Related papers: CAMEL: Curvature-Augmented Manifold Embedding and …

Hyperbolic geometry has emerged as an effective latent space for representing complex networks, owing to its ability to capture hierarchical organization and heterogeneous connectivity patterns using low-dimensional embeddings. As a result,…

We develop a rigorous theoretical framework for principal manifold estimation that recovers a latent low-dimensional manifold from a point cloud observed in a high-dimensional ambient space. Our framework accommodates manifolds with…

Adaptive representations are increasingly indispensable for reducing the in-memory and on-disk footprints of large-scale data. Usual solutions are designed broadly along two themes: reducing data precision, e.g., through compression, or…

Low-rank metric learning aims to learn better discrimination of data subject to low-rank constraints. It keeps the intrinsic low-rank structure of datasets and reduces the time cost and memory usage in metric learning. However, it is still…

Linear discriminant analysis (LDA) is a widely used algorithm in machine learning to extract a low-dimensional representation of high-dimensional data, it features to find the orthogonal discriminant projection subspace by using the Fisher…

This is a tutorial and survey paper for Locally Linear Embedding (LLE) and its variants. The idea of LLE is fitting the local structure of manifold in the embedding space. In this paper, we first cover LLE, kernel LLE, inverse LLE, and…

This paper generalizes recent advances on quadratic manifold (QM) dimensionality reduction by developing kernel methods-based nonlinear-augmentation dimensionality reduction. QMs, and more generally feature map-based nonlinear corrections,…

Manifold learning offers nonlinear dimensionality reduction of high-dimensional datasets. In this paper, we bring geometry processing to bear on manifold learning by introducing a new approach based on metric connection for generating a…

Graph embeddings play a critical role in graph representation learning, allowing machine learning models to explore and interpret graph-structured data. However, existing methods often rely on opaque, high-dimensional embeddings, limiting…

Multidimensional scaling visualizes dissimilarities among objects and reduces data dimensionality. While many methods address symmetric proximity data, asymmetric and especially three-way proximity data (capturing relationships across…

Extreme Learning Machines (ELM) provide a fast alternative to traditional gradient-based learning in neural networks, offering rapid training and robust generalization capabilities. Its theoretical basis shows its universal approximation…

Probabilistic time-series forecasting enables reliable decision making across many domains. Most forecasting problems have diverse sources of data containing multiple modalities and structures. Leveraging information as well as uncertainty…

Humans can naturally understand an image in depth with the aid of rich knowledge accumulated from daily lives or professions. For example, to achieve fine-grained image recognition (e.g., categorizing hundreds of subordinate categories of…

Reward models play a fundamental role in aligning large language models with human preferences. Existing methods predominantly follow two paradigms: scalar discriminative preference models, which are efficient but lack interpretability, and…

Methods based on class activation maps (CAM) provide a simple mechanism to interpret predictions of convolutional neural networks by using linear combinations of feature maps as saliency maps. By contrast, masking-based methods optimize a…

Multilayer Extreme Learning Machine (ML-ELM) and its variants have proven to be an effective technique for the classification of different natural signals such as audio, video, acoustic and images. In this paper, a Hybrid Multilayer Extreme…

This work presents a novel Bayesian framework for unsupervised domain adaptation (UDA) in medical image segmentation. While prior works have explored this clinically significant task using various strategies of domain alignment, they often…

The kernel mean embedding of probability distributions is commonly used in machine learning as an injective mapping from distributions to functions in an infinite dimensional Hilbert space. It allows us, for example, to define a distance…

Representing a manifold of very high-dimensional data with generative models has been shown to be computationally efficient in practice. However, this requires that the data manifold admits a global parameterization. In order to represent…

Graph embedding based retrieval has become one of the most popular techniques in the information retrieval community and search engine industry. The classical paradigm mainly relies on the flat Euclidean geometry. In recent years,…