Few-shot image classification aims at exploring transferable features from base classes to recognize images of the unseen novel classes with only a few labeled images. Existing methods usually compare the support features and query features, which are implemented by either matching the global feature vectors or matching the local feature maps at the same position. However, few labeled images fail to capture all the diverse context and intraclass variations, leading to mismatch issues for existing methods. On one hand, due to the misaligned position and cluttered background, existing methods suffer from the object mismatch issue. On the other hand, due to the scale inconsistency between images, existing methods suffer from the scale mismatch issue. In this article, we propose the bilaterally normalized scale-consistent Sinkhorn distance (BSSD) to solve these issues. First, instead of same-position matching, we use the Sinkhorn distance to find an optimal matching between images, mitigating the object mismatch caused by misaligned position. Meanwhile, we propose the intraimage and interimage attentions as the bilateral normalization on the Sinkhorn distance to suppress the object mismatch caused by background clutter. Second, local feature maps are enhanced with the multiscale pooling strategy, making the Sinkhorn distance possible to find a consistent matching scale between images. Experimental results show the effectiveness of the proposed approach, and we achieve the state-of-the-art on three few-shot benchmarks.
This article addresses the challenge of scale variations in crowd-counting problems from a multidimensional measure-theoretic perspective. We start by formulating crowd counting as a measure-matching problem, based on the assumption that discrete measures can express the scattered ground truth and the predicted density map. In this context, we introduce the Sinkhorn counting loss and extend it to the semi-balanced form, which alleviates the problems including entropic bias, distance destruction, and amount constraints.
Single-cell technologies allow us to gain insights into cellular processes at unprecedented resolution. In stem cell and developmental biology snapshot data allow us to characterize how the transcriptional states of cells change between successive cell types. Here, we show how approximate Bayesian computation (ABC) can be employed to calibrate mathematical models against single-cell data.
Due to the high-dimensionality, redundancy, and non-linearity of the near-infrared (NIR) spectra data, as well as the influence of attributes such as producing area and grade of the sample, which can all affect the similarity measure between samples. This paper proposed a t-distributed stochastic neighbor embedding algorithm based on Sinkhorn distance (St-SNE) combined with multi-attribute data information. Firstly, the Sinkhorn distance was introduced which can solve problems such as KL divergence asymmetry and sparse data distribution in high-dimensional space, thereby constructing probability distributions that make low-dimensional space similar to high-dimensional space.
Department of Chemistry and Pharmaceutical Sciences, Amsterdam Institute of Molecular and Life Sciences (AIMMS), Faculty of Science, Vrije Universiteit Amsterdam, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands.
Understanding the character of electronic excitations is important in computational and reaction mechanistic studies, but their classification from simulations remains an open problem. Distances based on optimal transport have proven very useful in a plethora of classification problems and, therefore, seem a natural tool to try to tackle this challenge. We propose and investigate a new diagnostic Θ based on the Sinkhorn divergence from optimal transport.
Traditional loss functions such as cross-entropy loss often quantify the penalty for each mis-classified training sample without adequately considering its distance from the ground truth class distribution in the feature space. Intuitively, the larger this distance is, the higher the penalty should be. With this observation, we propose a penalty called distance-weighted Sinkhorn (DWS) loss.
