The selection of model's parameters plays an important role in the
application of support vector classification (SVC). The commonly used method of
selecting model's parameters is the k-fold cross validation with grid search
(CV). It is extremely time-consuming because it needs to train a large number
of SVC models. In this paper, a new method is proposed to train SVC with the
selection of model's parameters. Firstly, training SVC with the selection of
model's parameters is modeled as a minimax optimization problem
(MaxMin-L2-SVC-NCH), in which the minimization problem is an optimization
problem of finding the closest points between two normal convex hulls
(L2-SVC-NCH) while the maximization problem is an optimization problem of
finding the optimal model's parameters. A lower time complexity can be expected
in MaxMin-L2-SVC-NCH because CV is abandoned. A gradient-based algorithm is
then proposed to solve MaxMin-L2-SVC-NCH, in which L2-SVC-NCH is solved by a
projected gradient algorithm (PGA) while the maximization problem is solved by
a gradient ascent algorithm with dynamic learning rate. To demonstrate the
advantages of the PGA in solving L2-SVC-NCH, we carry out a comparison of the
PGA and the famous sequential minimal optimization (SMO) algorithm after a SMO
algorithm and some KKT conditions for L2-SVC-NCH are provided. It is revealed
that the SMO algorithm is a special case of the PGA. Thus, the PGA can provide
more flexibility. The comparative experiments between MaxMin-L2-SVC-NCH and the
classical parameter selection models on public datasets show that
MaxMin-L2-SVC-NCH greatly reduces the number of models to be trained and the
test accuracy is not lost to the classical models. It indicates that
MaxMin-L2-SVC-NCH performs better than the other models. We strongly recommend
MaxMin-L2-SVC-NCH as a preferred model for SVC task.

本文提出了一种新的支持向量机分类器模型参数选择方法 —— 最小最大 L2-SVC-NCH，并采用基于梯度的算法来解决该方法中的优化问题，与传统的参数选择模型相比，该方法在减少模型训练数量的同时保持了测试准确度。

MaxMin-L2-SVC-NCH：一种训练支持向量分类器并选择模型参数的新方法

MaxMin-L2-SVC-NCH: A New Method to Train Support Vector Classifier with  the Selection of Model's Parameters

Active learning is of great interest for many practical applications,
especially in industry and the physical sciences, where there is a strong need
to minimize the number of costly experiments necessary to train predictive
models. However, there remain significant challenges for the adoption of active
learning methods in many practical applications. One important challenge is
that many methods assume a fixed model, where model hyperparameters are chosen
a priori. In practice, it is rarely true that a good model will be known in
advance. Existing methods for active learning with model selection typically
depend on a medium-sized labeling budget. In this work, we focus on the case of
having a very small labeling budget, on the order of a few dozen data points,
and develop a simple and fast method for practical active learning with model
selection. Our method is based on an underlying pool-based active learner for
binary classification using support vector classification with a radial basis
function kernel. First we show empirically that our method is able to find
hyperparameters that lead to the best performance compared to an oracle model
on less separable, difficult to classify datasets, and reasonable performance
on datasets that are more separable and easier to classify. Then, we
demonstrate that it is possible to refine our model selection method using a
weighted approach to trade-off between achieving optimal performance on
datasets that are easy to classify, versus datasets that are difficult to
classify, which can be tuned based on prior domain knowledge about the dataset.

本研究开发了一种基于支持向量分类的基础池式主动学习器的快速简单的实践方法，旨在解决很少标记数据点的情况下进行模型选择的挑战，并通过加权方法让模型在易于分类数据集和难以分类数据集之间取得平衡的最佳性能。

小数据的模型选择实用主动学习

Practical Active Learning with Model Selection for Small Data

Estimation of facial expressions, as spatio-temporal processes, can take
advantage of kernel methods if one considers facial landmark positions and
their motion in 3D space. We applied support vector classification with kernels
derived from dynamic time-warping similarity measures. We achieved over 99%
accuracy - measured by area under ROC curve - using only the 'motion pattern'
of the PCA compressed representation of the marker point vector, the so-called
shape parameters. Beyond the classification of full motion patterns, several
expressions were recognized with over 90% accuracy in as few as 5-6 frames from
their onset, about 200 milliseconds.

应用动态时间规整相似度的核方法和支持向量分类器，只使用主成分分析压缩后的标记点向量的运动模式（形状参数）就可以准确地识别面部表情，包括全运动模式和数种表情。

使用时间序列核心进行情感表达分类

Emotional Expression Classification using Time-Series Kernels

We discuss a general technique that can be used to form a differentiable
bound on the optima of non-differentiable or discrete objective functions. We
form a unified description of these methods and consider under which
circumstances the bound is concave. In particular we consider two concrete
applications of the method, namely sparse learning and support vector
classification.

本文讨论了一种形成非可微或离散目标函数最优解可微分界限的通用技术，提供了这些方法的统一描述，并且考虑了边界凸性的情况。特别地，我们考虑了该方法的两个具体应用：稀疏学习和支持向量分类。