# Spherical Principal Component Analysis

arXiv: https://arxiv.org/abs/1903.06877 · HTML: https://mlsanity.com/paper/1903.06877/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Mar 2019.

## Built on by (most cited first, 10 of 10)

- [Principal Component Analysis in Space Forms](https://mlsanity.com/paper/2301.02750/) (2023)
- [Rethinking Symmetric Matrix Factorization: A More General and Better Clustering Perspective](https://mlsanity.com/paper/2209.02528/) (2022)
- [Spherical Matrix Factorization](https://mlsanity.com/paper/2111.14536/) (2021)
- [Enriched Robust Multi-View Kernel Subspace Clustering](https://mlsanity.com/paper/2205.10495/) (2022)
- [Multi-Task Learning with Prior Information](https://mlsanity.com/paper/2301.01572/) (2023)
- [Uniformity First: Uniformity-aware Test-time Adaptation of Vision-language Models against Image Corruption](https://mlsanity.com/paper/2505.12912/) (2025)
- [Exact Sparse Orthogonal Dictionary Learning](https://mlsanity.com/paper/2103.09085/) (2021)
- [Robust Principal Component Analysis: A Construction Error Minimization Perspective](https://mlsanity.com/paper/2111.12132/) (2021)
- [Heavy-Tailed Principal Component Analysis](https://mlsanity.com/paper/2603.11308/) (2026)
- [Hyperspherical Contrastive Representations Unlock Planning and Exploration](https://mlsanity.com/paper/2610.20409/) (2026)

## Abstract (arXiv)

Principal Component Analysis (PCA) is one of the most important methods to handle high dimensional data. However, most of the studies on PCA aim to minimize the loss after projection, which usually measures the Euclidean distance, though in some fields, angle distance is known to be more important and critical for analysis. In this paper, we propose a method by adding constraints on factors to unify the Euclidean distance and angle distance. However, due to the nonconvexity of the objective and constraints, the optimized solution is not easy to obtain. We propose an alternating linearized minimization method to solve it with provable convergence rate and guarantee. Experiments on synthetic data and real-world datasets have validated the effectiveness of our method and demonstrated its advantages over state-of-art clustering methods.