We present a scalable algorithm for the individually fair ($p$,
$k$)-clustering problem introduced by Jung et al. and Mahabadi et al. Given $n$
points $P$ in a metric space, let $\delta(x)$ for $x\in P$ be the radius of the
smallest ball around $x$ containing at least $n / k$ points. A clustering is
then called individually fair if it has centers within distance $\delta(x)$ of
$x$ for each $x\in P$. While good approximation algorithms are known for this
problem no efficient practical algorithms with good theoretical guarantees have
been presented. We design the first fast local-search algorithm that runs in
~$O(nk^2)$ time and obtains a bicriteria $(O(1), 6)$ approximation. Then we
show empirically that not only is our algorithm much faster than prior work,
but it also produces lower-cost solutions.

我们提出了一种可扩展的算法来解决由 Jung et al. 和 Mahabadi et al. 引入的个体公平（$p$, $k$）- 聚类问题。我们设计了首个快速局部搜索算法，具有～$O (nk^2)$ 的运行时间，并获得了（O (1), 6）的二对象近似解，然后我们通过实验证明了我们的算法不仅比以前的工作快得多，而且产生了更低成本的解决方案。

一个可扩展的算法用于个体公平的 K-means 聚类

A Scalable Algorithm for Individually Fair K-means Clustering

Cross-view person matching and 3D human pose estimation in multi-camera
networks are particularly difficult when the cameras are extrinsically
uncalibrated. Existing efforts generally require large amounts of 3D data for
training neural networks or known camera poses for geometric constraints to
solve the problem. However, camera poses and 3D data annotation are usually
expensive and not always available. We present a method, PME, that solves the
two tasks without requiring either information. Our idea is to address
cross-view person matching as a clustering problem using each person as a
cluster center, then obtain correspondences from person matches, and estimate
3D human poses through multi-view triangulation and bundle adjustment. We solve
the clustering problem by introducing a "size constraint" using the number of
cameras and a "source constraint" using the fact that two people from the same
camera view should not match, to narrow the solution space to a small feasible
region. The 2D human poses used in clustering are obtained through a
pre-trained 2D pose detector, so our method does not require expensive 3D
training data for each new scene. We extensively evaluate our method on three
open datasets and two indoor and outdoor datasets collected using arbitrarily
set cameras. Our method outperforms other methods by a large margin on
cross-view person matching, reaches SOTA performance on 3D human pose
estimation without using either camera poses or 3D training data, and shows
good generalization ability across five datasets of various environment
settings.

通过将跨视图人物匹配视为一个聚类问题，利用人物匹配获得对应关系，通过多视图三角测量和束调整估计三维人体姿势，本方法在无需相机位置和三维训练数据的情况下，优于其他方法对跨视角人物匹配，在三维人体姿势估计方面达到了目前技术水平，并在不同环境设置的五个数据集上展现了良好的泛化能力。

多视角人物匹配与任意非标定相机网络下的三维姿态估计

Multi-View Person Matching and 3D Pose Estimation with Arbitrary  Uncalibrated Camera Networks

This paper addresses the problem of registering multiple point sets.
Solutions to this problem are often approximated by repeatedly solving for
pairwise registration, which results in an uneven treatment of the sets forming
a pair: a model set and a data set. The main drawback of this strategy is that
the model set may contain noise and outliers, which negatively affects the
estimation of the registration parameters. In contrast, the proposed
formulation treats all the point sets on an equal footing. Indeed, all the
points are drawn from a central Gaussian mixture, hence the registration is
cast into a clustering problem. We formally derive batch and incremental EM
algorithms that robustly estimate both the GMM parameters and the rotations and
translations that optimally align the sets. Moreover, the mixture's means play
the role of the registered set of points while the variances provide rich
information about the contribution of each component to the alignment. We
thoroughly test the proposed algorithms on simulated data and on challenging
real data collected with range sensors. We compare them with several
state-of-the-art algorithms, and we show their potential for surface
reconstruction from depth data.

本文提出了一种用高斯混合模型来处理 3D 点云配准问题的算法，能够更好地估计注册参数，并可以用于重建表面。

批量和增量期望最大化的多点集联合对齐

Joint Alignment of Multiple Point Sets with Batch and Incremental  Expectation-Maximization

Imperfect-recall abstraction has emerged as the leading paradigm for
practical large-scale equilibrium computation in incomplete-information games.
However, imperfect-recall abstractions are poorly understood, and only weak
algorithm-specific guarantees on solution quality are known. In this paper, we
show the first general, algorithm-agnostic, solution quality guarantees for
Nash equilibria and approximate self-trembling equilibria computed in
imperfect-recall abstractions, when implemented in the original
(perfect-recall) game. Our results are for a class of games that generalizes
the only previously known class of imperfect-recall abstractions where any
results had been obtained. Further, our analysis is tighter in two ways, each
of which can lead to an exponential reduction in the solution quality error
bound.
We then show that for extensive-form games that satisfy certain properties,
the problem of computing a bound-minimizing abstraction for a single level of
the game reduces to a clustering problem, where the increase in our bound is
the distance function. This reduction leads to the first imperfect-recall
abstraction algorithm with solution quality bounds. We proceed to show a divide
in the class of abstraction problems. If payoffs are at the same scale at all
information sets considered for abstraction, the input forms a metric space.
Conversely, if this condition is not satisfied, we show that the input does not
form a metric space. Finally, we use these results to experimentally
investigate the quality of our bound for single-level abstraction.

本文介绍了一种针对不完备信息博弈的先前未被充分理解的模型（不完全回忆抽象）的解决方案和解决质量保证方法，并提出了一种抽象算法，以求得单层游戏的最小边界。