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Functional binary datasets occur frequently in real practice, whereas discrete characteristics of the data can bring challenges to model estimation. In this paper, we propose a sparse logistic functional principal component analysis…
Due to advances in sensors, growing large and complex medical image data have the ability to visualize the pathological change in the cellular or even the molecular level or anatomical changes in tissues and organs. As a consequence, the…
In light of the rapidly growing large-scale data in federated ecosystems, the traditional principal component analysis (PCA) is often not applicable due to privacy protection considerations and large computational burden. Algorithms were…
Multi-sensor data that track system operating behaviors are widely available nowadays from various engineering systems. Measurements from each sensor over time form a curve and can be viewed as functional data. Clustering of these…
Pre-training over mixtured multi-task, multi-domain, and multi-modal data remains an open challenge in vision perception pre-training. In this paper, we propose GPPF, a General Perception Pre-training Framework, that pre-trains a task-level…
Integrative analysis of multivariate functional time series (MFTS) is both critical and challenging across many scientific domains. Such data often exhibit complex multi-way dependencies arising from within-curve structures, temporal…
The Theory of Functional Connections (TFC) is a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The functionals derived from this method, called \emph{constrained expressions},…
Data integration, or the strategic analysis of multiple sources of data simultaneously, can often lead to discoveries that may be hidden in individualistic analyses of a single data source. We develop a new unsupervised data integration…
This work aims at performing Functional Principal Components Analysis (FPCA) with Horvitz-Thompson estimators when the observations are curves collected with survey sampling techniques. One important motivation for this study is that FPCA…
The standard approach to modeling the human brain as a complex system is with a network, where the basic unit of interaction is a pairwise link between two brain regions. While powerful, this approach is limited by the inability to assess…
This paper investigates the intrinsic group structures within the framework of large-dimensional approximate factor models, which portrays homogeneous effects of the common factors on the individuals that fall into the same group. To this…
Phylogenetic analysis of DNA or other data commonly gives rise to a collection or sample of inferred evolutionary trees. Principal Components Analysis (PCA) cannot be applied directly to collections of trees since the space of evolutionary…
The positioning of this research falls within the scalar-on-function classification literature, a field of significant interest across various domains, particularly in statistics, mathematics, and computer science. This study introduces an…
Principal component analysis (PCA) is a popular dimension reduction technique for vector data. Factored PCA (FPCA) is a probabilistic extension of PCA for matrix data, which can substantially reduce the number of parameters in PCA while…
Spectral clustering has emerged as one of the most effective clustering algorithms due to its superior performance. However, most existing models are designed for centralized settings, rendering them inapplicable in modern decentralized…
Neuronal activity in the brain generates synchronous oscillations of the Local Field Potential (LFP). The traditional analyses of the LFPs are based on decomposing the signal into simpler components, such as sinusoidal harmonics. However, a…
The characteristics (or numerical patterns) of a feature vector in the transform domain of a perturbation model differ significantly from those of its corresponding feature vector in the input domain. These differences - caused by the…
The estimation of time-varying networks for functional Magnetic Resonance Imaging (fMRI) data sets is of increasing importance and interest. In this work, we formulate the problem in a high-dimensional time series framework and introduce a…
Countries across the globe have been pushing strict regulations on the protection of personal or private data collected. The traditional centralized machine learning method, where data is collected from end-users or IoT devices, so that it…
We propose a novel two-phase approach to functional network estimation of multi-subject functional Magnetic Resonance Imaging (fMRI) data, which applies model-based image segmentation to determine a group-representative connectivity map. In…