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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…
Supervised manifold learning methods learn data representations by preserving the geometric structure of data while enhancing the separation between data samples from different classes. In this work, we propose a theoretical study of…
This paper describes a hierarchical learning strategy for generating sparse representations of multivariate datasets. The hierarchy arises from approximation spaces considered at successively finer scales. A detailed analysis of stability,…
We introduce and develop a novel approach to outlier detection based on adaptation of random subspace learning. Our proposed method handles both high-dimension low-sample size and traditional low-dimensional high-sample size datasets.…
A common belief in high-dimensional data analysis is that data are concentrated on a low-dimensional manifold. This motivates simultaneous dimension reduction and regression on manifolds. We provide an algorithm for learning gradients on…
Large-scale Hierarchical Classification (HC) involves datasets consisting of thousands of classes and millions of training instances with high-dimensional features posing several big data challenges. Feature selection that aims to select…
When performing classification tasks, raw high dimensional features often contain redundant information, and lead to increased computational complexity and overfitting. In this paper, we assume the data samples lie on a single underlying…
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…
Dimensionality reduction (DR) techniques help analysts to understand patterns in high-dimensional spaces. These techniques, often represented by scatter plots, are employed in diverse science domains and facilitate similarity analysis among…
In the context of classification problems, Deep Learning (DL) approaches represent state of art. Many DL approaches are based on variations of standard multi-layer feed-forward neural networks. These are also referred to as deep networks.…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
The discovering of low-dimensional manifolds in high-dimensional data is one of the main goals in manifold learning. We propose a new approach to identify the effective dimension (intrinsic dimension) of low-dimensional manifolds. The scale…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
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…
In this work we show that the classification performance of high-dimensional structural MRI data with only a small set of training examples is improved by the usage of dimension reduction methods. We assessed two different dimension…
It is often possible to perform reduced order modelling by specifying linear subspace which accurately captures the dynamics of the system. This approach becomes especially appealing when linear subspace explicitly depends on parameters of…
An analysis of high-dimensional data can offer a detailed description of a system but is often challenged by the curse of dimensionality. General dimensionality reduction techniques can alleviate such difficulty by extracting a few…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
Analyzing high-dimensional data with manifold learning algorithms often requires searching for the nearest neighbors of all observations. This presents a computational bottleneck in statistical manifold learning when observations of…
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…