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 智能系统学报  2019, Vol. 14 Issue (5): 882-888  DOI: 10.11992/tis.201808005 0

### 引用本文

ZHANG Ying, WANG Jun, BAO Guoqiang, et al. A novel unsupervised fuzzy feature learning method for computer-aided diagnosis of autism[J]. CAAI Transactions on Intelligent Systems, 2019, 14(5), 882-888. DOI: 10.11992/tis.201808005.

### 文章历史

A novel unsupervised fuzzy feature learning method for computer-aided diagnosis of autism
ZHANG Ying , WANG Jun , BAO Guoqiang , ZHANG Chunxiang , WANG Shitong
School of Digital Media, Jiangnan University, Wuxi 214122, China
Abstract: Studies have shown that the behavioral and cognitive defect of patients with autism have a close relationship with potential brain dysfunction. For the high-dimensional rs-fMRI features, traditional linear feature extraction method cannot always discriminatively extract the important information for classification. To this end, a novel method for fMRI data based on both unsupervised fuzzy feature mapping and multi-view support vector machine is proposed in this study, which aims to build a classification model for computer aided diagnosis of autism. In this method, the original features are first mapped to a linear separable high-dimensional space using the rule precursor learning method of multi-output Takagi-Sugeno-Kang (TSK) fuzzy system; then the manifold regularization learning framework is introduced. On the basis of this, a novel unsupervised fuzzy feature learning method is used to obtain the nonlinear low-dimensional embedding representation of the original output eigenvector. Finally, a multi-view support vector machine (SVM) algorithm is used for classification. The experimental results show that the proposed method can effectively extract important features from the rs-fMRI data and improve the interpretability of the model on the premise of ensuring a superior and stable classification performance of the model.
Key words: autism    functional magnetic resonance imaging    functional connectivity    Pearson’s correlation    feature selection    unsupervised fuzzy feature mapping    manifold regularization framework    support vector machine

1 实验数据集及处理

2 基于fMRI数据的无监督模糊特征学习方法 2.1 方法流程

1）根据预处理后的静息态功能磁共振成像数据，提取出各脑区的平均时间序列信号，计算脑区之间的Pearson系数，得到低阶功能连接矩阵 ${{M}}_{{\rm{tr}}}^{\rm{l}}$

2）将低阶功能连接矩阵的每一行作为各脑区的特征描述，再次计算脑区之间的Pearson系数，得到高阶功能连接矩阵 ${{M}}_{{\rm{tr}}}^{\rm{h}}$

3）分别取低阶和高阶功能连接矩阵 ${{M}}_{{\rm{tr}}}^{\rm{l}}$ ${{M}}_{{\rm{tr}}}^{\rm{h}}$ 的上三角阵，按行串联形成新的特征向量，然后将所有对象的特征向量进行排列，生成基于低阶和高阶功能连接的所有对象的特征矩阵；对两种不同的特征矩阵计算各特征与类标的相关性，选择与类标相关性最高的D个特征，构成矩阵 ${{X}}_{{\rm{tr}}}^{\rm{l}} = \left( {{{\left( {{{x}}_1^{\rm{tr,l}}} \right)}^{\rm{T}}};{{\left( {{{x}}_2^{\rm{tr,l}}} \right)}^{\rm{T}}}; \cdots ;{{\left( {{{x}}_N^{\rm{tr,l}}} \right)}^{\rm{T}}}} \right) \in {{\bf{R}}^{N \times D}}$ ${{X}}_{{\rm{tr}}}^{\rm{h}} = \left( {{\left( {{{x}}_1^{\rm{tr,h}}} \right)}^{\rm{T}}}; \right.$ $\left.{{\left( {{{x}}_2^{\rm{tr,h}}} \right)}^{\rm{T}}};\cdots;{{\left( {{{x}}_N^{\rm{tr,h}}} \right)}^{\rm{T}}} \right) \in {{\bf{R}}^{N \times D}}$ ，其中 ${{x}}_i^{\rm{tr,l}} \in {{\bf{R}}^D}$ ${{x}}_i^{\rm{tr,h}} \in {{\bf{R}}^D}$ i = $1,2, \cdots ,N$

4）使用无监督模糊特征映射方法对低阶和高阶功能连接的特征矩阵进行特征学习，得到相应的变换矩阵 ${{{\beta}} _g}$ ，并将 ${{X}}_{{\rm{tr}}}^{\rm{l}}$ ${{X}}_{{\rm{tr}}}^{\rm{h}}$ 变换到低维空间中得到相应的嵌入矩阵 ${{E}}_{{\rm{tr}}}^{\rm{l}}$ ${{E}}_{{\rm{tr}}}^{\rm{h}}$

