Deep Learning With Functional Inputs

Thind, Barinder; Multani, Kevin; Cao, Jiguo

doi:10.1080/10618600.2022.2097914

Cited by 12 publications

(1 citation statement)

References 37 publications

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“…In addition to these two main strategies, many researchers have explored the classification of functional data from other perspectives. For example Fan et al [7] proposed an algorithm for functional data classification based on the random forest algorithm; Rossi and Villa [8] combined the kernel method with the support vector machine algorithm to classify functional data; Thind et al [9] based on feedforward neural network to classify functional data; Fuchs et al [10] Classification of functional data based on nearest neighbor classification method; Rossi et al [11] Classification of functional data based on multilayer perceptron machine algorithm; Ke Chien-Kun's [12] classification model for Riemannian manifold functional data; Vommi Amukta Malyada et al [13] Fuzzy KNN Hybrid Filtering and Encapsulated Feature Selection Classification based on Bonferroni Mean.…”

Section: Introductionmentioning

confidence: 99%

A Functional Data Classification Model Utilizing Functional Mahalanobis Distance and Regenerative Kernel Methods

2023

jeis

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The classification of functional data is an important research direction in modern data mining. In this paper, we propose a similarity measurement method for functional data based on functional Mahalanobis distance and regenerative kernel theory, considering the scenario where the predictor variable is a random function and the response variable is a categorical scalar. This method is then applied to functional kernel principal component analysis. During the classification phase, classic algorithms such as support vector machines and random forests can be combined to accomplish the task of classifying functional data. In empirical analysis, compared to the regenerative kernel based on Euclidean distance and the Euclidean distance regenerative kernel based on B-spline basis functions, the proposed method achieves better classification results. Furthermore, this similarity measurement can also be utilized in other machine learning algorithms based on regenerative kernel theory, thereby developing corresponding analysis methods for functional data.

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Section: Introductionmentioning

confidence: 99%

A Functional Data Classification Model Utilizing Functional Mahalanobis Distance and Regenerative Kernel Methods

2023

jeis

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Functional Data Analysis: An Introduction and Recent Developments

Gertheiss,

Rügamer,

Liew

et al. 2024

Biometrical J

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Functional data analysis (FDA) is a statistical framework that allows for the analysis of curves, images, or functions on higher dimensional domains. The goals of FDA, such as descriptive analyses, classification, and regression, are generally the same as for statistical analyses of scalar‐valued or multivariate data, but FDA brings additional challenges due to the high‐ and infinite dimensionality of observations and parameters, respectively. This paper provides an introduction to FDA, including a description of the most common statistical analysis techniques, their respective software implementations, and some recent developments in the field. The paper covers fundamental concepts such as descriptives and outliers, smoothing, amplitude and phase variation, and functional principal component analysis. It also discusses functional regression, statistical inference with functional data, functional classification and clustering, and machine learning approaches for functional data analysis. The methods discussed in this paper are widely applicable in fields such as medicine, biophysics, neuroscience, and chemistry and are increasingly relevant due to the widespread use of technologies that allow for the collection of functional data. Sparse functional data methods are also relevant for longitudinal data analysis. All presented methods are demonstrated using available software in R by analyzing a dataset on human motion and motor control. To facilitate the understanding of the methods, their implementation, and hands‐on application, the code for these practical examples is made available through a code and data supplement and on GitHub.

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Functional data analysis using deep neural networks

Wang,

Zhang,

Cao

et al. 2024

WIREs Computational Stats

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Functional data analysis is an evolving field focused on analyzing data that reveals insights into curves, surfaces, or entities within a continuous domain. This type of data is typically distinguished by the inherent dependence and smoothness observed within each data curve. Traditional functional data analysis approaches have predominantly relied on linear models, which, while foundational, often fall short in capturing the intricate, nonlinear relationships within the data. This paper seeks to bridge this gap by reviewing the integration of deep neural networks into functional data analysis. Deep neural networks present a transformative approach to navigating these complexities, excelling particularly in high‐dimensional spaces and demonstrating unparalleled flexibility in managing diverse data constructs. This review aims to advance functional data regression, classification, and representation by integrating deep neural networks with functional data analysis, fostering a harmonious and synergistic union between these two fields. The remarkable ability of deep neural networks to adeptly navigate the intricate functional data highlights a wealth of opportunities for ongoing exploration and research across various interdisciplinary areas.This article is categorized under: Data: Types and Structure > Time Series, Stochastic Processes, and Functional Data Statistical Learning and Exploratory Methods of the Data Sciences > Deep Learning Statistical Learning and Exploratory Methods of the Data Sciences > Neural Networks

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Deep Learning With Functional Inputs

Cited by 12 publications

References 37 publications

A Functional Data Classification Model Utilizing Functional Mahalanobis Distance and Regenerative Kernel Methods

A Functional Data Classification Model Utilizing Functional Mahalanobis Distance and Regenerative Kernel Methods

Functional Data Analysis: An Introduction and Recent Developments

Functional data analysis using deep neural networks

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