Enhancing Characteristic Gene Selection and Tumor Classification by the Robust Laplacian Supervised Discriminative Sparse PCA

K-nearest-neighbors induced topological PCA for single cell RNA-sequence data analysis

Single-cell RNA sequencing (scRNA-seq) is widely used to reveal heterogeneity in cells, which has given us insights into cell-cell communication, cell differentiation, and differential gene expression. However, analyzing scRNA-seq data is a challenge due to sparsity and the large number of genes involved. Therefore, dimensionality reduction and feature selection are important for removing spurious signals and enhancing downstream analysis. Traditional PCA, a main workhorse in dimensionality reduction, lacks the ability to capture geometrical structure information embedded in the data, and previous graph Laplacian regularizations are limited by the analysis of only a single scale. We propose a topological Principal Components Analysis (tPCA) method by the combination of persistent Laplacian (PL) technique and L2,1 norm regularization to address multiscale and multiclass heterogeneity issues in data. We further introduce a k-Nearest-Neighbor (kNN) persistent Laplacian technique to improve the robustness of our persistent Laplacian method. The proposed kNN-PL is a new algebraic topology technique which addresses the many limitations of the traditional persistent homology. Rather than inducing filtration via the varying of a distance threshold, we introduced kNN-tPCA, where filtrations are achieved by varying the number of neighbors in a kNN network at each step, and find that this framework has significant implications for hyper-parameter tuning. We validate the efficacy of our proposed tPCA and kNN-tPCA methods on 11 diverse benchmark scRNA-seq datasets, and showcase that our methods outperform other unsupervised PCA enhancements from the literature, as well as popular Uniform Manifold Approximation (UMAP), t-Distributed Stochastic Neighbor Embedding (tSNE), and Projection Non-Negative Matrix Factorization (NMF) by significant margins. For example, tPCA provides up to 628%, 78%, and 149% improvements to UMAP, tSNE, and NMF, respectively on classification in the F1 metric, and kNN-tPCA offers 53%, 63%, and 32% improvements to UMAP, tSNE, and NMF, respectively on clustering in the ARI metric.

PLPCA: Persistent Laplacian-Enhanced PCA for Microarray Data Analysis

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. Its primary objective is to identify a subset of disease-causing genes from a vast pool of thousands of genes. However, PCA possesses inherent limitations that hinder its interpretability, introduce class ambiguity, and fail to capture complex geometric structures in the data. Although these limitations have been partially addressed in the literature by incorporating various regularizers, such as graph Laplacian regularization, existing PCA based methods still face challenges related to multiscale analysis and capturing higher-order interactions in the data. To address these challenges, we propose a novel approach called Persistent Laplacian-enhanced Principal Component Analysis (PLPCA). PLPCA amalgamates the advantages of earlier regularized PCA methods with persistent spectral graph theory, specifically persistent Laplacians derived from algebraic topology. In contrast to graph Laplacians, persistent Laplacians enable multiscale analysis through filtration and can incorporate higher-order simplicial complexes to capture higher-order interactions in the data. We evaluate and validate the performance of PLPCA using ten benchmark microarray data sets that exhibit a wide range of dimensions and data imbalance ratios. Our extensive studies over these data sets demonstrate that PLPCA provides up to 12% improvement to the current state-of-the-art PCA models on five evaluation metrics for classification tasks after dimensionality reduction.

Quantitative Detection of Gastrointestinal Tumor Markers Using a Machine Learning Algorithm and Multicolor Quantum Dot Biosensor

This work was to explore the application value of gastrointestinal tumor markers based on gene feature selection model of principal component analysis (PCA) algorithm and multicolor quantum dots (QDs) immunobiosensor in the detection of gastrointestinal tumors. Based on the PCA method, the neighborhood rough set algorithm was introduced to improve it, and the tumor gene feature selection model (OPCA) was established to analyze its classification accuracy and accuracy. Four kinds of coupled biosensors were fabricated based on QDs, namely, 525 nm Cd Se/Zn S QDs-carbohydrate antigen 125 (QDs525-CA125 McAb), 605 nm Cd Se/Zn S QDs-cancer antigen 19-9 (QDs605-CA19-9 McAb), 645 nm Cd Se/Zn S QDs-anticancer embryonic antigen (QDs 645-CEA McAb), and 565 nm Cd Se/Zn S QDs-anti-alpha-fetoprotein (QDs565-AFP McAb). The quantum dot-antibody conjugates were identified and quantified by fluorescence spectroscopy and ultraviolet absorption spectroscopy. The results showed that the classification precision of OPCA model in colon tumor and gastric cancer datasets was 99.52% and 99.03%, respectively, and the classification accuracy was 94.86% and 94.2%, respectively, which were significantly higher than those of other algorithms. The fluorescence values of AFP McAb, CEA McAb, CA19-9 McAb, and CA125 McAb reached the maximum when the conjugation concentrations were 25 µg/mL, 20 µg/mL, 30 µg/mL, and 30 µg/m, respectively. The highest recovery rate of AFP was 98.51%, and its fluorescence intensity was 35.78 ± 2.99, which was significantly higher than that of other antigens (P < 0.001). In summary, the OPCA model based on PCA algorithm can obtain fewer feature gene sets and improve the accuracy of sample classification. Intelligent immunobiosensors based on machine learning algorithms and QDs have potential application value in gastrointestinal gene feature selection and tumor marker detection, which provides a new idea for clinical diagnosis of gastrointestinal tumors.