Review of clustering methods for functional data across various fields.
problem Identify heterogeneous morphological patterns in continuous functions.
method Comprehensive review and systematic taxonomy of existing methods.
result Proposes a new taxonomy linking functional data clustering to conventional multivariate methods.
RSF models censored functional data for better survival analysis.
problem Modeling survival trajectories with censored data.
method Random Survival Forest for Censored Functional Data (RSF).
result Good performance in predicting survival variables.
FDApy simplifies analysis of functional data in Python.
problem Analysis of irregularly sampled functional data.
method Implementation of tools for representation, dimension reduction, and dataset generation.
result Efficient analysis of functional data, including irregularly sampled data.
New neural network models for complex functional data analysis.
problem Complex relations between functional predictors and responses.
method Function-on-Function regression models using neural networks with continuous hidden layers.
result Demonstrated power and flexibility in handling complex functional models.
Proposes a neural network autoencoder for smoothing and representation learning of functional data.
problem Lack of sufficient nonlinear representations in existing methods for functional data analysis.
method Develops a neural network autoencoder architecture to process functional data directly, learning both smoothing and representation.
result Outperforms traditional methods in prediction, classification, and computational efficiency.
A new method for clustering functional data outperforms existing methods.
problem Clustering heterogeneous functional linear regression data.
method funWeightClust, a family of parsimonious models based on cluster weighted models.
result funWeightClust outperforms existing methods in simulations and real-world traffic analysis.
Proposes a deep neural network for multi-dimensional functional data classification.
problem Classifying multi-dimensional functional data with non-Gaussian distributions.
method Trains a deep neural network on the principle components of the training data.
result FDNN achieves minimax optimality when log density ratio has a locally connected modular structure.
New neural network models for functional data.
problem Handling non-linear functional data.
method Functional Direct Neural Network (FDNN) and Functional Basis Neural Network (FBNN) with gradient-based optimization.
result Demonstrated effectiveness in complex functional models.
Two new methods improve forecasting of functional time series data.
problem Forecasting of functional time-dependent data.
method Functional Singular Spectrum Analysis (FSFA) based forecasting methods.
result Our methods outperform existing algorithms for periodic stochastic processes.
Novel method converts time series data into functional data for high dimensional classification.
problem Small sample size problem in high dimensional time series data.
method Classwise Functional Principal Component Analysis (PCA) followed by Bayesian linear classifier.
result Demonstrated efficacy on synthetic and real data sets.
Enhances Random Forest for imbalanced functional data classification.
problem Challenges in classifying imbalanced functional data.
method Functional Random Forest with Adaptive Cost-Sensitive Splitting (FRF-ACS).
result Significantly improves minority class recall and predictive performance.
This paper connects functional data analysis with machine learning techniques.
problem Lack of theoretical analysis for functional depths.
method Viewing functional depths as kernel mean embeddings in machine learning.
result Facilitates answers to open questions about functional depths.
SFM generates smooth functional data without exposing real data.
problem Challenges in statistical analysis of functional data.
method Copula framework and smooth flow construction.
result SFM produces high-quality synthetic functional data.
Geometric approach improves functional outlier detection.
problem Detecting outliers in functional data sets.
method Developed a geometric perspective on functional manifold for outlier detection.
result Improved understanding and differentiation of outliers.
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of reproducing kernel Hilbert space theory to learn from such functional data. Basi…
Generative models learn distributions of continuous functions.
problem Training generative models on discretized grids limits model size and data type.
method Parameterize data points by continuous functions, learn distributions over these functions.
result Models can learn rich distributions of functions independently of data type and resolution.
New model for network analysis using functional data.
problem Existing network models treat nodes as functions, but this paper introduces functional edges.
method Transform adjacency matrix into functional adjacency tensor, apply Tucker decomposition, regularize basis matrices, and solve tensor completion problem.
result The model effectively captures community structure and handles irregular functional edge data.
