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摘要: 步态识别作为生物特征识别中的一种，具有远距离、非接触和难以模仿等优点.其中视角或行走方向的变化使提取的人体轮廓产生巨大差异，是影响步态识别系统性能的最主要因素之一.本文首先介绍了现有的多角度步态数据库，然后根据特征提取方式的不同，将当前已提出的方法分为三维模型法、视角不变性特征法、映射投影法和深度神经网络法四类，并详细阐述了每一类的原理、特点以及优缺点.最后，结合实际应用指出当前研究的局限性与发展趋势.Abstract: As one of biometric identification methods, gait recognition has many advantages. It is suitable for human identification at a long distance, requiring no contact and hard to imitate. One of the most important factors that affect the performance of gait recognition is that the change of view or the direction of the walk, which makes the human silhouette have a large variation. We first introduce the existing multi-view gait database. Then according to the characteristics of different extraction methods, the current approaches are divided into four kinds:three-dimensional model, view-invariant features, subspace projection as well as deep neural network, and analyses are conducted on their principle, advantages and disadvantages. Finally the limitations of current research and development trend are pointed out.
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Key words:
- Gait recognition /
- multi-view /
- behavioral characteristics recognition /
- biometrics
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随着大数据时代的到来, 人们对数据的处理正面临巨大挑战.在大数据应用研究中, 高维数据分析与研究是其主要内容之一.在现代机器学习与统计学的研究背景下, 高维数据所引发的维数灾难主要表现为:众多低维空间中表现良好的算法在面对高维数据时性能急剧下降.其主要原因有: 1)维数增加导致数据空间体积急剧膨胀、同等数量样本分布非常稀疏, 难以形成有效的簇; 2)高维空间中存在测度``集中现象", 使样本点间距离度量的类区分性随着维数增加而减弱; 3)样本数据包含大量冗余信息对聚类或分类无用, 甚至会降低算法的性能.基于上述原因, 对降维方法进行研究是十分有必要的.
总体上说, 面向聚类的降维方法均为无监督降维方法, 可分为线性降维和非线性降维.当前, 多数无监督线性降维方法假设观测数据落在一个低维流形子空间中, 通过寻找高维空间到低维子空间的线性投影实降维, 如主成分分析(Principal component analysis, PCA)[1]、局部保持投影(Locality preserving projections, LPP)[2]、近邻保持嵌入(Neighborhood preserving embedding, NPE)[3]和稀疏保持投影(Sparsity preserving projections, SPP)[4]. PCA是最经典的线性降维方法, 以最大化投影散度为目标, 但未考虑样本间的近邻结构关系, 不适合分布于流形上的非线性数据; LPP和NPE则考虑了样本间的近邻结构, LPP以保持降维前后样本间的近邻关系不变为目标, 而NPE旨在保持降维前后样本间的局部近邻结构; SPP的优化目标是使降维前后样本间的稀疏表示结构得以保持.但当数据非线性分布时, 上述线性降维算法就会失效.为弥补线性降维算法的不足, 各种非线性扩展方法被提出, 如核主成分分析(Kernel component analysis, KPCA)[5]和局部线性嵌入(Locally linear embedding, LLE)[6]. KPCA是PCA基于核技巧的非线性推广, 用于对非线性分布数据降维; LLE以保持投影前后局部线性关系不变为目的构造目标函数.然而这些非线性降维方法无法求出显式的映射函数, 当有新样本加入时, 需要重新学习优化模型.
极限学习机(Extreme learning machine, ELM)[7-8]最早被用于训练单隐层前馈神经网络, 具有学习速度快、泛化能力强等特点, 为有监督学习如分类和回归提供了简单有效的方法[9-10]. 2014年, Huang等基于流形正则的思想将ELM推广到无监督学习任务, 提出了一种新的非线性降维方法无监督极限学习机(Unsupervised extreme learning machine, US-ELM)[11].该方法很好地利用了ELM的逼近能力, 通过非线性映射将原数据投影到低维空间中, 并能够得到显式的非线性映射函数.但该方法利用高斯函数描述近邻样本间的相似度, 由于高斯函数用到距离测度, 难以避免地也存在高维空间中测度``集中现象", 即样本点间高斯相似性度量的类区分性随着维数增加而减弱, 进而影响降维算法性能.此外, US-ELM直接利用给定高斯函数计算样本近邻表示系数, 不具有数据自适应性.
