相关论文: Preserving Vector Space Properties in Dimensionali…

In recent years, deep metric learning has achieved promising results in learning high dimensional semantic feature embeddings where the spatial relationships of the feature vectors match the visual similarities of the images. Similarity…

Due to the curse of dimensionality and the limitation on training data, approximating high-dimensional functions is a very challenging task even for powerful deep neural networks. Inspired by the Nonlinear Level set Learning (NLL) method…

It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…

Learning well-separated features in high-dimensional spaces, such as text or image embeddings, is crucial for many machine learning applications. Achieving such separation can be effectively accomplished through the dispersion of…

Dimensionality reduction techniques play important roles in the analysis of big data. Traditional dimensionality reduction approaches, such as principal component analysis (PCA) and linear discriminant analysis (LDA), have been studied…

Learning on Grassmann manifold has become popular in many computer vision tasks, with the strong capability to extract discriminative information for imagesets and videos. However, such learning algorithms particularly on high-dimensional…

Deep Metric Learning (DML) learns a non-linear semantic embedding from input data that brings similar pairs together while keeping dissimilar data away from each other. To this end, many different methods are proposed in the last decade…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

Deep metric learning has yielded impressive results in tasks such as clustering and image retrieval by leveraging neural networks to obtain highly discriminative feature embeddings, which can be used to group samples into different classes.…

We investigate the effect of the dimensionality of the representations learned in Deep Neural Networks (DNNs) on their robustness to input perturbations, both adversarial and random. To achieve low dimensionality of learned representations,…

Several self-supervised learning (SSL) approaches have shown that redundancy reduction in the feature embedding space is an effective tool for representation learning. However, these methods consider a narrow notion of redundancy, focusing…

Dimensionality reduction is the essence of many data processing problems, including filtering, data compression, reduced-order modeling and pattern analysis. While traditionally tackled using linear tools in the fluid dynamics community,…

Different notions on regularity of sets and of collection of sets play an important role in the analysis of the convergence of projection algorithms in nonconvex scenarios. While some projection algorithms can be applied to feasibility…

While classic control theory offers state of the art solutions in many problem scenarios, it is often desired to improve beyond the structure of such solutions and surpass their limitations. To this end, residual policy learning (RPL)…

To address functional-output regression, we introduce projection learning (PL), a novel dictionary-based approach that learns to predict a function that is expanded on a dictionary while minimizing an empirical risk based on a functional…

Deep Metric Learning (DML), a widely-used technique, involves learning a distance metric between pairs of samples. DML uses deep neural architectures to learn semantic embeddings of the input, where the distance between similar examples is…

Lifelong learning (LL) aims to improve a predictive model as the data source evolves continuously. Most work in this learning paradigm has focused on resolving the problem of 'catastrophic forgetting,' which refers to a notorious dilemma…

Dimensionality reduction is a fundamental technique in machine learning and data analysis, enabling efficient representation and visualization of high-dimensional data. This paper explores five key methods: Principal Component Analysis…

We introduce Frequency Domain Perceptual Loss (FDPL), a loss function for single image super resolution (SR). Unlike previous loss functions used to train SR models, which are all calculated in the pixel (spatial) domain, FDPL is computed…

In this paper we present a mathematical framework on linking of embeddings of compact topological spaces into Euclidean spaces and separability of linked embeddings under a specific class of dimension reduction maps. As applications of the…