The paper explores transferring functions from one data space to another.
problem Approximating a function on a new data set using a learned function from an old data set.
method Transfer learning from one data space to another, focusing on subsets of the target data space.
result Local smoothness of the function and its lifting are related.
New functional ME models for predicting heterogeneous functional data.
problem Statistical analysis of heterogeneous functional data for prediction.
method Functional Mixtures-of-Experts (FME) models with Lasso-like regularization for sparsity.
result Accurate capture of complex nonlinear relationships and clustering of heterogeneous regression data.
Efficiently analyzes multidimensional functional data using separable basis functions.
problem Curse of dimensionality in traditional functional data analysis.
method Marginal product basis systems for multidimensional data, tensor decomposition, differential operator-based penalties.
result Efficient estimation of multidimensional functional data representations.
A new algorithm for learning from functional data across multiple machines.
problem Handling large-scale functional data analysis.
method Distributed Gradient Descent Functional Learning (DGDFL) algorithm.
result First theoretical understanding and optimal learning rates for DGDFL.
Diffusion Maps improves on Functional PCA for non-linear functional data.
problem Functional PCA's linear manifold assumption fails for non-linear functional data.
method Extends Diffusion Maps to functional data and compares it to Functional PCA.
result Diffusion Maps outperforms Functional PCA in non-linear functional data analysis.
This paper presents a general notion of Mahalanobis distance for functional data that extends the classical multivariate concept to situations where the observed data are points belonging to curves generated by a stochastic process. More precisely, a new semi-distance for functional observations that generalize the usu…
A new clustering method for functional data using skewed distributions.
problem Clustering functional data with skewed distributions.
method Mixtures of functional linear regression models and three skewed multivariate distributions (variance-gamma, skew-t, normal-inverse Gaussian).
result The proposed method funWeightClustSkew performs well on simulated and real data.
Regularized MFPCA smooths multivariate functional data for clearer patterns.
problem Challenges in controlling roughness of multivariate functional PCs.
method ReMFPCA incorporates a roughness penalty in a penalized framework to smooth PCs.
result Smoothed multivariate functional PCs reveal clearer patterns.
Robust deep neural networks estimate multi-dimensional functional data robustly.
problem Estimating location function from multi-dimensional functional data robustly.
method Deep neural networks with ReLU activation, robust to outliers and model misspecification.
result Uniform convergence rates for robust deep neural network estimators.
A novel online framework for analyzing multidimensional functional data.
problem Analysis of multidimensional functional data streams poses significant challenges.
method Online functional principal component analysis using tensor product splines on a Stiefel manifold with Riemannian stochastic gradient descent.
result Efficient and scalable modeling of multidimensional functional data.
Paper proposes FVC for functional data classification.
problem Challenges in high-dimensional temporal data.
method Ensemble learning of diverse functional representations.
result FVC enhances predictive accuracy over individual models.
Neural networks improve functional data classification.
problem Lack of effective classification methods for functional data.
method Extended deep learning methodologies to functional data for classification.
result Demonstrated superior performance in spectrographic data classification.
Paper stabilizes persistent homology rank functions for statistical inference.
problem Stability issues in persistent homology rank functions.
method Derive stability results for rank functions under FDA metrics.
result Rank functions stabilize, improving statistical inference.
Enhances clustering for functional data, robust to outliers.
problem Challenges of clustering infinite-dimensional functional data and outlier sensitivity.
method Extends OCLUST algorithm to handle functional data, trimming outliers.
result Strong performance in clustering and outlier identification on simulated and real-world datasets.
Functional data analysis involves data described by regular functions rather than by a finite number of real valued variables. While some robust data analysis methods can be applied directly to the very high dimensional vectors obtained from a fine grid sampling of functional data, all methods benefit from a prior simp…
Bayesian data sketching speeds up inference for large functional data.
problem Slow posterior computations in Bayesian varying coefficient models for large data.
method Compress functional response and predictor matrix using random linear transformation.
result Fully model-based Bayesian inference on compressed data.