针对上述问题, 本文对US-ELM进行改进, 同时考虑非线性数据的局部线性表示和全局稀疏表示.其中, 局部线性表示用于解决非线性流形数据的刻画问题, 以获取数据的局部结构[12];全局稀疏表示用于描述数据的全局结构[13];并通过加权参数融合近邻线性表示信息和稀疏表示信息.由此, 我们提出基于稀疏和近邻保持的极限学习机降维方法(SNP-ELM), 使得降维前后样本间的局部近邻表示关系和全局稀疏性保持不变. SNP-ELM通过学习得到近邻表示系数, 较之US-ELM具有更好的数据自适应性.
1. 极限学习机
极限学习机本质上是一种单隐含层前馈神经网络, 其结构如图 1所示[14]. ELM网络的训练主要分为两个阶段.第一个阶段是ELM网络结构构建, 隐含层将输入数据映射到$n$维的特征空间中, $n_h $为隐节点个数.定义隐含层关于${x_i}$的输出向量为。其中, $x\in {\mathbf R}^m$, 是第$i$个隐节点的输出, 其输出函数可以表示为:
$ \begin{equation} \hbox{$h_i(x)=g(a_i, b_i, x), a_i\in {\mathbf R}^m, b_i\in {\mathbf R}$} \end{equation} $
(1) 其中, $g(a_i, b_i, x)$为非线性激励函数, 常用的函数有Sigmoid函数和Gaussian函数.本文采用Sigmoid函数, 其表达式为:
$ \begin{equation} g(a_i, b_i, x)=\frac{1}{1+\exp(-a_ix+b_i)} \end{equation} $
(2) 式中, $a_i$为第$i$个隐节点的输入权值, $b_i$为第$i$个隐节点的偏差, 在ELM网络中输入权向量$a_i$和隐节点偏差$b_i$是随机产生的.
对于数据集$X$, ELM隐藏层输出为:
$ \begin{align} H(X)&=\left[ \begin{array}{c} h(x_1)\\ \vdots\\ h(x_n)\\ \end{array} \right]=\nonumber\\ &\left[ \begin{array}{ccc} g(a_1, b_1, x_1)&\cdots&g(a_{n_h}, b_{n_h}, x_1)\\ \vdots&\ddots&\vdots\\ g(a_1, b_1, x_n)&\cdots&g(a_{n_h}, b_{n_h}, x_n)\\ \end{array} \right] \end{align} $
(3) 若隐藏层到输出层的权重矩阵为$\beta=[\beta_1, \beta_2, \cdots, \beta_m]$, 则ELM网络的输出为
$ \begin{equation} Y=H(X) \beta \end{equation} $
(4) 第二阶段是基于ELM网络结构求解输出权重矩阵$\beta$, 通常根据ELM网络学习任务的不同构建不同的模型来求解输出权重矩阵$\beta$.经典的ELM模型用于解决有监督学习问题, 如:分类和回归.对于含$n$个样本的训练集, $x_i$为输入变量, $y_i$为输出变量, 则其模型表示:
$ \begin{equation} \begin{split} &\min \left(\frac{1}{2}||\beta||^2 +\frac{C}{2}\sum\limits_{i=1}^{N}e_i^2\right)\\ {\rm s. t.}&\quad y_i=h(x_i)\beta+e_i, i=1, \cdots, n \end{split} \end{equation} $
(5) 其中, 目标函数的第一项为正则项, 用来控制模型的复杂度; 第二项为表示误差, $e_i \in {\mathbf R}^d$是第$i$个样本的误差向量, $C$为惩罚系数.
