无限最大间隔线性判别投影模型

文伟; 曹雪菲; 陈渤; 韩勋; 张学峰; 王鹏辉; 刘宏伟

doi:10.11999/JEIT170256

无限最大间隔线性判别投影模型

doi: 10.11999/JEIT170256

基金项目:

国家杰出青年科学基金(61525105)，国家自然科学基金(61201292, 61322103, 61372132)，全国优秀博士学位论文作者专项资金(FANEDD-201156)，陕西省自然科学基础研究计划(2016JQ6048)，航空科学基金(20142081009)，上海航天科技创新基金(SAST2015009)，航空电子系统射频综合仿真航空科技重点实验室基金

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出版历程
- 收稿日期: 2017-03-29
- 修回日期: 2017-09-21
- 刊出日期: 2017-12-19

Infinite Max-margin Linear Discriminant Projection Model

Funds:

The National Science Fund for Distinguished Young Scholars (61525105), The National Natural Science Foundation of China (61201292, 61322103, 61372132), The Program for New Century Excellent Talents in University (FANEDD-201156), The Natural Science Basic Research Plan in Shaanxi Province (2016JQ6048), The Avaation Science Fund (20142081009), Shanghai Aerospca Science, Technology Innovation Fund (SAST2015009), The Key Laboratory Fund of RF Integrated Laboratory in Avionics System

摘要

摘要: 针对具有多模分布结构的高维数据的分类问题，该文提出一种无限最大间隔线性判别投影(iMMLDP)模型。与现有全局投影方法不同，模型通过联合Dirichlet过程及最大间隔线性判别投影(MMLDP)模型将数据划分为若干个局部区域，并在每一个局部学习一个最大边界线性判别投影分类器。组合各局部分类器，实现全局非线性的投影与分类。iMMLDP模型利用贝叶斯框架联合建模，将聚类、投影及分类器进行联合学习，可以有效发掘数据的隐含结构信息，因而，可以较好地对非线性可分数据，尤其是具有多模分布特性数据进行分类。得益于非参数贝叶斯先验技术，可以有效避免模型选择问题，即局部区域划分数量。基于仿真数据集、公共数据集及雷达实测数据集验证了所提方法的有效性。
- 最大间隔线性判别投影 /
- 非参数贝叶斯 /
- Dirichlet过程混合模型
Abstract: An infinite Max-Margin Linear Discriminant Projection (iMMLDP) model is developed to deal with the classification problem on multimodal distributed high-dimensional data. Different from global projection, iMMLDP divides the data into a set of local regions via Dirichlet Process (DP) mixture model and meanwhile learns a linear Max-Margin Linear Discriminant Projection (MMLDP) classifier in each local region. By assembling these local classifiers, a flexible nonlinear classifier is constructed. Under this framework, iMMLDP combines dimensionality reduction, clustering and supervised classification in a principled way, therefore, an underlying structure of the data could be uncovered. As a result, the model can handle the classification of data with global nonlinear structure, especially the data with multi-modally distributed structure. With the help of Bayesian nonparametric prior, the model selection problem (e.g. the number of local regions) can be avoided. The proposed model is implemented on synthesized and real-world data, including multi-modally distributed datasets and measured radar high range resolution profile (HRRP) data, to validate its efficiency and effectiveness.
- Max-Margin Linear Discriminant Projection (MMLDP) /
- Bayesian nonparametric /
- Dirichlet Process Mixture (DPM) model

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