Functional Principal Component

Functional principal component analysis (FPCA) is a dimensionality reduction technique used to represent complex, high-dimensional functional data (e.g., curves, time series) with a smaller set of uncorrelated principal components, capturing the most significant variations within the data. Current research emphasizes improving FPCA's application in classification tasks, often integrating it with machine learning models like random forests and neural networks (including autoencoders) to enhance predictive power and interpretability. This work is driven by the need for efficient and robust methods to analyze increasingly large and complex functional datasets across diverse fields, leading to improved model accuracy and insights in applications ranging from medical diagnosis to financial modeling.

Papers

August 23, 2024

Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations
Fabrizio Maturo, Annamaria Porreca
Functional Data Analysis Classification Tree Permutation Importance Learning Classifier Functional Principal Component

August 22, 2024

Demystifying Functional Random Forests: Novel Explainability Tools for Model Transparency in High-Dimensional Spaces
Fabrizio Maturo, Annamaria Porreca
Random Forest High Dimensional Space Functional Data Analysis Model Transparency Explainability Tool Functional Principal Component Partial Dependence Plot

February 20, 2024

Multivariate Functional Linear Discriminant Analysis for the Classification of Short Time Series with Missing Data
Rahul Bordoloi, Clémence Réda, Orell Trautmann, Saptarshi Bej, Olaf Wolkenhauer
Classification Code Multiclass Classification Missing Data Discriminant Analysis Multivariate Approach Functional Principal Component

January 17, 2024

Functional Autoencoder for Smoothing and Representation Learning
Sidi Wu, Cédric Beaulac, Jiguo Cao
Representation Learning Neural Network Autoencoder Functional Data Analysis Smoothing Factor Functional Principal Component Nonlinear Representation Functional Learning

January 11, 2024

A new computationally efficient algorithm to solve Feature Selection for Functional Data Classification in high-dimensional spaces
Tobia Boschi, Francesca Bonin, Rodrigo Ordonez-Hurtado, Alessandra Pascale, Jonathan Epperlein
Feature Selection Efficient Algorithm High Dimensional Space Non Functional Property Functional Principal Component

July 10, 2023

Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data
Ziyu Xie, Mahmoud Yaseen, Xu Wu
Deeper Network Bayesian Uncertainty Functional Principal Component Transient Imaging Data Clad Characteristic Inverse UQ

June 14, 2023

Fault Detection in Induction Motors using Functional Dimensionality Reduction Methods
María Barroso, José M. Bossio, Carlos M. Alaíz, Ángela Fernández
Fault Detection Diffusion Map Functional Principal Component Motor Health Monitoring Induction Motor

May 18, 2023

Functional sufficient dimension reduction through information maximization with application to classification
Xinyu Li, Jianjun Xu, Wenquan Cui, Haoyang Cheng
Application Proficiency Functional Regression Information Maximization Functional Principal Component Sufficient Dimension Reduction

May 17, 2023

Extracting a functional representation from a dictionary for non-rigid shape matching
Michele Colombo, Giacomo Boracchi, Simone Melzi
Dense Correspondence French Dictionary Shape Matching Functional Map Non Rigid Shape Functional Principal Component Functional Representation Functional Correspondence

April 27, 2023

Functional Diffusion Maps
María Barroso, Carlos María Alaíz, Ángela Fernández, Jose Luis Torrecilla
Manifold Learning Functional Data Analysis Diffusion Map Functional Principal Component

March 1, 2023

FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs
Vedant Choudhary, Sebastian Jaimungal, Maxime Bergeron
Market Volatility Functional Data Analysis Neural Stochastic Differential Equation Functional Principal Component Statistical Arbitrage High Risk Business Scenario

January 1, 2023

A Functional approach for Two Way Dimension Reduction in Time Series
Aniruddha Rajendra Rao, Haiyan Wang, Chetan Gupta
Time Series Dimension Reduction Functional Data Analysis Functional Principal Component Functional Learning Functional Model

June 22, 2022

Functional Nonlinear Learning
Haixu Wang, Jiguo Cao
Functional Data Analysis Functional Principal Component Functional Learning Functional Data

May 17, 2022

Deep Neural Network Classifier for Multi-dimensional Functional Data
Shuoyang Wang, Guanqun Cao, Zuofeng Shang
Deep Learning Classifier Functional Principal Component Functional Deep Neural Network Functional Data

Functional Principal Component

Papers

Augmented Functional Random Forests: Classifier Construction and Unbiased Functional Principal Components Importance through Ad-Hoc Conditional Permutations

Demystifying Functional Random Forests: Novel Explainability Tools for Model Transparency in High-Dimensional Spaces

Multivariate Functional Linear Discriminant Analysis for the Classification of Short Time Series with Missing Data

Functional Autoencoder for Smoothing and Representation Learning

A new computationally efficient algorithm to solve Feature Selection for Functional Data Classification in high-dimensional spaces

Functional PCA and Deep Neural Networks-based Bayesian Inverse Uncertainty Quantification with Transient Experimental Data

Fault Detection in Induction Motors using Functional Dimensionality Reduction Methods

Functional sufficient dimension reduction through information maximization with application to classification

Extracting a functional representation from a dictionary for non-rigid shape matching

Functional Diffusion Maps

FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs

A Functional approach for Two Way Dimension Reduction in Time Series

Functional Nonlinear Learning

Deep Neural Network Classifier for Multi-dimensional Functional Data