近年来, Huang等将ELM推广到无监督学习, 提出基于流形无监督极限学习机, 其模型为:
$ \begin{equation} \begin{split} \min\limits_{\beta \in {\mathbf R}^{n_h \times d}} &\left\{||\beta||^2+\lambda {\rm tr}(\beta^\mathit{\boldsymbol{T}}H(X)^\mathit{\boldsymbol{T}}LH(X)\beta)\right\} \\ {\rm s. t.}\quad&(H(X)\beta)^\mathit{\boldsymbol{T}}H(X)\beta=I \ \end{split} \end{equation} $
(6) 第二项为流形正则项, 目的是使网络结构输出$Y$保持原输入数据$X$的流形结构不变, 其中, ${\rm tr}(\cdot)$表示矩阵的迹, $ L$为数据$X$的拉普拉斯矩阵, $I$为单位阵, $H(X)\in {\mathbf R}^{n\times n_h}$为隐含层输出矩阵. US-ELM将输入数据投影到$d$维空间中, 当$d <m$时, US-ELM是一种非线性降维方法.
2. 基于稀疏和近邻保持的极限学习机降维
US-ELM算法引入流形正则化的思想, 使得原始数据的流形结构经过US-ELM投影后得以保持, 即若在原空间近邻的两个样本在投影空间中仍然保持近邻[2]. US-ELM算法的流形结构直接用Gaussian距离刻画, 随着数据维数的增加, 该距离度量的类分类性会随之减弱.针对这一问题, 本文采用近邻表示来自适应地获取数据的低流形结构, 同时用稀疏表示来挖掘数据的全局结构.在此基础上提出SNP-ELM算法, 使得数据在新的投影空间中保持其在原空间的近邻和稀疏表示结构.
2.1 近邻表示和稀疏表示
近邻表示[4]:在样本集中用$x_i$的$k$近邻进行线性表示$x_i$, 其表达式为:
$ \begin{equation} \min\left \|x_i-\sum\limits_{x_i\in N_k(x_i)}w_{ij}x_j\right\| \end{equation} $
(7) 其中, $N_k(x_i)$表示$x_i$的$k$近邻, $w_{ij}$为近邻表示系数, 当$x_i\in N_k(x_i)$时, $w_{ij}=0$.
稀疏表示[5]:样本$x_i$可大致由该样本集中的少量样本线性表示.而当$x_i$由整个样本空间$X$进行线性表示时, 其表示系数是稀疏的.其数学模型表示为:
$ \begin{equation} \begin{split} \ &\min _{s_i}||s_i||_0\\ {\rm s. t.}\quad& x_i=Xs_i \end{split} \end{equation} $
(8) 其中, $s_i\in {\mathbf R}^n$为稀疏表示系数, $||s||_0$是$s$非零元素个数.由于$l_0$范数非凸且NP难, 因此用凸的$l_1$范数代替.同时为了确保稀疏表示的平移不变性, 我们引入表示系数和为1的约束, 则式$(8)$变为:
$ \begin{equation} \begin{split} \ &\min\limits_{s_i}||s_i||_1\\ {\rm s. t.}\quad& x_i=Xs_i, 1=I_is_i \end{split} \end{equation} $
(9) 其中, $I_1$为所有元素均为1的$n$维向量.式$(9)$是凸的, 可以利用线性规划方法求解, 如基追踪算法(Basis pursuit, BP)[15].
2.2 基于稀疏和近邻保持的极限学习机降维算法
SNP-ELM模型为:
$ \begin{align} \min\limits_\beta\big\{ ||\beta||_F^2+&\lambda\sum\limits_{i=1}^n||(h(x_i)\beta)^\mathit{\boldsymbol{T}}- \nonumber\\&(H(X)\beta)^\mathit{\boldsymbol{T}}(\delta w_i+\eta s_i)||_2^2\big\} \end{align} $
(10) 第二项的目的是使得投影后的数据保持原数据的近邻和稀疏表示结构, 其中为近邻表示系数矩阵, 表示$x_i$的近邻表示系数, 可以用模型$(7)$求解: $S=[s_1, s_2, \cdots, s_n]$为稀疏表示系数矩阵, $s_i$表示$x_i$的稀疏表示系数, 可以用模型$(9)$求解. 和是权重系数, 分别反映$W$和$S$的重要性.映射函数为$y=f(x)=(h(x)\beta)^\mathit{\boldsymbol{T}}$.
