منابع مشابه
A Principal Component Analysis for Trees
The active field of Functional Data Analysis (about understanding the variation in a set of curves) has been recently extended to Object Oriented Data Analysis, which considers populations of more general objects. A particularly challenging extension of this set of ideas is to populations of treestructured objects. We develop an analog of Principal Component Analysis for trees, based on the not...
متن کاملDimension reduction in principal component analysis for trees
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas to the more general space of rooted and labeled trees. We re-define concepts such as tree-line and forward principal component tree-line for this more genera...
متن کاملPrincipal Component Projection Without Principal Component Analysis
We show how to efficiently project a vector onto the top principal components of a matrix, without explicitly computing these components. Specifically, we introduce an iterative algorithm that provably computes the projection using few calls to any black-box routine for ridge regression. By avoiding explicit principal component analysis (PCA), our algorithm is the first with no runtime dependen...
متن کاملA Randomized Algorithm for Principal Component Analysis
Principal component analysis (PCA) requires the computation of a low-rank approximation to a matrix containing the data being analyzed. In many applications of PCA, the best possible accuracy of any rank-deficient approximation is at most a few digits (measured in the spectral norm, relative to the spectral norm of the matrix being approximated). In such circumstances, existing efficient algori...
متن کاملCompression of Breast Cancer Images By Principal Component Analysis
The principle of dimensionality reduction with PCA is the representation of the dataset ‘X’in terms of eigenvectors ei ∈ RN of its covariance matrix. The eigenvectors oriented in the direction with the maximum variance of X in RN carry the most relevant information of X. These eigenvectors are called principal components [8]. Ass...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Applied Statistics
سال: 2009
ISSN: 1932-6157
DOI: 10.1214/09-aoas263