Related papers: Locally Linear Embedding and its Variants: Tutoria…

We present the Procrustes measure, a novel measure based on Procrustes rotation that enables quantitative comparison of the output of manifold-based embedding algorithms (such as LLE (Roweis and Saul, 2000) and Isomap (Tenenbaum et al,…

The recovery of the intrinsic geometric structures of data collections is an important problem in data analysis. Supervised extensions of several manifold learning approaches have been proposed in the recent years. Meanwhile, existing…

High-dimensional data analysis has been an active area, and the main focuses have been variable selection and dimension reduction. In practice, it occurs often that the variables are located on an unknown, lower-dimensional nonlinear…

Visualizing high-dimensional data is essential for understanding biomedical data and deep learning models. Neighbor embedding methods, such as t-SNE and UMAP, are widely used but can introduce misleading visual artifacts. We find that the…

Feature engineering plays an important role in the success of a machine learning model. Most of the effort in training a model goes into data preparation and choosing the right representation. In this paper, we propose a robust feature…

We propose a kernel-spectral embedding algorithm for learning low-dimensional nonlinear structures from high-dimensional and noisy observations, where the datasets are assumed to be sampled from an intrinsically low-dimensional manifold and…

Recommender systems have become an essential component of many online platforms, providing personalized recommendations to users. A crucial aspect is embedding techniques that convert the high-dimensional discrete features, such as user and…

We present Contextualized Local Visual Embeddings (CLoVE), a self-supervised convolutional-based method that learns representations suited for dense prediction tasks. CLoVE deviates from current methods and optimizes a single loss function…

Graph kernels based on the $1$-dimensional Weisfeiler-Leman algorithm and corresponding neural architectures recently emerged as powerful tools for (supervised) learning with graphs. However, due to the purely local nature of the…

Neighbor Embedding (NE) aims to preserve pairwise similarities between data items and has been shown to yield an effective principle for data visualization. However, even the best existing NE methods such as Stochastic Neighbor Embedding…

Samples from intimate (non-linear) mixtures are generally modeled as being drawn from a smooth manifold. Scenarios where the data contains multiple intimate mixtures with some constituent materials in common can be thought of as manifolds…

This paper introduces a new method for semi-supervised learning on high dimensional nonlinear manifolds, which includes a phase of unsupervised basis learning and a phase of supervised function learning. The learned bases provide a set of…

This paper provides a new similarity detection algorithm. Given an input set of multi-dimensional data points, where each data point is assumed to be multi-dimensional, and an additional reference data point for similarity finding, the…

We introduce Variational Joint Embedding (VJE), a reconstruction-free latent-variable framework for non-contrastive self-supervised learning in representation space. VJE maximizes a symmetric conditional evidence lower bound (ELBO) on…

Classical nonlinear dimensionality reduction (NLDR) techniques like t-SNE, Isomap, and LLE excel at creating low-dimensional embeddings for data visualization but fundamentally lack the ability to map these embeddings back to the original…

Uniform Manifold Approximation and Projection (UMAP) is one of the state-of-the-art methods for dimensionality reduction and data visualization. This is a tutorial and survey paper on UMAP and its variants. We start with UMAP algorithm…

Parametric embedding methods such as parametric t-SNE (pt-SNE) have been widely adopted for data visualization and out-of-sample data embedding without further computationally expensive optimization or approximation. However, the…

The graph embedding (GE) methods have been widely applied for dimensionality reduction of hyperspectral imagery (HSI). However, a major challenge of GE is how to choose proper neighbors for graph construction and explore the spatial…

Data living on manifolds commonly appear in many applications. Often this results from an inherently latent low-dimensional system being observed through higher dimensional measurements. We show that under certain conditions, it is possible…

The objective in extreme multi-label learning is to train a classifier that can automatically tag a novel data point with the most relevant subset of labels from an extremely large label set. Embedding based approaches make training and…