SICA: subjectively interesting component analysis

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.

Dimensionality reduction through convolutional autoencoders for fracture patterns prediction

Single-cell RNA sequencing (scRNA-seq) in multi-condition experiments enables the systematic assessment of treatment effects. Analyzing scRNA-seq data relies on linear dimensionality reduction (DR) methods like principal component analysis (PCA). These methods decompose high-dimensional gene expression profiles into interpretable factor representations and prototypical expression patterns (components). However, integrating study covariates within linear DR frameworks remains a challenging task. We present scPCA, a flexible DR framework that jointly models cellular heterogeneity and conditioning variables, allowing it to recover an integrated factor representation and reveal transcriptional changes across conditions and components of the decomposition. We show that scPCA extracts an interpretable latent representation by analyzing unstimulated and IFNß-treated PBMCs and show its utility in mitigating batch effects. We examine age-related changes in rodent lung cell populations, uncovering a previously unreported surge in Ccl5 expression in T cells. We illustrate how scPCA may be employed to identify coordinated transcriptional changes across multiple time-points in depolarized visual cortex neurons. Finally, we show that scPCA elucidates transcriptional shifts in CRISPR-Cas9 chordin knockout zebrafish single-cell data despite large difference cell abundance across conditions. scPCA is a general method applicable beyond scRNA-seq to other high-dimensional datasets.

Dimensionality reduction is an unsupervised learning task aimed at creating a low-dimensional summary and/or extracting the most salient features of a dataset. Principal component analysis is a linear dimensionality reduction method in the sense that each principal component is a linear combination of the input variables. To allow features that are nonlinear functions of the input variables, many nonlinear dimensionality reduction (NLDR) methods have been proposed. In this article, we propose novel NLDR methods based on bottleneck deep autoencoders. Our contributions are 2-fold: (1) We introduce a monotonicity constraint into bottleneck deep autoencoders for estimating a single nonlinear component and propose two methods for fitting the model. (2) We propose a new, forward stepwise deep learning architecture for estimating multiple nonlinear components. The former helps extract interpretable, monotone components when the assumption of monotonicity holds, and the latter helps evaluate reconstruction errors in the original data space for a range of components. We conduct numerical studies to compare different model fitting methods and use two real data examples from the studies of human immune responses to HIV to illustrate the proposed methods. Supplementary materials for this article are available online.

The recent explosion in procurement and availability of high-dimensional gene- and protein-expression profile datasets for cancer diagnostics has necessitated the development of sophisticated machine learning tools with which to analyze them. A major limitation in the ability to accurate classify these high-dimensional datasets stems from the 'curse of dimensionality', occurring in situations where the number of genes or peptides significantly exceeds the total number of patient samples. Previous attempts at dealing with this issue have mostly centered on the use of a dimensionality reduction (DR) scheme, Principal Component Analysis (PCA), to obtain a low-dimensional projection of the high-dimensional data. However, linear PCA and other linear DR methods, which rely on Euclidean distances to estimate object similarity, do not account for the inherent underlying nonlinear structure associated with most biomedical data. The motivation behind this work is to identify the appropriate DR methods for analysis of high-dimensional gene- and protein-expression studies. Towards this end, we empirically and rigorously compare three nonlinear (Isomap, Locally Linear Embedding, Laplacian Eigenmaps) and three linear DR schemes (PCA, Linear Discriminant Analysis, Multidimensional Scaling) with the intent of determining a reduced subspace representation in which the individual object classes are more easily discriminable.

Statistical methods have been getting constant development since 1970s. However, the statistical methods of the big data are no longer restricted with these methods which are listed in the textbook. This paper mainly demonstrates the Discrimination Analysis of Multivariate Statistical Analysis, Linear Dimensionality Reduction and Nonlinear Dimensionality Reduction Method under the circumstances of the wide range of applications of high-dimensional data. This paper includes three parts. To begin with, the paper illustrates a developing trend from the data to the high-dimensional. Meanwhile, it analyzes the impacts of the high-dimensional data on discriminate analysis methods. The second part represents the necessity of the dimensionality reduction studies in the era of the high-dimensional data overflowing. Then, the paper focuses on introducing the main methods of the linear dimensionality reduction. In addition, this paper covers the basic idea of the nonlinear dimensionality reduction. Moreover, it systematically analyzes the breakthrough of the traditional methods. Furthermore, it chronologically demonstrates the developing trend of the dimensionality reduction method. The final part shows a comprehensive and systematic conclusion to the whole essay and describes a developing prospect of the dimension reduction methods in the future. The purpose of this essay is to design a framework of a performance system which is subject to the characteristics of China High-tech enterprises. It based on the analysing the principles and significance of the performance system of High-tech enterprises. The framework will promote the standardize management of High-tech enterprises of China.

