منابع مشابه
Deep nets for local manifold learning
The problem of extending a function f defined on a training data C on an unknown manifold X to the entire manifold and a tubular neighborhood of this manifold is considered in this paper. For X embedded in a high dimensional ambient Euclidean space R, a deep learning algorithm is developed for finding a local coordinate system for the manifold without eigen–decomposition, which reduces the prob...
متن کاملLocal Smoothing for Manifold Learning
We propose methods for outlier handling and noise reduction using weighted local linear smoothing for a set of noisy points sampled from a nonlinear manifold. The methods can be used by manifold learning methods such as Isomap, LLE and LTSA as a preprocessing step to obtain a more accurate reconstruction of the underlying nonlinear manifolds. Weighted PCA is used as a building block for our met...
متن کاملThe Local Dimension of Deep Manifold
Based on our observation that there exists a dramatic drop for the singular values of the fully connected layers or a single feature map of the convolutional layer, and that the dimension of the concatenated feature vector almost equals the summation of the dimension on each feature map, we propose a singular value decomposition (SVD) based approach to estimate the dimension of the deep manifol...
متن کاملLocal Linear Smoothing for Nonlinear Manifold Learning
In this paper, we develop methods for outlier removal and noise reduction based on weighted local linear smoothing for a set of noisy points sampled from a nonlinear manifold. The methods can be used by manifold learning methods such as Isomap, LLE and LTSA as a preprocessing procedure so as to obtain a more accurate reconstruction of the underlying nonlinear manifolds. Weighted principal compo...
متن کاملNon-Local Manifold Tangent Learning
We claim and present arguments to the effect that a large class of manifold learning algorithms that are essentially local and can be framed as kernel learning algorithms will suffer from the curse of dimensionality, at the dimension of the true underlying manifold. This observation suggests to explore non-local manifold learning algorithms which attempt to discover shared structure in the tang...
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: Frontiers in Applied Mathematics and Statistics
سال: 2018
ISSN: 2297-4687
DOI: 10.3389/fams.2018.00012