Related papers: Functional Diffusion Maps
The continuous advances in data collection and storage techniques allow us to observe and record real-life processes in great detail. Examples include financial transaction data, fMRI images, satellite photos, earths pollution distribution…
We introduce the Linearized Diffusion Map (LDM), a novel linear dimensionality reduction method constructed via a linear approximation of the diffusion-map kernel. LDM integrates the geometric intuition of diffusion-based nonlinear methods…
Despite their widespread success, the application of deep neural networks to functional data remains scarce today. The infinite dimensionality of functional data means standard learning algorithms can be applied only after appropriate…
The analysis of data sets arising from multiple sensors has drawn significant research attention over the years. Traditional methods, including kernel-based methods, are typically incapable of capturing nonlinear geometric structures. We…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
Principal Component Analysis (PCA) is a fundamental data preprocessing tool in the world of machine learning. While PCA is often thought of as a dimensionality reduction method, the purpose of PCA is actually two-fold: dimension reduction…
The problem of complex data analysis is a central topic of modern statistical science and learning systems and is becoming of broader interest with the increasing prevalence of high-dimensional data. The challenge is to develop statistical…
We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on…
Methodologies for multidimensionality reduction aim at discovering low-dimensional manifolds where data ranges. Principal Component Analysis (PCA) is very effective if data have linear structure. But fails in identifying a possible…
Functional data are typically modeled as sample paths of smooth stochastic processes in order to mitigate the fact that they are often observed discretely and noisily, occasionally irregularly and sparsely. The smoothness assumption is…
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…
In the last few decades, building regression models for non-scalar variables, including time series, text, image, and video, has attracted increasing interests of researchers from the data analytic community. In this paper, we focus on a…
Functional data analysis is becoming increasingly popular to study data from real-valued random functions. Nevertheless, there is a lack of multiple testing procedures for such data. These are particularly important in factorial designs to…
Samples of curves, or functional data, usually present phase variability in addition to amplitude variability. Existing functional regression methods do not handle phase variability in an efficient way. In this paper we propose a functional…
In this paper, we show how convolutional neural networks (CNN) can be used in regression and classification learning problems of noisy and non-noisy functional data. The main idea is to transform the functional data into a 28 by 28 image.…
Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. The complexity of big data often makes dimension reduction techniques necessary before conducting…
The rise in data has led to the need for dimension reduction techniques, especially in the area of non-scalar variables, including time series, natural language processing, and computer vision. In this paper, we specifically investigate…
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
Deep functional maps have recently emerged as a powerful tool for solving non-rigid shape correspondence tasks. Methods that use this approach combine the power and flexibility of the functional map framework, with data-driven learning for…