# PLPCA: Persistent Laplacian Enhanced-PCA for Microarray Data Analysis

arXiv: https://arxiv.org/abs/2306.06292 · HTML: https://mlsanity.com/paper/2306.06292/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 46 references that are in the map.
- First posted on arXiv 9 Jun 2023.

## Builds on (most cited first, 3 of 3)

- [Persistent Laplacians: properties, algorithms and implications](https://mlsanity.com/paper/2012.02808/) (2020)
- [CCP: Correlated Clustering and Projection for Dimensionality Reduction](https://mlsanity.com/paper/2206.04189/) (2022)
- [Supervised Discriminative Sparse PCA for Com-Characteristic Gene Selection and Tumor Classification on Multiview Biological Data](https://mlsanity.com/paper/1905.11837/) (2019)

## Built on by (most cited first, 4 of 4)

- [Analyzing Single Cell RNA Sequencing with Topological Nonnegative Matrix Factorization](https://mlsanity.com/paper/2310.15744/) (2023)
- [Analyzing scRNA-seq data by CCP-assisted UMAP and t-SNE](https://mlsanity.com/paper/2306.13750/) (2023)
- [Multiscale Topology in Interactomic Network: From Transcriptome to Antiaddiction Drug Repurposing](https://mlsanity.com/paper/2312.01272/) (2023)
- [Lipschitz Bounds for Persistent Laplacian Eigenvalues under One-Simplex Insertions](https://mlsanity.com/paper/2506.21352/) (2025)

## Abstract (arXiv)

Over the years, Principal Component Analysis (PCA) has served as the baseline approach for dimensionality reduction in gene expression data analysis. It 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 classification 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 improved PCA 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 incorporate higher-order simplicial complexes to capture higher-order interactions in the data. We evaluate and validate the performance of PLPCA using benchmark microarray datasets that involve normal tissue samples and four different cancer tissues. Our extensive studies demonstrate that PLPCA outperforms all other state-of-the-art models for classification tasks after dimensionality reduction.