Related papers: An Explicit Nonlinear Mapping for Manifold Learnin…
Most of existing manifold learning methods rely on Mean Squared Error (MSE) or $\ell_2$ norm. However, for the problem of image quality assessment, these are not promising measure. In this paper, we introduce the concept of an image…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Manifold learning has been proven to be an effective method for capturing the implicitly intrinsic structure of non-Euclidean data, in which one of the primary challenges is how to maintain the distortion-free (isometry) of the data…
Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…
Deep learning is the mainstream technique for many machine learning tasks, including image recognition, machine translation, speech recognition, and so on. It has outperformed conventional methods in various fields and achieved great…
In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying…
Manifold learning is a popular and quickly-growing subfield of machine learning based on the assumption that one's observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. This thesis presents a mathematical…
The manifold hypothesis presumes that high-dimensional data lies on or near a low-dimensional manifold. While the utility of encoding geometric structure has been demonstrated empirically, rigorous analysis of its impact on the learnability…
Representation learning is currently a very hot topic in modern machine learning, mostly due to the great success of the deep learning methods. In particular low-dimensional representation which discriminates classes can not only enhance…
Meshes are ubiquitous in visual computing and simulation, yet most existing machine learning techniques represent meshes only indirectly, e.g. as the level set of a scalar field or deformation of a template, or as a disordered triangle soup…
We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information…
Semi-supervised learning algorithms typically construct a weighted graph of data points to represent a manifold. However, an explicit graph representation is problematic for neural networks operating in the online setting. Here, we propose…
Drawing motivation from the manifold hypothesis, which posits that most high-dimensional data lies on or near low-dimensional manifolds, we apply manifold learning to the space of neural networks. We learn manifolds where datapoints are…
Manifold learning is a fundamental task at the core of data analysis and visualisation. It aims to capture the simple underlying structure of complex high-dimensional data by preserving pairwise dissimilarities in low-dimensional…
Deep neural networks have gained tremendous success in a broad range of machine learning tasks due to its remarkable capability to learn semantic-rich features from high-dimensional data. However, they often require large-scale labelled…
Recently manifold learning algorithm for dimensionality reduction attracts more and more interests, and various linear and nonlinear, global and local algorithms are proposed. The key step of manifold learning algorithm is the neighboring…
We analyze the performance of a class of manifold-learning algorithms that find their output by minimizing a quadratic form under some normalization constraints. This class consists of Locally Linear Embedding (LLE), Laplacian Eigenmap,…
We present a novel framework for learning cost-efficient latent representations in problems with high-dimensional state spaces through nonlinear dimension reduction. By enriching linear state approximations with low-order polynomial terms…
Majority of the current dimensionality reduction or retrieval techniques rely on embedding the learned feature representations onto a computable metric space. Once the learned features are mapped, a distance metric aids the bridging of gaps…
We study the problem of learning local metrics for nearest neighbor classification. Most previous works on local metric learning learn a number of local unrelated metrics. While this "independence" approach delivers an increased flexibility…