognition. However, in practical applications, data is always corrupted by noises. For the corrupted data, samples from the same class may not be distributed in the nearest area, thus LPP may lose its effectiveness. In this paper, it is assumed that data is grossly corrupted and the noise matrix is sparse. Based on these assumptions, we propose a novel dimensionality reduction method, named low-rank preserving projections (LRPP) for image classification. LRPP learns a low-rank weight matrix by projecting the data on a low-dimensional subspace. We use the L21 norm as a sparse constraint on the noise matrix and the nuclear norm as a low-rank constraint on the weight matrix. LRPP keeps the global structure of the data during the dimensionality reduction procedure and the learned low rank weight matrix can reduce the disturbance of noises in the data. LRPP can learn a robust subspace from the corrupted data. To verify the performance of LRPP in image dimensionality reduction and classification, we compare LRPP with the state-of-the-art dimensionality reduction methods. The experimental results show the effectiveness and the feasibility of the proposed method with encouraging results.

Calcium imaging has been widely adopted for its ability to record from large neuronal populations. To summarize the time course of neural activity, dimensionality reduction methods, which have been applied extensively to population spiking activity, may be particularly useful. However, it is unclear if the dimensionality reduction methods applied to spiking activity are appropriate for calcium imaging. We thus carried out a systematic study of design choices based on standard dimensionality reduction methods. We also developed a method to perform deconvolution and dimensionality reduction simultaneously (Calcium Imaging Linear Dynamical System, CILDS). CILDS most accurately recovered the single-trial, low-dimensional time courses from simulated calcium imaging data. CILDS also outperformed the other methods on calcium imaging recordings from larval zebrafish and mice. More broadly, this study represents a foundation for summarizing calcium imaging recordings of large neuronal populations using dimensionality reduction in diverse experimental settings.

Stacked generalization (SG) is a hierarchical architecture, which combines classifiers in order to boost the performance of overall system by integrating the individual classifiers. Two-layered version of SG has been utilized in many image analysis researches and shown to be an effective tool for enhancing the performance measure of the individual classifiers in a number of various cases. However, due to its layered architecture and integration approach, it inherits some problems such as curse of dimensionality, i.e. necessity for more samples, and higher computational time for classification. In this work, the effect of two different dimensionality reduction methods, namely linear and non-linear, between layers of SG are analyzed to attack the curse of dimensionality problem. In the experimental part, the comparisons of these approaches with respect to each other and SG-without-dimensionality-reduction are presented. According to test results, it is concluded that dimensionality reduction has a positive effect on the performance of SG, i.e. both linear and nonlinear dimensionality reduction approaches performs better than SG architecture, and nonlinear dimensionality reduction achieves better classification accuracy than linear dimensionality reduction.

High-dimensional features often cause computational complexity and dimensionality curse. Feature selection and feature extraction are the two mainstream methods for dimensionality reduction. Feature selection but not feature extraction can preserve the critical information and maintain the physical meaning simultaneously. Herein, we proposed a dimensionality reduction method based on rough set theory (DRM-RST) for feature selection. We defined the hyperspectral image as a decision system, extracted the features as decision attributes, and selected the effective features based on information entropy. We used the Washington D.C. Mall dataset and New York dataset to evaluate the performance of DRM-RST on dimensionality reduction. Compared with full band classification, 184 or 185 redundant bands were removed in DRM-RST, respectively. DRM-RST achieved similar accuracy (overall accuracy >94%) by SVM classifier and reduced computing time by about 85%. We further compared the dimensionality reduction efficiency of DRM-RST against other popular methods, including ReliefF, Sequential Backward Elimination (SBE) and Information Gain (IG). The Producer’s accuracy (PA) and User’s accuracy (UA) of DRM-RST was greater than that of ReliefF and IG. DRM-RST showed greater stability of accuracy than SBE in dimensionality reduction when using for different datasets. Collectively, this study provides a new method for dimensionality reduction that can reduce computational complexity and alleviate dimensionality curse.