令$Z=\delta W+\eta S$, 则式$(10)$可写成:
$ \begin{equation} \min\limits_\beta \left\{||\beta||_F^2+\lambda\sum\limits_{i=1}^n||(h(x_i)\beta)^\mathit{\boldsymbol{T}}-(H(X)\beta)^\mathit{\boldsymbol{T}}z_i||_2^2\right\} \end{equation} $
(11) 通过简单的代数运算, 可以得到:
$ \begin{align} \sum\limits_{i=1}^n||&(h(x_i) \beta)^\mathit{\boldsymbol{T}}-(H^\mathit{\boldsymbol{T}}(X)\beta) z_i||_2^2=\nonumber\\ &{\rm tr}\Bigg(\beta^\mathit{\boldsymbol{T}}\Bigg(\sum\limits_{i=1}^n(h^\mathit{\boldsymbol{T}}(x_i)- H^\mathit{\boldsymbol{T}}(X)z_i)\times\nonumber\\ &(h^\mathit{\boldsymbol{T}}(x_i)-H^\mathit{\boldsymbol{T}}(X)z_i)^\mathit{\boldsymbol{T}}\Bigg)\beta\Bigg) \end{align} $
(12) 令$e_i$为$n$维单位向量, 则式$(12)$等价于:
$ \begin{align} \small\begin{split} &{\rm tr}\Bigg(\beta^\mathit{\boldsymbol{T}}\left(\sum\limits_{i=1}^n(H^\mathit{\boldsymbol{T}}(X)e_i- H^\mathit{\boldsymbol{T}}(X)z_i)\right)\times\nonumber\\ &\qquad (H^\mathit{\boldsymbol{T}}(X)e_i-H^\mathit{\boldsymbol{T}}(X)z_i)^\mathit{\boldsymbol{T}})\beta\Bigg)=\nonumber\\ &\qquad {\rm tr}\left(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)\left(\sum\limits_{i=1}^n(e_i-z_i) (e_i-z_i)^\mathit{\boldsymbol{T}}\right)H(X)\beta\right)=\nonumber\\ &\qquad {\rm tr}\Bigg(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)\Bigg(\sum\limits_{i=1}^n\Big(e_ie_i^\mathit{\boldsymbol{T}} -z_ie_i^\mathit{\boldsymbol{T}}-\nonumber\\ &\qquad e_iz_i^\mathit{\boldsymbol{T}}z_iz_i^\mathit{\boldsymbol{T}}\Big)\Bigg)H(X)\beta\Bigg)=\nonumber\\ &\qquad{\rm tr}(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)(I-Z-Z^\mathit{\boldsymbol{T}}+ Z^\mathit{\boldsymbol{T}}Z)H(X)\beta)\end{split}\\ \end{align} $
(13) 式$(11)$可变形为:
$ \begin{align} \min\limits_\beta&\big\{||\beta||_F^2+\lambda {\rm tr}(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)\times\nonumber\\ & (I-Z-Z^\mathit{\boldsymbol{T}}+Z^\mathit{\boldsymbol{T}}Z)H(X)\beta)\big\} \end{align} $
(14) 为避免平凡解, 在此引入约束$(H(X)\beta)^\mathit{\boldsymbol{T}}H(X)\beta=I$, 则模型变为:
$ \begin{align} \min\limits_\beta &\big\{||\beta||_F^2+\lambda {\rm tr}(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)\nonumber\\ &(I-Z-Z^\mathit{\boldsymbol{T}}+Z^\mathit{\boldsymbol{T}}Z)H(X)\beta)\big\}\nonumber\\ {\rm s. t.}\quad& (H(X)\beta)^\mathit{\boldsymbol{T}}H(X)\beta=I \end{align} $
(15) 2.3 模型求解
为求解模型$(15)$, 利用拉格朗日乘子法, 得到以下拉格朗日函数:
$ \begin{align} L(\beta)= &{\rm tr}(\beta^\mathit{\boldsymbol{T}}\beta)+\frac{\lambda}{2} {\rm tr}(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)AH(X)\beta)-\nonumber\\ &\theta {\rm tr}(\beta^\mathit{\boldsymbol{T}}H^\mathit{\boldsymbol{T}}(X)H(X)\beta-I) \end{align} $
(16) 其中, $A=I-Z-Z^\mathit{\boldsymbol{T}}+Z^\mathit{\boldsymbol{T}}Z$, 令, 得:
$ \begin{equation} \left(I+\frac{\lambda}{2}H^\mathit{\boldsymbol{T}}(X)AH(X)\right)\beta=\theta H^\mathit{\boldsymbol{T}}(X)H(X)\beta \end{equation} $
(17) 求解广义特征值问题$(17)$得到最小的$d$个特征值及对应的特征向量构成最优的输出权重矩阵$\beta^*$.
