Submodular maximization has been widely studied over the past decades, mostly
because of its numerous applications in real-world problems. It is well known
that the standard greedy algorithm guarantees a worst-case approximation factor
of 1-1/e when maximizing a monotone submodular function under a cardinality
constraint. However, empirical studies show that its performance is
substantially better in practice. This raises a natural question of explaining
this improved performance of the greedy algorithm. In this work, we define
sharpness for submodular functions as a candidate explanation for this
phenomenon. The sharpness criterion is inspired by the concept of strong
convexity in convex optimization. We show that the greedy algorithm provably
performs better as the sharpness of the submodular function increases. This
improvement ties in closely with the faster convergence rates of first order
methods for sharp functions in convex optimization. Finally, we perform a
computational study to empirically support our theoretical results and show
that sharpness explains the greedy performance better than other justifications
in the literature.

通过定义锐度作为子模函数改善贪心算法性能的候选解释，本文探讨了贪心算法在最大化单调子模函数下的性能问题，显示子模函数的锐度影响贪心算法的表现，通过计算实验和理论结果，支持本文的说法。

贪心算法的不合理有效性：贪心算法适应尖锐度

On the Unreasonable Effectiveness of the Greedy Algorithm: Greedy Adapts  to Sharpness

In video based face recognition, face images are typically captured over
multiple frames in uncontrolled conditions, where head pose, illumination,
shadowing, motion blur and focus change over the sequence. Additionally,
inaccuracies in face localisation can also introduce scale and alignment
variations. Using all face images, including images of poor quality, can
actually degrade face recognition performance. While one solution it to use
only the "best" subset of images, current face selection techniques are
incapable of simultaneously handling all of the abovementioned issues. We
propose an efficient patch-based face image quality assessment algorithm which
quantifies the similarity of a face image to a probabilistic face model,
representing an "ideal" face. Image characteristics that affect recognition are
taken into account, including variations in geometric alignment (shift,
rotation and scale), sharpness, head pose and cast shadows. Experiments on
FERET and PIE datasets show that the proposed algorithm is able to identify
images which are simultaneously the most frontal, aligned, sharp and well
illuminated. Further experiments on a new video surveillance dataset (termed
ChokePoint) show that the proposed method provides better face subsets than
existing face selection techniques, leading to significant improvements in
recognition accuracy.

提出一种有效的基于 patch 的人脸图像质量评估算法，该算法综合考虑了人脸图像的几何对齐、锐度、头部姿势等因素，能够识别最正面、对齐、锐利和照明良好的图像，并在实验中表明在人脸子集的选择方面，该方法优于现有技术，使人脸识别准确度显著提高。