Radial Visualization technique is a non linear dimensionality reduction method. Radial Visualization projects multivariate data in the 2-dimensional visual space inside the unit circle. Radial Visualization supports display both the samples and the attributes that provides useful information of data structures. In this article, we introduced a new variant of Radial Visualization for visualizing high dimensional data set that named Arc Radial Visualization. The new proposal that modified Radial Visualization supported more space to display high dimensional datasets. Our method provides an improvement in visualizing cluster structures of high dimensional data sets on the Radial Visualization. We present our proposal method with two quality measurements and proved the effectiveness of our approach for several real datasets.

Face recognition technology has evolved as an enchanting solution to address the contemporary needs in order to perform identification and verification of identity claims. By advancing the feature extraction methods and dimensionality reduction techniques in the application of pattern recognition, a number of face recognition systems has been developed with distinct degrees of success. Locality preserving projection (LPP) is a recently proposed method for unsupervised linear dimensionality reduction. LPP preserve the local structure of face image space which is usually more significant than the global structure preserved by principal component analysis (PCA) and linear discriminant analysis (LDA). This paper focuses on a systematic analysis of locality-preserving projections and the application of LPP in combination with an existing technique This combined approach of LPP through MPCA can preserve the global and the local structure of the face image which is proved very effective. Proposed approach is tested using the AT & T face database. Experimental results show the significant improvements in the face recognition performance in comparison with some previous methods.

Detection of maize seed germination rate based on improved locally linear embedding

Divergent Projection Analysis for Unsupervised Dimensionality Reduction

Navigating the complex landscape of single-cell transcriptomic data presents significant challenges. Central to this challenge is the identification of a meaningful representation of high-dimensional gene expression patterns that sheds light on the structural and functional properties of cell types. Pursuing model interpretability and computational simplicity, we often look for a linear transformation of the original data that aligns with key phenotypic features of cells. In response to this need, we introduce factorized linear discriminant analysis (FLDA), a novel method for linear dimensionality reduction. The crux of FLDA lies in identifying a linear function of gene expression levels that is highly correlated with one phenotypic feature while minimizing the influence of others. To augment this method, we integrate it with a sparsity-based regularization algorithm. This integration is crucial as it selects a subset of genes pivotal to a specific phenotypic feature or a combination thereof. To illustrate the effectiveness of FLDA, we apply it to transcriptomic datasets from neurons in the Drosophila optic lobe. We demonstrate that FLDA not only captures the inherent structural patterns aligned with phenotypic features but also uncovers key genes associated with each phenotype.

Enhanced locality preserving projections using robust path based similarity

Large-scale multiparameter screening has become increasingly feasible and straightforward to perform thanks to developments in technologies such as high-content microscopy and high-throughput flow cytometry. The automated toolkits for analyzing similarities and differences between large numbers of tested conditions have not kept pace with these technological developments. Thus, effective analysis of multiparameter screening datasets becomes a bottleneck and a limiting factor in unbiased interpretation of results. Here we introduce compaRe, a toolkit for large-scale multiparameter data analysis, which integrates quality control, data bias correction, and data visualization methods with a mass-aware gridding algorithm-based similarity analysis providing a much faster and more robust analyses than existing methods. Using mass and flow cytometry data from acute myeloid leukemia and myelodysplastic syndrome patients, we show that compaRe can reveal interpatient heterogeneity and recognizable phenotypic profiles. By applying compaRe to high-throughput flow cytometry drug response data in AML models, we robustly identified multiple types of both deep and subtle phenotypic response patterns, highlighting how this analysis could be used for therapeutic discoveries. In conclusion, compaRe is a toolkit that uniquely allows for automated, rapid, and precise comparisons of large-scale multiparameter datasets, including high-throughput screens.

Identifying collective variables (CVs) for chemical reactions is essential to reduce the 3N-dimensional energy landscape into lower dimensional basins and barriers of interest. However, in condensed phase processes, the nonmeaningful motions of bulk solvent often overpower the ability of dimensionality reduction methods to identify correlated motions that underpin collective variables. Yet solvent can play important indirect or direct roles in reactivity, and much can be lost through treatments that remove or dampen solvent motion. This has been amply demonstrated within principal component analysis (PCA), although less is known about the behavior of nonlinear dimensionality reduction methods, e.g., uniform manifold approximation and projection (UMAP), that have become recently utilized. The latter presents an interesting alternative to linear methods though often at the expense of interpretability. This work presents distance-attenuated projection methods of atomic coordinates that facilitate the application of both PCA and UMAP to identify collective variables in the presence of explicit solvent and further the specific identity of solvent molecules that participate in chemical reactions. The performance of both methods is examined in detail for two reactions where the explicit solvent plays very different roles within the collective variables. When applied to raw molecular dynamics data in solution, both PCA and UMAP representations are dominated by bulk solvent motions. On the other hand, when applied to data preprocessed by our attenuated projection methods, both PCA and UMAP identify the appropriate collective variables (though varying sensitivity is observed due to the presence of explicit solvent that results from the projection method). Importantly, this approach allows identification of specific solvent molecules that are relevant to the CVs and their importance.

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.