Related papers: Sampling-enabled scalable manifold learning unveil…

Deep learning methods have played a more and more important role in hyperspectral image classification. However, the general deep learning methods mainly take advantage of the information of sample itself or the pairwise information between…

Deep clustering has increasingly been demonstrating superiority over conventional shallow clustering algorithms. Deep clustering algorithms usually combine representation learning with deep neural networks to achieve this performance,…

Manifold learning techniques have become increasingly valuable as data continues to grow in size. By discovering a lower-dimensional representation (embedding) of the structure of a dataset, manifold learning algorithms can substantially…

Many approaches in the field of machine learning and data analysis rely on the assumption that the observed data lies on lower-dimensional manifolds. This assumption has been verified empirically for many real data sets. To make use of this…

Manifold learning is a hot research topic in the field of computer science and has many applications in the real world. A main drawback of manifold learning methods is, however, that there is no explicit mappings from the input data…

We present a robust multiple manifolds structure learning (RMMSL) scheme to robustly estimate data structures under the multiple low intrinsic dimensional manifolds assumption. In the local learning stage, RMMSL efficiently estimates local…

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…

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 approaches seek the intrinsic, low-dimensional data structure within a high-dimensional space. Mainstream manifold learning algorithms, such as Isomap, UMAP, $t$-SNE, Diffusion Map, and Laplacian Eigenmaps do not use data…

Data clustering, the task of grouping observations according to their similarity, is a key component of unsupervised learning -- with real world applications in diverse fields such as biology, medicine, and social science. Often in these…

Machine learning for differential equations paves the way for computationally efficient alternatives to numerical solvers, with potentially broad impacts in science and engineering. Though current algorithms typically require simulated…

Clustering algorithms partition a dataset into groups of similar points. The clustering problem is very general, and different partitions of the same dataset could be considered correct and useful. To fully understand such data, it must be…

Manifold theory has been the central concept of many learning methods. However, learning modern CNNs with manifold structures has not raised due attention, mainly because of the inconvenience of imposing manifold structures onto the…

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…

Cluster analysis plays a very important role in data analysis. In these years, cluster ensemble, as a cluster analysis tool, has drawn much attention for its robustness, stability, and accuracy. Many efforts have been done to combine…

Unsupervised learning has gained prominence in the big data era, offering a means to extract valuable insights from unlabeled datasets. Deep clustering has emerged as an important unsupervised category, aiming to exploit the non-linear…

Semi-supervised clustering techniques have emerged as valuable tools for leveraging prior information in the form of constraints to improve the quality of clustering outcomes. Despite the proliferation of such methods, the ability to…

How do computers and intelligent agents view the world around them? Feature extraction and representation constitutes one the basic building blocks towards answering this question. Traditionally, this has been done with carefully engineered…

We present a new technique that enables manifold learning to accurately embed data manifolds that contain holes, without discarding any topological information. Manifold learning aims to embed high dimensional data into a lower dimensional…

Learning the manifold structure of remote sensing images is of paramount relevance for modeling and understanding processes, as well as to encapsulate the high dimensionality in a reduced set of informative features for subsequent…