Related papers: Adaptive Functional Principal Component Analysis
In many applications, we collect independent samples from interconnected populations. These population distributions share some latent structure, so it is advantageous to jointly analyze the samples. One effective way to connect the…
Principal Component Analysis (PCA) is a powerful and popular dimensionality reduction technique. However, due to its linear nature, it often fails to capture the complex underlying structure of real-world data. While Kernel PCA (kPCA)…
We apply principal component analysis, a method frequently used in image processing and unsupervised machine learning, to characterize particle displacements observed in the steady shear flow of amorphous solids. PCA produces a…
When considering functional principal component analysis for sparsely observed longitudinal data that take values on a nonlinear manifold, a major challenge is how to handle the sparse and irregular observations that are commonly…
In this paper, we address the problem of dimension reduction for time series of functional data $(X_t\colon t\in\mathbb{Z})$. Such {\it functional time series} frequently arise, e.g., when a continuous-time process is segmented into some…
Principal Component Analysis (PCA) finds a linear mapping and maximizes the variance of the data which makes PCA sensitive to outliers and may cause wrong eigendirection. In this paper, we propose techniques to solve this problem; we use…
Head-related transfer function (HRTF) plays an important role in the construction of 3D auditory display. This paper presents an individual HRTF modeling method using deep neural networks based on spatial principal component analysis. The…
Forecasting 3D human motion is an important embodiment of fine-grained understanding and cognition of human behavior by artificial agents. Current approaches excessively rely on implicit network modeling of spatiotemporal relationships and…
P-spline models have achieved great popularity both in statistical and in applied research. A possible drawback of P-spline is that they assume a smooth transition of the covariate effect across its whole domain. In some practical…
Distributed algorithms and theories are called for in this era of big data. Under weaker local signal-to-noise ratios, we improve upon the celebrated one-round distributed principal component analysis (PCA) algorithm designed in the spirit…
In recent years, Artificial Intelligence techniques have proved to be very successful when applied to problems in physical sciences. Here we apply an unsupervised Machine Learning (ML) algorithm called Principal Component Analysis (PCA) as…
The Few-Shot Segmentation (FSS) aims to accomplish the novel class segmentation task with a few annotated images. Current FSS research based on meta-learning focus on designing a complex interaction mechanism between the query and support…
We introduce directional regularity, a new definition of anisotropy for multivariate functional data. Instead of taking the conventional view, which determines anisotropy as a notion of smoothness along a dimension, directional regularity…
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…
Decomposing knowledge into interchangeable pieces promises a generalization advantage when there are changes in distribution. A learning agent interacting with its environment is likely to be faced with situations requiring novel…
Slow Feature Analysis (SFA) extracts slowly varying features from a quickly varying input signal. It has been successfully applied to modeling the visual receptive fields of the cortical neurons. Sufficient experimental results in…
The ability to attend to salient regions of a visual scene is an innate and necessary preprocessing step for both biological and engineered systems performing high-level visual tasks (e.g. object detection, tracking, and classification).…
Accurate molecular property prediction (MPP) is a critical step in modern drug development. However, the scarcity of experimental validation data poses a significant challenge to AI-driven research paradigms. Under few-shot learning…
A reduced-rank mixed effects model is developed for robust modeling of sparsely observed paired functional data. In this model, the curves for each functional variable are summarized using a few functional principal components, and the…
We propose a nonparametric method to explicitly model and represent the derivatives of smooth underlying trajectories for longitudinal data. This representation is based on a direct Karhunen--Lo\`eve expansion of the unobserved derivatives…