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When analyzing empirical data, we often find that global linear models overestimate the number of parameters required. In such cases, we may ask whether the data lies on or near a manifold or a set of manifolds (a so-called multi-manifold)…
Because hyperspectral remote sensing images contain a lot of redundant information and the data structure is highly non-linear, leading to low classification accuracy of traditional machine learning methods. The latest research shows that…
Datasets such as images, text, or movies are embedded in high-dimensional spaces. However, in important cases such as images of objects, the statistical structure in the data constrains samples to a manifold of dramatically lower…
Real-world vision based applications require fine-grained classification for various area of interest like e-commerce, mobile applications, warehouse management, etc. where reducing the severity of mistakes and improving the classification…
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…
Datasets with significant proportions of noisy (incorrect) class labels present challenges for training accurate Deep Neural Networks (DNNs). We propose a new perspective for understanding DNN generalization for such datasets, by…
The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…
Kernel methods play a critical role in many machine learning algorithms. They are useful in manifold learning, classification, clustering and other data analysis tasks. Setting the kernel's scale parameter, also referred to as the kernel's…
The manifold hypothesis (real world data concentrates near low-dimensional manifolds) is suggested as the principle behind the effectiveness of machine learning algorithms in very high dimensional problems that are common in domains such as…
Large-scale classification of data where classes are structurally organized in a hierarchy is an important area of research. Top-down approaches that exploit the hierarchy during the learning and prediction phase are efficient for large…
Multimodal deep learning methods capture synergistic features from multiple modalities and have the potential to improve accuracy for stress detection compared to unimodal methods. However, this accuracy gain typically comes from high…
Deep metric learning aims to construct an embedding space where samples of the same class are close to each other, while samples of different classes are far away from each other. Most existing deep metric learning methods attempt to…
Multi-scale inference is commonly used to improve the results of semantic segmentation. Multiple images scales are passed through a network and then the results are combined with averaging or max pooling. In this work, we present an…
Despite the fact that nonlinear subspace learning techniques (e.g. manifold learning) have successfully applied to data representation, there is still room for improvement in explainability (explicit mapping), generalization…
Based on the manifold hypothesis, real-world data often lie on a low-dimensional manifold, while normalizing flows as a likelihood-based generative model are incapable of finding this manifold due to their structural constraints. So, one…
System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…
Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central…
Deep dictionary learning seeks multiple dictionaries at different image scales to capture complementary coherent characteristics. We propose a method for learning a hierarchy of synthesis dictionaries with an image classification goal. The…
We propose a novel algorithm for supervised dimensionality reduction named Manifold Partition Discriminant Analysis (MPDA). It aims to find a linear embedding space where the within-class similarity is achieved along the direction that is…
Deep Metric Learning (DML) plays a critical role in various machine learning tasks. However, most existing deep metric learning methods with binary similarity are sensitive to noisy labels, which are widely present in real-world data. Since…