This paper describes how face recognition can be effected using 3D shape information extracted from single 2D image views. We characterise the shape of the field of facial normals using a statistical model based on principal geodesic analysis. The model can be fitted to 2D brightness images of faces to recover a vector of shape parameters. Since it captures variations in a field of surface norm...

This paper describes how graph-spectral methods can be used to transform the node correspondence problem into one of point-set alignment. We commence by using the ISOMAP algorithm to embed the nodes of a graph in a low-dimensional Euclidean space. With the nodes in the graph transformed to points in a metric space, we can recast the problem of graph-matching into that of aligning the points. He...

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...

In recent years, there has been a surge of interest in spectral manifold learning techniques. Despite the interest, only little work has focused on the empirical behavior of these techniques. We construct synthetic data of variable complexity and observe the performance of the techniques as they are subjected to increasingly difficult problems. We evaluate performance in terms of both a classif...

Dimensionality reduction is the search for a small set of variables to describe a large set of observed dimensions. Some benefits of dimensionality reduction include data visualization, compact representation, and decreased processing time. In this paper, we review two nonlinear techniques for dimensionality reduction: Isometric Feature Mapping (Isomap) and Locally Linear Embedding (LLE), and a...

A Face Recognition System is used to automatically identify or verify a person from digital image. Since capturing of face image is not very difficult process and does not require too much cooperation of the subject, it keeps the interest of researchers alive. In this paper, combination of linear and combination of nonlinear dimensionality reduction techniques are implemented separately for fac...

Several unsupervised learning algorithms based on an eigendecomposition provide either an embedding or a clustering only for given training points, with no straightforward extension for out-of-sample examples short of recomputing eigenvectors. This paper provides a unified framework for extending Local Linear Embedding (LLE), Isomap, Laplacian Eigenmaps, Multi-Dimensional Scaling (for dimension...

fMRI data is represented in a space with very high dimensionality. Because of this, classifiers such as SVM and Naive Bayes may overfit this data. Dimensionality reduction methods are intended to extract features from data in a high dimensional space. Training a classifier on data in a lower dimension may improve the true error of the classifier beyond the performance obtained by training in a ...

Dimension reduction is defined as the process of mapping high-dimensional data to a lowerdimensional vector space. Most machine learning and data mining techniques may not be effective for high-dimensional data. In order to handle this data adequately, its dimensionality needs to be reduced. Dimensionality reduction is also needed for visualization, graph embedding, image retrieval and a variet...

Manifold learning and finding low-dimensional structure in data is an important task. Many algorithms for this purpose embed data in Euclidean space, an approach which is destined to fail on non-flat data. This paper presents a non-iterative algebraic method for embedding the data into hyperbolic and spherical spaces. We argue that these spaces are often better than Euclidean space in capturing...