5）基于4）得到的嵌入矩阵 ${{E}}_{{\rm{tr}}}^{\rm{l}}$ ${{E}}_{{\rm{tr}}}^{\rm{h}}$ ，分别计算相应的核矩阵。

6）将2种不同的核矩阵进行线性组合得到复合核矩阵。

7）构造相应的SVM分类器。

 Download: 图 1 无监督模糊特征学习方法的框架流程图 Fig. 1 The framework of an unsupervised fuzzy feature learning method
2.2 低阶和高阶功能连接矩阵的生成

2.3 基于流形正则化约束的模糊特征学习

 $\begin{split} & {\rm{if}}\;\;\;\;{x_1}\;{\rm{is}}\;A_1^k \wedge {x_2}\;{\rm{is}}\;A_2^k \wedge \cdots\;\wedge {x_D} \wedge\;A_D^k, {\rm{then}} \\ & \left\{ \begin{array}{l} f_1^k\left( {{x}} \right) = \beta _0^{k,1} + \beta _1^{k,1}{x_1} + \cdots + \beta _D^{k,1}{x_D}\\ f_2^k\left( {{x}} \right) = \beta _0^{k,2} + \beta _1^{k,2}{x_1} + \cdots + \beta _D^{k,2}{x_D}\\ \qquad\qquad\qquad \vdots \\ f_S^k\left( {{x}} \right) = \beta _0^{k,S} + \beta _1^{k,S}{x_1} + \cdots + \beta _D^{k,S}{x_D} \end{array} \right. \end{split}$

 ${\mu _{A_d^k}}\left( {{x_d}} \right) = {\rm{exp}}\left( {\frac{{ - {{\left( {{x_d} - c_d^k} \right)}^2}}}{{2\delta _d^k}}} \right)$ (1)

 ${\mu ^k}\left( x \right) = \prod\limits_{d = 1}^D {{\mu _{A_d^k}}\left( {{x_d}} \right)}$ (2)
 ${\tilde \mu ^k}\left( x \right) = \frac{{{\mu ^k}\left( x \right)}}{{\displaystyle\sum\limits_{k = 1}^K {{\mu ^k}\left( x \right)} }}$ (3)

 $c_d^k = \sum\limits_{i = 1}^N {{u_{ik}}{x_{id}}} /\sum\limits_{i = 1}^N {{u_{ik}}}$ (4)
 $\delta _d^k = h \cdot \sum\limits_{i = 1}^N {{u_{ik}}{{\left( {{x_{id}} - c_d^k} \right)}^2}} /\sum\limits_{i = 1}^N {{u_{ik}}}$ (5)

 ${y_s} = \sum\limits_{k = 1}^K {{{\tilde \mu }^k}\left( {{x}} \right) \cdot f_s^k\left( {{x}} \right)}$ (6)

${{X}} = \left( {{{x}}_1^{\rm{T}};{{x}}_2^{\rm{T}};\cdots;{{x}}_N^{\rm{T}}} \right)$ 1为全1列向量，多输出TSK模糊系统的建模过程可用式(7)~ (13)的计算方法表述[15]

 ${{{X}}_e} = \left( {{\bf{1}},{{X}}} \right)$ (7)
 ${\tilde {{X}}^k} = {\rm{diag}}\left( {{{\tilde \mu }^k}\left( {{{{x}}_1}} \right),{{\tilde \mu }^k}\left( {{{{x}}_2}} \right), \cdots ,{{\tilde \mu }^k}\left( {{{{x}}_N}} \right)} \right){{{X}}_e}$ (8)
 ${{{X}}_g} = {\left( {{{\left( {{{\tilde {{X}}}^1}} \right)}^{\rm{T}}}{{\left( {{{\tilde {{X}}}^2}} \right)}^{\rm{T}}} \cdots {{\left( {{{\tilde {{X}}}^K}} \right)}^{\rm{T}}}} \right)^{\rm{T}}}$ (9)
 ${{{\beta}} ^{s,k}} = {\left( {\beta _0^{s,k},\beta _1^{s,k}, \cdots ,\beta _D^{s,k}} \right)^{\rm{T}}}$ (10)
 ${{{\beta}} ^s} = {\left( {{{\left( {{{{\beta}} ^{s,1}}} \right)}^{\rm{T}}},{{\left( {{{{\beta}} ^{s,2}}} \right)}^{\rm{T}}}, \cdots ,{{\left( {{{{\beta}} ^{s,K}}} \right)}^{\rm{T}}}} \right)^{\rm{T}}}$ (11)
 ${{{\beta}} _g} = \left[ {{{{\beta}} ^1}\quad{{{\beta}} ^2}\quad \cdots\quad {{{\beta}} ^S}} \right]$ (12)
 $f\left( {{X}} \right) = {{{X}}_g}{{{\beta}} _g}$ (13)

