.png){kind=icon}
返回
Efficient manifold approximation with spherelets
.png){kind=icon}
PRE
AI
DOI：10.1111/rssb.12508.png)
.png){kind=icon}
原文求助.png){kind=icon}
分享.png){kind=icon}
收藏
摘要
En 中文
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich literature on approximating the unknown manifold, and on exploiting such approximations in clustering, data compression, and prediction. Most of the literature relies on linear or locally linear approximations. In this article, we propose a simple and general alternative, which instead uses spheres, an approach we refer to as spherelets. We develop spherical principal components analysis (SPCA), and provide theory on the convergence rate for global and local SPCA, while showing that spherelets can provide lower covering numbers and mean squared errors for many manifolds. Results relative to state-of-the-art competitors show gains in ability to accurately approximate manifolds with fewer components. Unlike most competitors, which simply output lower-dimensional features, our approach projects data onto the estimated manifold to produce fitted values that can be used for model assessment and cross validation. The methods are illustrated with applications to multiple data sets.
Keyword:
curvature
dimensionality reduction
manifold learning
spherical principal component analysis
期刊
J
IF:
3.6
论文数:
1.5K
被引数:
3.2W
机构
引用论文
.png){kind=icon}
分享收藏Antimalarial Flavonoid-Glycoside from Acacia pennata with Inhibitory Potential Against PfDHFR-TS: An In-silico Study抗疟疾黄酮苷（来源于Acacia pennata），对PfDHFR-TS具有抑制潜力：一项计算机模拟研究
OAAI
OAAI分享收藏
查看更多内容