Generative method avoids function estimation for data generation.
problem Challenges in function estimation for generative models.
method Deterministic point transport with gradient descent.
result Data generation possible without function estimation.
New methods for functional data analysis improve manifold methods for continuous data.
problem Challenges in evaluating embeddings for functional data.
method Transfer manifold methods from tabular and image data to functional data, define a theoretical framework, and propose nuanced evaluation strategies.
result Manifold methods can be successfully applied to functional data, but careful evaluation is needed.
Proposes FunNoL for better curve classification and reconstruction in multivariate functional data.
problem Linear methods fail to capture nonlinear structures in multivariate functional data.
method Functional nonlinear learning (FunNoL) method using nonlinear mapping.
result FunNoL outperforms FPCA in curve classification and reconstruction, especially in multivariate settings.
A machine learning method selects optimal orthonormal bases for functional data analysis.
problem Lack of formal criteria for choosing initial orthonormal bases in functional data methods.
method Proposes a machine learning algorithm to learn and place knots for efficient orthogonal spline bases (splinets).
result Demonstrates efficiency, especially for sparse functional data and complex physical systems.
Study reveals Data Shapley's inconsistent performance in data selection tasks.
problem Inconsistency of Data Shapley's performance in data selection across different settings.
method Hypothesis testing framework and identification of utility functions.
result Data Shapley's performance is no better than random selection without specific constraints.
FNNs detect EEG signals without position dependence.
problem Detecting EEG signals without position dependence.
method Shift invariant functional neural networks (FNNs) using FDA methods.
result FNNs outperform FDA benchmarks in EEG classification.
A new method for functional data classification using supervised manifold learning.
problem Improving classification of functional data.
method Supervised manifold learning approach considering label information.
result The proposed method achieves highly competitive performance compared to existing methods.
Detecting anomalies in multivariate functional data using Bayesian nonparametric methods.
problem Detecting anomalies in functional data.
method Bayesian nonparametric approach with infinite mixture of multi-output Gaussian processes.
result Anomalous observations assigned to small mixture components.
In many applications, input data are sampled functions taking their values in infinite dimensional spaces rather than standard vectors. This fact has complex consequences on data analysis algorithms that motivate modifications of them. In fact most of the traditional data analysis tools for regression, classification a…
Generative models for function-valued data in infinite dimensions.
problem Lack of semantics relating discretized data to underlying functional forms.
method Generalized diffusion models to function space, using Gaussian measures on Hilbert spaces.
result Explicit specification of function space allows unconditional and conditional generation of function-valued data.
funLOCI identifies clusters in functional data.
problem Identifying similar behavior in functional data.
method Divisive hierarchical clustering with additive model.
result funLOCI reduces the number of local clusters.
New simulations advise caution in choosing principal components for multivariate functional data.
problem Inaccurate selection of principal components in multivariate functional data.
method Extensive simulations investigating the reliability of percentage of variance explained thresholds.
result Conventional threshold methods may fail to accurately explain overall variance in multivariate functional data.
Deep networks adapt to function regularity and data distribution.
problem Understanding deep learning's adaptability to function regularity and data distribution.
method Developed nonparametric approximation and estimation theories for a broad class of functions using deep ReLU networks.
result Deep neural networks are adaptive to different regularity of functions and nonuniform data distributions.
The paper tackles noisy functional data by exploring a multivariate perspective.
problem Noisy functional data measured on discrete points.
method Factor model and principal components analysis.
result The latent signal can be accurately estimated using multivariate methods.
Enhances functional classifier performance with new tree-based methods and unbiased feature importance assessment.
problem Challenges of high-dimensional functional data and biased feature importance assessment.
method Augmented functional classification trees and random forests with ad-hoc conditional permutations for unbiased feature importance.
result Significant enhancement in predictive power of functional classifiers through new feature importance assessment.