 $\begin{array}{c} \mathop {\min }\limits_{{{{\beta}} _g} \in {R^{\left( {D + 1} \right)K \times S}}} \parallel {{{\beta}} _g}{\parallel _F} + {\textit{λ}} {\rm{tr}}\left( {{{\beta}} _g^{\rm{T}}{{X}}_g^{\rm{T}}{{L}}{{{X}}_g}{{{\beta}} _g}} \right) \\ {\rm{s.t.}} {\left( {{{{X}}_g}{{{\beta}} _g}} \right)^{\rm{T}}}{{{X}}_g}{{{\beta}} _g} = {{{I}}_S} \end{array}$ (14)

 $\left( {{{{I}}_N} + {\textit{λ}} {{L}}{{{X}}_g}{{X}}_g^{\rm{T}}} \right){{u}} = \gamma {{{X}}_g}{{X}}_g^{\rm{T}}{{u}}$ (15)

 ${{{\beta}} _g} = {{X}}_g^{\rm{T}}\left( {{{\tilde {{u}}}_2},{{\tilde {{u}}}_3},\cdots,{{\tilde {{u}}}_{S + 1}}} \right)$ (16)

 Download: 图 2 无监督模糊特征学习流程图 Fig. 2 Flowchart of unsupervised fuzzy feature learning

 ${{E}}_{{\rm{tr}}}^{\rm{l}}{\rm{ = }}{\left( {{{X}}_{\rm{tr}}^{\rm{l}}} \right)_g}{{\beta}} _g^{\rm{l}}$ (17)
 ${{E}}_{{\rm{tr}}}^{\rm{h}}{\rm{ = }}{\left( {{{X}}_{\rm{tr}}^{\rm{h}}} \right)_g}{{\beta}} _g^{\rm{h}}$ (18)
2.4 基于功能连接矩阵的多视角SVM

 ${{K}}_{{\rm{tr}}}^{\rm{l}} = {{E}}_{{\rm{tr}}}^{\rm{l}}{\left( {{{E}}_{{\rm{tr}}}^{\rm{l}}} \right)^{\rm{T}}}$ (19)
 ${{K}}_{{\rm{tr}}}^{\rm{h}} = {{E}}_{{\rm{tr}}}^{\rm{h}}{\left( {{{E}}_{{\rm{tr}}}^{\rm{h}}} \right)^{\rm{T}}}$ (20)

 ${{{K}}_{{\rm{tr}}}} = {\theta _1}{{K}}_{{\rm{tr}}}^{\rm{l}} + {\theta _2}{{K}}_{{\rm{tr}}}^{\rm{h}}$ (21)

3 实验结果与分析 3.1 性能指标及参数设置

 ${\rm{ACC}} = \frac{{{\rm{TP}} + {\rm{TN}}}}{{{\rm{TP}} + {\rm{FN}} + {\rm{TN}} + {\rm{FP}}}}$ (22)
 ${\rm{SEN}} = \frac{{{\rm{TP}}}}{{{\rm{TP}} + {\rm{FN}}}}$ (23)
 ${\rm{SPE}} = \frac{{{\rm{TN}}}}{{{\rm{TN}} + {\rm{FP}}}}$ (24)

3.2 分类结果及分析

M2SVC算法联合使用两个视角的数据进行分类，其分类结果要明显优于基于单视角的分类器LOFCC和HOFCC；而本文方法采用新型的模糊特征学习技术进行特征学习，在此基础上使用M2SVC进行分类，从而取得了比仅使用M2SVC更好的效果，这表明本文所使用的模糊特征学习技术能够得到更有鉴别能力的特征，这对自闭症的诊断具有更优的判别能力。

3.3 特征数目对实验结果的影响

 Download: 图 3 特征数目对分类结果的影响(NYU) Fig. 3 The influence of the number of feature learning on the classification results (NYU)
 Download: 图 4 特征数目对分类结果的影响(USM) Fig. 4 The influence of the number of feature learning on the classification results (USM)
4 结束语

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