当$n_h>n$时, $H^\mathit{\boldsymbol{T}}(X)H(X)$的维数比较高, 直接求解式$(17)$广义特征值问题, 需要消耗较大的内存.为解决这个问题, 令$\beta=H^\mathit{\boldsymbol{T}}(X)\alpha$, 式$(17)$两边同时左乘$(H(X)H^\mathit{\boldsymbol{T}}(X))^{-1}H(X)$.得到:
$ \begin{equation} \left(I+\frac{\lambda}{2}AH(X)H^\mathit{\boldsymbol{T}}(X)\right)\alpha=\theta H(X)H^\mathit{\boldsymbol{T}}(X)\alpha \end{equation} $
(18) 易知模型$(17)$与模型$(18)$具有相同特征值.特征向量具有以下关系
$ \begin{equation} \beta^*=H^\mathit{\boldsymbol{T}}(X)\alpha^* \end{equation} $
(19) 因此解得广义特征值问题$(18)$的最小的$d$个特征值及对应的特征向量构成矩阵$\alpha^*$.进而可获得模型$(17)$的解矩阵$\beta^*=H^\mathit{\boldsymbol{T}}(X)\alpha^*$.
基于上述分析, 基于稀疏和近邻保持的极限学习机降维算法归纳如下:
算法1. SNP-ELM算法
输入:数据矩阵$X$, 参数$\lambda, \delta, \eta$.
输出:降维后样本矩阵$Y$.
1) 计算$k$近邻图.
2) 通过式(8)计算近邻重构矩阵$W$.
3) 通过式(10)计算稀疏重构矩阵$S$, 计算$Z=\delta W+\eta S$, $A=I-Z-Z^\mathit{\boldsymbol{T}}+Z^\mathit{\boldsymbol{T}}Z$.
4) 初始化ELM网络, $n_h$为隐藏层节点个数, 随机初始化输入权重, 偏置根据式$(3$)计算隐藏层输出矩阵.
5) 当$n>n_h$时, 利用式$(17)$计算得到输出权重矩阵$\beta$; 否则, 利用式$(18)$计算得到$\alpha$, 再计算输出权重矩阵$\beta=H^\mathit{\boldsymbol{T}}(X)\alpha$.
6) 计算降维后样本矩阵$Y=H(X)\beta$
2.4 算法分析
SNP-ELM算法中计算$k$近邻图的时间复杂度是O; 计算近邻重构矩阵$W$是求解了$n$次式$(8)$, 其时间复杂度为O$(nk^3)$; 用BP算法求解式$(10)$的时间复杂度为O$(n^3)$, 因此计算稀疏重构矩阵$S$的时间复杂度为O$(n^4)$; 计算广义特征值式$(18)$的时间复杂度为O$(n_h^3)$, 求解广义特征值式$(20)$的时间复杂度为O$(n^3)$.因此SNP-ELM算法的时间复杂度为O$(mn{\rm log}n+n^4+nk^3)$.
