Related papers: Sketching, Embedding, and Dimensionality Reduction…
We give a simple, low resource method to produce order embeddings from ontologies. Such embeddings map words to vectors so that order relations on the words, such as hypernymy/hyponymy, are represented in a direct way. Our method uses…
Data visualization and dimension reduction for regression between a general metric space-valued response and Euclidean predictors is proposed. Current Fr\'ech\'et dimension reduction methods require that the response metric space be…
We show that the symmetries of image formation by scattering enable graph-theoretic manifold-embedding techniques to extract structural and timing information from simulated and experimental snapshots at extremely low signal. The approach…
Dimensionality reduction methods, also known as projections, are frequently used for exploring multidimensional data in machine learning, data science, and information visualization. Among these, t-SNE and its variants have become very…
Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has…
Sketch-based image retrieval (SBIR) is a challenging task due to the large cross-domain gap between sketches and natural images. How to align abstract sketches and natural images into a common high-level semantic space remains a key problem…
We initiate the study of sub-linear sketching and streaming techniques for estimating the output size of common dictionary compressors such as Lempel-Ziv '77, the run-length Burrows-Wheeler transform, and grammar compression. To this end,…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
We propose a fast, distance-preserving, binary embedding algorithm to transform a high-dimensional dataset $\mathcal{T}\subseteq\mathbb{R}^n$ into binary sequences in the cube $\{\pm 1\}^m$. When $\mathcal{T}$ consists of well-spread (i.e.,…
Distances are pervasive in machine learning. They serve as similarity measures, loss functions, and learning targets; it is said that a good distance measure solves a task. When defining distances, the triangle inequality has proven to be a…
Low-dimensional embeddings are a cornerstone in the modelling and analysis of complex networks. However, most existing approaches for mining network embedding spaces rely on computationally intensive machine learning systems to facilitate…
Sparse embeddings of data form an attractive class due to their inherent interpretability: Every dimension is tied to a term in some vocabulary, making it easy to visually decipher the latent space. Sparsity, however, poses unique…
Humans effortlessly grasp the connection between sketches and real-world objects, even when these sketches are far from realistic. Moreover, human sketch understanding goes beyond categorization -- critically, it also entails understanding…
We give a dimensionality reduction procedure to approximate the sum of distances of a given set of $n$ points in $R^d$ to any "shape" that lies in a $k$-dimensional subspace. Here, by "shape" we mean any set of points in $R^d$. Our…
Deep networks have achieved excellent results in perceptual tasks, yet their ability to generalize to variations not seen during training has come under increasing scrutiny. In this work we focus on their ability to have invariance towards…
Given a dataset of points in a metric space and an integer $k$, a diversity maximization problem requires determining a subset of $k$ points maximizing some diversity objective measure, e.g., the minimum or the average distance between two…
Estimating the number of distinct elements in a data stream is well understood when repeated elements are identical. In modern settings, however, observations are high-dimensional and noisy, so repeated instances of the same object are only…
Diffusion models have demonstrated remarkable performance in text-to-image synthesis, producing realistic and high resolution images that faithfully adhere to the corresponding text-prompts. Despite their great success, they still fall…
Sketching and streaming algorithms are in the forefront of current research directions for cut problems in graphs. In the streaming model, we show that $(1-\epsilon)$-approximation for Max-Cut must use $n^{1-O(\epsilon)}$ space; moreover,…
Many metric learning tasks, such as triplet learning, nearest neighbor retrieval, and visualization, are treated primarily as embedding tasks where the ultimate metric is some variant of the Euclidean distance (e.g., cosine or Mahalanobis),…