Related papers: Isometric Multi-Manifolds Learning
This paper introduces a novel perspective about error in machine learning and proposes inverse feature learning (IFL) as a representation learning approach that learns a set of high-level features based on the representation of error for…
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…
Contagion maps exploit activation times in threshold contagions to assign vectors in high-dimensional Euclidean space to the nodes of a network. A point cloud that is the image of a contagion map reflects both the structure underlying the…
This paper presents a deep relational metric learning (DRML) framework for image clustering and retrieval. Most existing deep metric learning methods learn an embedding space with a general objective of increasing interclass distances and…
We present a framework for learning to guide geometric task and motion planning (GTAMP). GTAMP is a subclass of task and motion planning in which the goal is to move multiple objects to target regions among movable obstacles. A standard…
We consider the problem of selecting an optimal mask for an image manifold, i.e., choosing a subset of the pixels of the image that preserves the manifold's geometric structure present in the original data. Such masking implements a form of…
In monocular videos that capture dynamic scenes, estimating the 3D geometry of video contents has been a fundamental challenge in computer vision. Specifically, the task is significantly challenged by the object motion, where existing…
Image matting is generally modeled as a space transform from the color space to the alpha space. By estimating the alpha factor of the model, the foreground of an image can be extracted. However, there is some dimensional information…
Manifold learning methods are an invaluable tool in today's world of increasingly huge datasets. Manifold learning algorithms can discover a much lower-dimensional representation (embedding) of a high-dimensional dataset through non-linear…
Research on manifold learning within a density ridge estimation framework has shown great potential in recent work for both estimation and de-noising of manifolds, building on the intuitive and well-defined notion of principal curves and…
Real world data often lie on low-dimensional Riemannian manifolds embedded in high-dimensional spaces. This motivates learning degenerate normalizing flows that map between the ambient space and a low-dimensional latent space. However, if…
Deep learning can extract rich data representations if provided sufficient quantities of labeled training data. For many tasks however, annotating data has significant costs in terms of time and money, owing to the high standards of subject…
The latest deep learning approaches perform better than the state-of-the-art signal processing approaches in various image restoration tasks. However, if an image contains many patterns and structures, the performance of these CNNs is still…
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…
Multiple clustering has gathered significant attention in recent years due to its potential to reveal multiple hidden structures of the data from different perspectives. Most of multiple clustering methods first derive feature…
This paper presents a new scalable algorithm for cross-modal similarity preserving retrieval in a learnt manifold space. Unlike existing approaches that compromise between preserving global and local geometries, the proposed technique…
Due to the existence of various views or representations in many real-world data, multi-view learning has drawn much attention recently. Multi-view spectral clustering methods based on similarity matrixes or graphs are pretty popular.…
Multi-view learning algorithms typically assume a complete bipartite mapping between the different views in order to exchange information during the learning process. However, many applications provide only a partial mapping between the…
This article introduces a novel, geometric approach for multi-manifold clustering (MMC), i.e. for clustering a collection of potentially intersecting, d-dimensional manifolds into the individual manifold components. We first compute a…
We start by considering the problem of estimating intrinsic distances on a smooth submanifold. We show that minimax optimality can be obtained via a reconstruction of the surface, and discuss the use of a particular mesh construction -- the…