3. 实验
本文提出的SNP-ELM降维算法有两个重要目的, 其一是便于高维数据的可视化分析, 其二是面向聚类分析的降维可有效地提高聚类准确性, 故进行数据可视化及高维基因数据降维聚类实验, 两个实验的实验环境均为Win7系统, 内存4 GB, 所有方法均用Matlab2012b编程实现.两个实验均采用相同的参数设置, LPP、NPE、US-ELM和SNP-ELM的近邻数$k$均设为5; US-ELM和SNP-ELM的隐藏层节点个数均设为1 000; US-ELM的参数$\lambda$及SNP-ELM的参数$\lambda$统一取$\{10^{-4}, 10^{-3}, \cdots, 10^4\}$, SNP-ELM的参数$\delta$和$\eta$的搜索范围为$[-1, 1]$, 变化步长为0.2.
本文实验所对比的降维方法主要有以下几种: 1)线性降维方法: PCA、LPP、NPE和SPP; 2)非线性降维方法: LLE和US-ELM.其中LPP、NPE、LEE和US-ELM都使得降维后的数据保持原数据的近邻结构, SPP保持数据的稀疏表示结构, PCA的目标是使得降维后数据方差最大.
3.1 数据可视化实验
本实验中, 我们分别用PCA、LPP、NPE、SPP、LEE、US-ELM和SNP-ELM 7种方法将一个人造数据和一个真实的UCI数据Wine分别投影到一维和二维空间, 直观地展示SNP-ELM算法的性能, 并选取每个降维方法的最优结果进展示.
1) 一维可视化
本实验使用的三维人造数据如图 2所示, 该数据包含3类, 每类有50个样本, 该实验分别将数据降到一维, 实验结果如图 3所示.
从图 3可以看出PCA以投影后的样本方差最大为目标, 其降维结果近似于把该数据投影到$Z$轴方向, 但其将该数据投影到一维时三类数据的可分性较差. LPP、NPE、LLE和US-ELM均以降维后样本保持原样本的近邻结构为目的, 因此其降维效果略有改善.其中LLE和US-ELM是非线性降维方法, 其降维后不同类样本的分离程度较LPP和NPE高些.稀疏保持投影方法SPP以降维后样本保持原样本的稀疏结构为目的, 该方法将数据投影到一维后不同类样本的分离程度与US-ELM相当. SNP-ELM是一种非线性降维方法, 它使降维后样本同时保持数据的近邻结构和稀疏结构不变. SNP-ELM虽然无法使得该数据投影到一维后三类样本完全分离, 但其降维后不同类样本可分性是7种降维方法中最优的, 只有少数第三类样本与第二类样本相互重叠.
2) 二维可视化
本实验使用UCI数据集Wine数据, Wine数据包含来自3个类的178个样本, 每个样本有14个特征.实验结果如图 4所示.
由图 4可以看出, 经7种降维方法将Wine数据投影到2维时仍无法完全分离3类样本.但从不同类样本的重叠程度上可以看出, SPP将数据降到二维后3类数据完全重叠在一起, 降维效果最差.用PCA、LPP、NPE、LLE和US-ELM这5种方法降维后第一类数据能较好地分离, 而第二类和第三类数据完全重叠在一起.本文方法将Wine数据降到二维后, 不同类数据的重叠程度最低, 不同类样本的可分性最好.
3.2 基因表达数据实验
本实验采用高维基因表达数据测试本文方法与对比方法面向聚类任务时的降维效果.为了观察本文降维方法将数据投影到不同维数, 特别是投影到较低维时基因表达数据聚类效果, 将数据分别投影到维.该实验以降维后样本的$k$-means聚类准确率衡量降维质量, 实验中的聚类准确类采用文献[13]的计算方法.计算公式如下:
$ \begin{equation} ACC=\frac{1}{n}\sum\limits_{i=1}^n\delta(s_i, {\rm map}(r_i)) \end{equation} $
(20) 其中, $n$为样本数, $\delta(x, y)$表示当$x=y$时, $\delta=1$, 否则$\delta=0$; $s_i$和$r_i$分别为样本原始类标签和经聚类算法聚类后得到的类标签: map$(r_i)$将聚类得到的类标签映射成与样本数据自带的类标签等价的类标签.
1) 实验数据集
实验所选用的6个公开的基因数据集: SBCRT、DLBCL、Leukemia2、Prostate[16]、Prostate0和Colon[17], 这些数据的详细描述见表 1.
