Related papers: Isometric Multi-Manifolds Learning
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…
Sparse coding has been popularly used as an effective data representation method in various applications, such as computer vision, medical imaging and bioinformatics, etc. However, the conventional sparse coding algorithms and its manifold…
This paper proposes an out-of-sample extension framework for a global manifold learning algorithm (Isomap) that uses temporal information in out-of-sample points in order to make the embedding more robust to noise and artifacts. Given a set…
High-dimensional data is commonly encountered in numerous data analysis tasks. Feature selection techniques aim to identify the most representative features from the original high-dimensional data. Due to the absence of class label…
In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…
Autoencoding is a popular method in representation learning. Conventional autoencoders employ symmetric encoding-decoding procedures and a simple Euclidean latent space to detect hidden low-dimensional structures in an unsupervised way.…
Cross-manifold clustering is a hard topic and many traditional clustering methods fail because of the cross-manifold structures. In this paper, we propose a Multiple Flat Projections Clustering (MFPC) to deal with cross-manifold clustering…
Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular,…
Learned denoisers play a fundamental role in various signal generation (e.g., diffusion models) and reconstruction (e.g., compressed sensing) architectures, whose success derives from their ability to leverage low-dimensional structure in…
Training a classifier with high mean accuracy from a manifold-distributed dataset can be challenging. This problem is compounded further when there are only few labels available for training. For transfer learning to work, both the source…
Imbalanced learning is important and challenging since the problem of the classification of imbalanced datasets is prevalent in machine learning and data mining fields. Sampling approaches are proposed to address this issue, and…
Learning a single universal policy that can perform a diverse set of manipulation tasks is a promising new direction in robotics. However, existing techniques are limited to learning policies that can only perform tasks that are encountered…
Incomplete multi-view unsupervised feature selection (IMUFS), which aims to identify representative features from unlabeled multi-view data containing missing values, has received growing attention in recent years. Despite their promising…
Using evolutionary computation algorithms to solve multiple tasks with knowledge sharing is a promising approach. Image feature learning can be considered as a multitask problem because different tasks may have a similar feature space.…
An important task in image processing and neuroimaging is to extract quantitative information from the acquired images in order to make observations about the presence of disease or markers of development in populations. Having a…
We introduce manifold-learning flows (M-flows), a new class of generative models that simultaneously learn the data manifold as well as a tractable probability density on that manifold. Combining aspects of normalizing flows, GANs,…
Most masked point cloud modeling (MPM) methods follow a regression paradigm to reconstruct the coordinate or feature of masked regions. However, they tend to over-constrain the model to learn the details of the masked region, resulting in…
In this paper, we propose a novel Joint framework for Deep Multi-view Clustering (DMJC), where multiple deep embedded features, multi-view fusion mechanism and clustering assignments can be learned simultaneously. Our key idea is that the…
Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…
Algorithms proposed for solving high-dimensional optimization problems with no derivative information frequently encounter the "curse of dimensionality," becoming ineffective as the dimension of the parameter space grows. One feature of a…