Related papers: Localized Functional Principal Component Analysis …
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…
Principal Component Analysis (PCA) is a foundational technique in machine learning for dimensionality reduction of high-dimensional datasets. However, PCA could lead to biased outcomes that disadvantage certain subgroups of the underlying…
This paper focuses on the analysis of spatially correlated functional data. The between-curve correlation is modeled by correlating functional principal component scores of the functional data. We propose a Spatial Principal Analysis by…
Principal components analysis (PCA) is a well-known technique for approximating a tabular data set by a low rank matrix. Here, we extend the idea of PCA to handle arbitrary data sets consisting of numerical, Boolean, categorical, ordinal,…
Multilinear Principal Component Analysis (MPCA) is a widely utilized method for the dimension reduction of tensor data. However, the integration of MPCA into federated learning remains unexplored in existing research. To tackle this gap,…
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction that is useful for various data science problems. However, many applications involve heterogeneous data that varies in quality due to noise…
Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…
In the era of big data, reducing data dimensionality is critical in many areas of science. Widely used Principal Component Analysis (PCA) addresses this problem by computing a low dimensional data embedding that maximally explain variance…
Principal component analysis (PCA) is a widely used technique for data analysis and dimension reduction with numerous applications in science and engineering. However, the standard PCA suffers from the fact that the principal components…
Principal component analysis (PCA) is a popular dimension reduction technique often used to visualize high-dimensional data structures. In genomics, this can involve millions of variables, but only tens to hundreds of observations.…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
Dimensionality reduction is critical across various domains of science including neuroscience. Probabilistic Principal Component Analysis (PPCA) is a prominent dimensionality reduction method that provides a probabilistic approach unlike…
Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…
Robust principal component analysis (RPCA) is a widely used technique for recovering low-rank structure from matrices with missing entries and sparse, possibly large-magnitude corruptions. Although numerous algorithms achieve accurate point…
For covariance test in functional data analysis, existing methods are developed only for fully observed curves, whereas in practice, trajectories are typically observed discretely and with noise. To bridge this gap, we employ a…
Sparse principal component analysis addresses the problem of finding a linear combination of the variables in a given data set with a sparse coefficients vector that maximizes the variability of the data. This model enhances the ability to…
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…
Sparse principal component analysis (SPCA) addresses the poor interpretability and variable redundancy often encountered by principal component analysis (PCA) in high-dimensional data. However, SPCA typically imposes uniform penalties on…
Principal component analysis (PCA) is traditionally implemented through a covariance or kernel matrix, leading-eigenvector extraction, and hard rank-$k$ projection. These steps can be computationally costly in high-dimensional and…
Principal component analysis (PCA) is a well-established tool in machine learning and data processing. The principal axes in PCA were shown to be equivalent to the maximum marginal likelihood estimator of the factor loading matrix in a…