Related papers: Filtrated Common Functional Principal Components f…
We propose localized functional principal component analysis (LFPCA), looking for orthogonal basis functions with localized support regions that explain most of the variability of a random process. The LFPCA is formulated as a convex…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
A new classification method for functional data is proposed in this paper. This work is motivated by the need to identify features that discriminate between neurological conditions on which local field potentials (LFPs) were recorded.…
Local field potentials (LFPs) are routinely measured experimentally in brain tissue, and exhibit strong low-pass frequency filtering properties, with high frequencies (such as action potentials) being visible only at very short distances…
Functional time series (FTS) data have become increasingly available in real-world applications. Research on such data typically focuses on two objectives: curve reconstruction and forecasting, both of which require efficient dimension…
Multivariate Functional Principal Component Analysis (MFPCA) is a valuable tool for exploring relationships and identifying shared patterns of variation in multivariate functional data. However, controlling the roughness of the extracted…
The first recording of electrical potential from brain activity was reported already in 1875, but still the interpretation of the signal is debated. To take full advantage of the new generation of microelectrodes with hundreds or even…
Functional principal component analysis (FPCA) is a widely used technique in functional data analysis for identifying the primary sources of variation in a sample of random curves. The eigenfunctions obtained from standard FPCA typically…
A common class of methods for analyzing of multivariate time series, stationary and nonstationary, decomposes the observed series into latent sources. Methods such as principal compoment analysis (PCA), independent component analysis (ICA)…
The advance of modern sensor technologies enables collection of multi-stream longitudinal data where multiple signals from different units are collected in real-time. In this article, we present a non-parametric approach to predict the…
The literature on high-dimensional functional data focuses on either the dependence over time or the correlation among functional variables. In this paper, we propose a factor-guided functional principal component analysis (FaFPCA) method…
Many studies collect functional data from multiple subjects that have both multilevel and multivariate structures. An example of such data comes from popular neuroscience experiments where participants' brain activity is recorded using…
The local field potential (LFP) is as a measure of the combined activity of neurons within a region of brain tissue. While biophysical modeling schemes for LFP in cortical circuits are well established, there is a paramount lack of…
The ongoing transition from a linear (produce-use-dispose) to a circular economy poses significant challenges to current state-of-the-art information and communication technologies. In particular, the derivation of integrated, high-level…
We introduce Adaptive Functional Principal Component Analysis, a novel method to capture directions of variation in functional data that exhibit sharp changes in smoothness. We first propose a new adaptive scatterplot smoothing technique…
When functional data manifest amplitude and phase variations, a commonly-employed framework for analyzing them is to take away the phase variation through a function alignment and then to apply standard tools to the aligned functions. A…
Functional principal components (FPC's) provide the most important and most extensively used tool for dimension reduction and inference for functional data. The selection of the number, d, of the FPC's to be used in a specific procedure has…
Functional data typically contains amplitude and phase variation. In many data situations, phase variation is treated as a nuisance effect and is removed during preprocessing, although it may contain valuable information. In this note, we…
In this paper we review existing methods for robust functional principal component analysis (FPCA) and propose a new method for FPCA that can be applied to longitudinal data where only a few observations per trajectory are available. This…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…