Related papers: Elliptical Ordinal Embedding
Objective functions that optimize deep neural networks play a vital role in creating an enhanced feature representation of the input data. Although cross-entropy-based loss formulations have been extensively used in a variety of supervised…
A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating…
Manifold embedding algorithms map high-dimensional data down to coordinates in a much lower-dimensional space. One of the aims of dimension reduction is to find intrinsic coordinates that describe the data manifold. The coordinates returned…
Visualizing high-dimensional data has been a focus in data analysis communities for decades, which has led to the design of many algorithms, some of which are now considered references (such as t-SNE for example). In our era of overwhelming…
Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of…
Different types of two- and three-dimensional representations of a finite metric space are studied that focus on the accurate representation of the linear order among the distances rather than their actual values. Lower and upper bounds for…
We consider the problem of encoding a finite set of vectors into a small number of bits while approximately retaining information on the angular distances between the vectors. By deriving improved variance bounds related to binary Gaussian…
Conventional word embeddings represent words with fixed vectors, which are usually trained based on co-occurrence patterns among words. In doing so, however, the power of such representations is limited, where the same word might be…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
Graph embedding, representing local and global neighborhood information by numerical vectors, is a crucial part of the mathematical modeling of a wide range of real-world systems. Among the embedding algorithms, random walk-based algorithms…
The complexity of a learning task is increased by transformations in the input space that preserve class identity. Visual object recognition for example is affected by changes in viewpoint, scale, illumination or planar transformations.…
Previous work generally believes that improving the spatial invariance of convolutional networks is the key to object counting. However, after verifying several mainstream counting networks, we surprisingly found too strict pixel-level…
Oblivious low-distortion subspace embeddings are a crucial building block for numerical linear algebra problems. We show for any real $p, 1 \leq p < \infty$, given a matrix $M \in \mathbb{R}^{n \times d}$ with $n \gg d$, with constant…
We demonstrate that frequently appearing objects can be discovered by training randomly sampled patches from a small number of images (100 to 200) by self-supervision. Key to this approach is the pattern space, a latent space of patterns…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
Ordinal regression refers to classifying object instances into ordinal categories. Ordinal regression is crucial for applications in various areas like facial age estimation, image aesthetics assessment, and even cancer staging, due to its…
Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far…
Place embeddings generated from human mobility trajectories have become a popular method to understand the functionality of places. Place embeddings with high spatial resolution are desirable for many applications, however, downscaling the…
Recent methods for learning vector space representations of words have succeeded in capturing fine-grained semantic and syntactic regularities using vector arithmetic. However, these vector space representations (created through large-scale…
Exploiting internal spatial geometric constraints of sparse LiDARs is beneficial to depth completion, however, has been not explored well. This paper proposes an efficient method to learn geometry-aware embedding, which encodes the local…