舰船科学技术  2017, Vol. 39 Issue (12): 91-94 PDF

Unsupervised feature selection algorithm for underwater target recognition
YANG Hong-hui, LI Jiang-tao, SHEN Sheng, YAO Xiao-hui
School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an, 710072, China
Abstract: With the development of society, marine space becomes more and more important to human beings, and the demand for new automatic identification system for underwater targets is becoming more and more urgent. In the construction of the underwater target automatic identification system, the extracted features contain many redundant, irrelevant and noise features, which affect the efficiency of the system and reduce the accuracy of classification and recognition. To this end, we proposed a new feature selection algorithm for underwater target recognition-Unsupervised Feature Selection Algorithm Based on Graph Learning (UFSGL). The algorithm framework is optimized the transformation matrix and graph learning at the same time, and use the regularization method to optimize the smoothness of the weighted edge. Using the sonar dataset of UCI database to verify the performance of the algorithm, the results show that UFSGL algorithm can effectively reduce the number of features in feature subsets and improve the accuracy of classification recognition to a certain extent.
Key words: unsupervised     feature selection     graph learning     underwater target recognition
0 引　言

1 相关术语 1.1 范数

 ${\left\| A \right\|_{r,s}} = {\left( {\sum\limits_{i = 1}^e {{{\left( {\sum\limits_{j = 1}^f {{{\left| {{A_{ij}}} \right|}^r}} } \right)}^{s/r}}} } \right)^{1/s}}\text{。}$ (1)
1.2 局部保留投影

 $\arg \mathop {\min }\limits_W \sum\limits_{i,j = 1}^n {{{\left\| {{W^{\rm T}}{x_i} - {W^{\rm T}}{x_j}} \right\|}^2}{S_{ij}}}\text{。}$ (2)

LPP的基本思想是，寻找转换矩阵W，将高维数据X转换到低维矩阵XW，以用于最大化地保持X的局部结构的连接，最小化式（2）以确保当xixj相邻时， ${W^{\rm T}}{x_i}$ ${W^{\rm T}}{x_j}$ 也相邻。

2 自适应图学习无监督特征选择方法

2.1 图的构建

 ${{S}_{ij}}= {e^{ - \displaystyle\frac{{{{\left\| {{x_i} - {x_j}} \right\|}^2}}}{{2{\delta ^2}}}}}\text{。}$ (3)

 ${L} ={D} - {S}\text{。}$ (4)
2.2 目标函数

 $\begin{array}{l}\mathop {\min }\limits_{S,W} \sum\limits_{i,j = 1}^n {\left( {\left\| {{W^{\rm T}}{x_i} \!-\! {W^{\rm T}}{x_j}} \right\|_2^2{S_{ij}}} \right)} \!+\! \alpha \sum\limits_{i,j = 1}^n {S_{ij}^{}} \!+\! \beta {\left\| W \right\|_{2,1}}\\\begin{array}{*{20}{c}}{\rm s.t.} & {0 \leqslant {S_{ij}} \leqslant 1,{W^{\rm T}}{S_t}W = I}\text{。}\end{array}\end{array}$ (5)

3 目标函数的优化

 ${U_{ii}} = \frac{1}{{2{{\left\| {{w_i}} \right\|}_2}}}\text{。}$ (6)

 $\begin{array}{l}\mathop {\min }\limits_{S,W,U} tr\left( {{{W}^{\rm T}}{X}{{L}_S}{{X}^{\rm T}}W} \right) + \beta tr\left( {{{W}^{\rm T}}{UW}} \right)\text{，}\\\begin{array}{*{20}{c}}{\rm s.t.}&{{{W}^{\rm T}}{{S}_t}{W} = I}\text{。}\end{array}\end{array}$ (7)

 $\begin{array}{l}\mathop {\min }\limits_{W,U} tr\left( {{{W}^{\rm T}}\left( {{X}{{L}_S}{{X}^{\rm T}} + \beta {U}} \right){W}} \right),\\\begin{array}{*{20}{c}}{\rm s.t.}&{{{W}^{\rm T}}{{S}_t}{W} = I}{\text{。}}\end{array}\end{array}$ (8)

 ${L}({S_{ij}}) =\!\!\! \sum\limits_{i,j = 1}^n {\left( {\left\| {{{W}^{\rm T}}{x_i} \!-\! {{W}^{\rm T}}{x_j}} \right\|_2^2{{S}_{ij}}} \right)} \!\!+\!\! \alpha \sum\limits_{i,j = 1}^n {{{S}_{ij}}} + {\psi _{ij}}{{S}_{ij}}\text{。}$ (9)

 $\frac{{\partial {L}({{bm S}_{ij}})}}{{\partial {S_{ij}}}} = \left\| {{{W}^{\rm T}}{x_i} - {{W}^{\rm T}}{x_j}} \right\|_2^2 + \alpha + {\varPsi _{ij}}\text{。}$ (10)

 $\left( {\left\| {{{W}^{\rm T}}{x_i} - {{W}^{\rm T}}{x_j}} \right\|_2^2 + \alpha } \right){{S}_{ij}} = 0\text{。}$ (11)

 ${{\hat {S}}_{ij}} = \frac{{\alpha {{S}_{ij}}}}{{\left\| {{{W}^{\rm T}}{x_i} - {{W}^{\rm T}}{x_j}} \right\|_2^2}}\text{。}$ (12)

4 实验

4.1 数据介绍

4.2 参数设置

 图 1 $\alpha ,\beta$ 参数对分类识别正确率的影响 Fig. 1 Influence of parameters $\alpha ,\beta$ on the classification accuracy of sonar data

4.3 SVM分类实验及结果

 图 2 特征选择前后SVM分类识别正确率 Fig. 2 The SVM classification accuracy before and after the feature selection

5 结　语

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