Related papers: Resampling Sensitivity of High-Dimensional PCA
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…
Principal component analysis (PCA) is arguably the most popular tool in multivariate exploratory data analysis. In this paper, we consider the question of how to handle heterogeneous variables that include continuous, binary, and ordinal.…
We study the Order-$k$ ($k \geq 4$) spiked tensor model for the tensor principal component analysis (PCA) problem: given $N$ i.i.d. observations of a $k$-th order tensor generated from the model $\mathbf{T} = \lambda \cdot v_*^{\otimes k} +…
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…
Principal component analysis (PCA) has well-documented merits for data extraction and dimensionality reduction. PCA deals with a single dataset at a time, and it is challenged when it comes to analyzing multiple datasets. Yet in certain…
In this work, we develop a novel principal component analysis (PCA) for semimartingales by introducing a suitable spectral analysis for the quadratic variation operator. Motivated by high-dimensional complex systems typically found in…
In the current context of data explosion, online techniques that do not require storing all data in memory are indispensable to routinely perform tasks like principal component analysis (PCA). Recursive algorithms that update the PCA with…
Dimensionality reduction algorithms like principal component analysis (PCA) are workhorses of machine learning and neuroscience, but each has well-known limitations. Variants of PCA are simple and interpretable, but not flexible enough to…
STEM XEDS spectrum images can be drastically denoised by application of the principal component analysis (PCA). This paper looks inside the PCA workflow step by step on an example of a complex semiconductor structure consisting of a number…
Machine learning (ML) methods have proved to be a very successful tool in physical sciences, especially when applied to experimental data analysis. Artificial intelligence is particularly good at recognizing patterns in high dimensional…
Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant…
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…
We study the robust principal component analysis (RPCA) problem in a distributed setting. The goal of RPCA is to find an underlying low-rank estimation for a raw data matrix when the data matrix is subject to the corruption of gross sparse…
Principal component analysis (PCA) is a tool to capture factors that explain variation in data. Across domains, data are now collected across multiple contexts (for example, individuals with different diseases, cells of different types, or…
Probabilistic principal component analysis (PPCA) is a probabilistic reformulation of principal component analysis (PCA), under the framework of a Gaussian latent variable model. To improve the robustness of PPCA, it has been proposed to…
The high-dimensional feature space of the hyperspectral imagery poses major challenges to the processing and analysis of the hyperspectral data sets. In such a case, dimensionality reduction is necessary to decrease the computational…
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…
Many have suggested a bootstrap procedure for estimating the sampling variability of principal component analysis (PCA) results. However, when the number of measurements per subject ($p$) is much larger than the number of subjects ($n$),…
Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…
Factor models are a class of powerful statistical models that have been widely used to deal with dependent measurements that arise frequently from various applications from genomics and neuroscience to economics and finance. As data are…