相关论文: Principal arc analysis on direct product manifolds

In this paper we analyze approximate methods for undertaking a principal components analysis (PCA) on large data sets. PCA is a classical dimension reduction method that involves the projection of the data onto the subspace spanned by the…

Nowadays many real-world datasets can be considered as functional, in the sense that the processes which generate them are continuous. A fundamental property of this type of data is that in theory they belong to an infinite-dimensional…

Principal Component Analysis (PCA) is a widely used technique in exploratory data analysis, visualization, and data preprocessing, leveraging the concept of variance to identify key dimensions in datasets. In this study, we focus on the…

Analyzing high-dimensional data presents challenges due to the "curse of dimensionality'', making computations intensive. Dimension reduction techniques, categorized as linear or non-linear, simplify such data. Non-linear methods are…

We address shortcomings of principal component analysis (PCA) for visualizing high-dimensional data lying on a nonlinear low-dimensional manifold via two-dimensional scatterplots, focusing on a fossil teeth dataset from the early mammalian…

Principal component analysis (PCA) is a classical method for dimensionality reduction based on extracting the dominant eigenvectors of the sample covariance matrix. However, PCA is well known to behave poorly in the ``large $p$, small $n$''…

Principal manifolds serve as useful tool for many practical applications. These manifolds are defined as lines or surfaces passing through "the middle" of data distribution. We propose an algorithm for fast construction of grid…

Constructing an efficient parameterization of a large, noisy data set of points lying close to a smooth manifold in high dimension remains a fundamental problem. One approach consists in recovering a local parameterization using the local…

A general asymptotic framework is developed for studying consis- tency properties of principal component analysis (PCA). Our frame- work includes several previously studied domains of asymptotics as special cases and allows one to…

Principal Component Analysis (PCA) is the most common nonparametric method for estimating the volatility structure of Gaussian interest rate models. One major difficulty in the estimation of these models is the fact that forward rate curves…

Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not…

This paper defines fair principal component analysis (PCA) as minimizing the maximum mean discrepancy (MMD) between dimensionality-reduced conditional distributions of different protected classes. The incorporation of MMD naturally leads to…

Distributed principal component analysis (PCA) produces node-level estimates of both a mean vector and a principal subspace. Robustly aggregating these heterogeneous objects requires a relative scale between mean error and subspace error.…

Remote sensing observations, products and simulations are fundamental sources of information to monitor our planet and its climate variability. Uncovering the main modes of spatial and temporal variability in Earth data is essential to…

In many scientific disciplines, the features of interest cannot be observed directly, so must instead be inferred from observed behaviour. Latent variable analyses are increasingly employed to systematise these inferences, and Principal…

We study the Principal Component Analysis (PCA) problem in the distributed and streaming models of computation. Given a matrix $A \in R^{m \times n},$ a rank parameter $k < rank(A)$, and an accuracy parameter $0 < \epsilon < 1$, we want to…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Object Oriented Data Analysis is a new area in statistics that studies populations of general data objects. In this article we consider populations of tree-structured objects as our focus of interest. We develop improved analysis tools for…

We propose a stable version of Principal Component Analysis (PCA) in the general framework of a separable Hilbert space. It consists in interpreting the projection on the first eigenvectors as a step function applied to the spectrum of the…

Many pattern recognition methods rely on statistical information from centered data, with the eigenanalysis of an empirical central moment, such as the covariance matrix in principal component analysis (PCA), as well as partial least…