# CCP: Correlated Clustering and Projection for Dimensionality Reduction

arXiv: https://arxiv.org/abs/2206.04189 · HTML: https://mlsanity.com/paper/2206.04189/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 68 references that are in the map.
- First posted on arXiv 8 Jun 2022.

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

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [Persistent Laplacians: properties, algorithms and implications](https://mlsanity.com/paper/2012.02808/) (2020)
- [Grassmannian diffusion maps based dimension reduction and classification for high-dimensional data](https://mlsanity.com/paper/2009.07547/) (2020)

## Built on by (most cited first, 7 of 7)

- [PLPCA: Persistent Laplacian Enhanced-PCA for Microarray Data Analysis](https://mlsanity.com/paper/2306.06292/) (2023)
- [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)
- [K-Nearest-Neighbors Induced Topological PCA for scRNA Sequence Data Analysis](https://mlsanity.com/paper/2310.14521/) (2023)
- [Nearest Neighbor CCP-Based Molecular Sequence Analysis](https://mlsanity.com/paper/2409.04922/) (2024)
- [Multi-dimensional Persistent Sheaf Laplacians for Image Analysis](https://mlsanity.com/paper/2602.14846/) (2026)
- [Graph-Based Bidirectional Transformer Decision Threshold Adjustment Algorithm for Class-Imbalanced Molecular Data](https://mlsanity.com/paper/2406.06479/) (2024)

## Abstract (arXiv)

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated Clustering and Projection (CCP) offers a novel data domain strategy that does not need to solve any matrix. CCP partitions high-dimensional features into correlated clusters and then projects correlated features in each cluster into a one-dimensional representation based on sample correlations. Residue-Similarity (R-S) scores and indexes, the shape of data in Riemannian manifolds, and algebraic topology-based persistent Laplacian are introduced for visualization and analysis. Proposed methods are validated with benchmark datasets associated with various machine learning algorithms.