PCA
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Related Articles from SNS
Orthogonality and Dimensionality in Airline Cluster Analysis using PCA and Kernel PCA
Announce Type: new Abstract: To characterize the US airline profit cycles from 1995 to 2020, the authors of Renold et al. (2023) combine k-means clustering, principal component analysis, and system dynamic modelling. We replicate their clustering experiment in three spaces -- the original 7-dimensional raw-variable space, a 3-dimensional PC score space, and a 4-dimensional PC score space using their dataset gratefully included in the paper.
Anchor PCA
arXiv:2606.06233v1 Announce Type: cross Abstract: Principal component analysis (PCA) is one of the most widely used unsupervised dimension reduction techniques. We study PCA for data from multiple related domains. Since principal components generally differ across domains, one way to obtain a shared low-rank embedding is to perform PCA on the pooled data.
Improved Analysis of the Accelerated Noisy Power Method with Applications to Decentralized PCA
Announce Type: replace-cross Abstract: We analyze the Accelerated Noisy Power Method, an algorithm for Principal Component Analysis in the setting where only inexact matrix-vector products are available, which can arise for instance in decentralized PCA. While previous works have established that acceleration can improve convergence rates compared to the standard Noisy Power Method, these guarantees require overly restrictive upper bounds on the magnitude of the perturbations, limiting their...
What Does Debiasing Really Remove? A Geometric Study of PCA-Based Gender Debiasing in Word Embeddings
Announce Type: new Abstract: Debiasing methods based on principal component analysis (PCA) are broadly used to reduce gender bias in word embeddings used in LLMs, yet it remains unclear what aspects of bias they actually remove and how destructive this process is. These methods are based on the understanding that bias resides in a low-dimensional subspace, with the assumption that most of it can be captured by a few principal components. In this work, we conduct a systematic geometric...
Dimensionality Reduction for Cyberattack Classification: A Comparative Evaluation of PCA and Linear Predictive Coding
arXiv:2606.05584v1 Announce Type: new Abstract: High-dimensional feature representations are widely used in machine learning-based cyberattack detection systems. However, they increase computational complexity and may hinder deployment in resource-constrained environments. In this paper, we investigate feature compression techniques for cyberattack classification by comparing two dimensionality reduction approaches: Principal Component Analysis (PCA) and Linear Predictive Coding (LPC).
Finite-Iteration Local Dynamics and Warm Starts for Alternating Power Iteration in Spiked Tensor PCA
Announce Type: cross Abstract: We study simultaneous alternating power iteration for fixed-order asymmetric rank-one spiked tensor models. Our main contribution is a finite-iteration local theory that is independent of any particular initialization. Once the iterates enter a sufficiently small neighborhood of the planted rank-one direction, their error decomposes into a geometrically decaying transient and an intrinsic noise floor caused by fixed orthogonal noise contractions at the planted...
RPCASSM: Robust PCA State Space Model For Infrared Small Target Detection
arXiv:2606.01689v1 Announce Type: new Abstract: The detection and segmentation of infrared small targets have important application significance in the fields of surveillance and security, maritime rescue and so on. Due to the low occupancy of these targets in long-distance imaging, the mainstream visual state space model is inefficient and difficult to accurately model the target edge. The existing infrared state space models do not deviate from the mainstream visual state space structure...
Nonlinear Factor Decomposition via Kolmogorov-Arnold Networks: A Spectral Approach to Asset Return Analysis
arXiv:2603.28257v2 Announce Type: replace-cross Abstract: KAN-PCA is an autoencoder that uses a KAN as encoder and a linear map as decoder. It generalizes classical PCA by replacing linear projections with learned B-spline functions on each edge. The motivation is to capture more variance than classical PCA, which becomes inefficient during market crises when the linear assumption breaks down and correlations between assets change dramatically.
DropSynth-Gold: Golden Gate Assembly in Emulsions Extends Multiplexed Gene Libraries to Greater Lengths
The ability to synthesize longer genes at scale remains a central challenge in multiplexed gene synthesis. DropSynth is a pooled gene synthesis platform that enables highly multiplexed, compartmentalized assembly from microarray-derived oligonucleotides, but current implementations rely on polymerase cycling assembly (PCA), which constrains fragment number, construct length, and assembly fidelity. Here we present DropSynth-Gold, an evolution of the DropSynth platform that replaces PCA with...
A Robust Optimization Approach to Sparse Principal Component Analysis
arXiv:2606.03553v1 Announce Type: cross Abstract: While principal component analysis (PCA) is a fundamental tool for dimensionality reduction, its dense representations make it ill-suited for high-dimensional data. Existing methods address this by promoting sparsity through explicit $\ell_1$-penalties, but these are not obvious to tune due to the unsupervised nature of the task. In contrast, we propose Adversarial PCA (AdvPCA), which leverages robust optimization to achieve sparsity by...