Learning from data with low intrinsic dimension
نویسنده
چکیده
of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Chapter
منابع مشابه
A Scale-Based Approach to Finding Effective Dimensionality in Manifold Learning
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale space viewpoint is the key to our approach enabling us to meet the challenge of noisy data. Our approach finds the effective dimensionality of the data over...
متن کاملNearly Isometric Embedding by Relaxation
Many manifold learning algorithms aim to create embeddings with low or no distortion (isometric). If the data has intrinsic dimension d, it is often impossible to obtain an isometric embedding in d dimensions, but possible in s > d dimensions. Yet, most geometry preserving algorithms cannot do the latter. This paper proposes an embedding algorithm to overcome this. The algorithm accepts as inpu...
متن کاملAn Image Retrieval Method Based on Manifold Learning with Scale-Invariant Feature Control
Aiming at the problem of the traditional dimensionality reduction methods cannot recover the inherent structure, and scale invariant feature transform (SIFT) achieving low precision when reinstating images, an Image Retrieval Method Based on Manifold Learning with Scale-Invariant Feature is proposed. It aims to find low-dimensional compact representations of high-dimensional observation data an...
متن کاملLearning gradients on manifolds
A common belief in high dimensional data analysis is that data is concentrated on a low dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on manifolds for dimension reduction for high dimensional data with few observations. We obtain generalization error bounds for the gradient estimates and show tha...
متن کاملider: Intrinsic Dimension Estimation with R
Abstract In many data analyses, the dimensionality of the observed data is high while its intrinsic dimension remains quite low. Estimating the intrinsic dimension of an observed dataset is an essential preliminary step for dimensionality reduction, manifold learning, and visualization. This paper introduces an R package, named ider, that implements eight intrinsic dimension estimation methods,...
متن کامل