表 1 基因表达数据集描述Table 1 Summary of gene expression data sets数据集 样本数 基因数(维数) 类别数 SRBCT 83 2 308 4 DLBCL 77 5 469 2 Prostate0 102 6 033 2 Prostate 102 10 509 2 Leukemia2 72 11 225 3 Colon 62 2 000 2 2) 聚类准确率比较
为减少$k$-means初始中心随机选取以及US-ELM和SNP-ELM方法随机权重产生的随机误差.为便于比较, 减少实验结果随机性的影响, 实验中US-ELM和SNP-ELM分别运行10次, 再将每次降维后数据集执行10次$k$-means聚类, 取100次聚类准确率的平均值作为各自方法的最终准确率, 而其他降维方法的聚类准确率是10次$k$-means聚类准确率的平均值.最终实验结果如表 2所示, 表中给出聚类准确率的均值(方差、维数), 其中维数为每个数据最优聚类结果所对应的维数.对两种极限学习机降维方法US-ELM和SNP-ELM分别给出最优聚类结果所对应的参数. LPP、NPE、LLE、US-ELM和SNP-ELM这5种方法都在降维时保持了原始数据的近邻结构, SPP和SNP-ELM都保持了原始数据的稀疏结构, 其中LLE、US-ELM和SNP-ELM是非线性降维方法, SNP-ELM同时保持原始数据的近邻结构和稀疏结构.将这5种方法降维后的聚类准确率进行对比可以发现: 1)将NPE和LPP分别与LLE和US-ELM的准确率进行对比, 可以发现后者的准确率比前者高, 这是因为LEE和US-ELM分别是NPE和LPP的非线性推广, 非线性降维方法更适用于非线性分布的基因表达数据. 2) SPP与LPP、NPE进行比较其聚类结果各有千秋, 在DLBCL、Prostate0和Colon这3个数据集上SPP的结果较好, 而在其他数据集上LPP和NPE的结果较好, 这说明稀疏保持和近邻保持各有优势. 3) SNP-ELM的聚类准确率是最高的, 其主要原因是SNP-ELM既是非线性降维方法, 又同时保持了原始数据的近邻表示结构和稀疏表示结构使得降维后低维空间的数据保持了更多的判别信息.将表 2中的所有方法进行对比, 可以发现基于ELM的2种降维方法的准确率普遍优于其他降维方法.特别是SNP-ELM算法考虑到降维后样本局部近邻关系和全局稀疏性保持不变, 从而使其在全部6个基因数据降维后的聚类准确率最高, 且高于其他方法及US-ELM方法10 %以上.这说明SNP-ELM是一种有效的高维非线性降维方法.
表 2 基因数据集上聚类准确率(%)Table 2 Clustering accuracy comparison (variance) on gene expression data sets (%)Data $k$-means PCA LPP NPE SPP LLE US-ELM
$(\lambda)$SNP-ELM
$(\lambda, \eta, \delta)$Leukemia2 63.89 63.89 70.72 63.89 59.72 65.83 64.44 87.17 (0.00) (0.00, 2) (3.20, 4) (0, 32) (0.00, 72) (6.65, 4) (1.34, 2) (3.56, 8) (0.0001) (0.0001, $-$1, $-$1) SRBCT 43.61 48.86 64.19 48.43 38.55 49.76 64.55 82.92 (6.27) (2.09, 83) (2.21, 83) (0.76, 8) (0.00, 2) (4.33, 8) (10.29, 8) (6.03, 8) (0.1) (0.001, $-$0.4, 0) DLBCL 68.83 68.83 63.55 69.09 74.02 72.23 76.62 86.34 (0.00) (0.00, 2) (1.86, 8) (0.82, 32) (0.00, 4) (0.00, 2) (0.00, 32) (1.78, 8) (0.0001) (0.001, 0.2, $-$0.6) Prostate0 56.86 56.83 56.86 56.86 59.80 56.96 64.09 82.92 (0.00) (0.00, 2) (0.00, 2) (0.00, 4) (0.00, 102) (0.93, 4) (5.83, 2) (2.19, 102) (0.01) (0.1, 0.2, 0.8) Prostate 63.33 63.73 59.80 59.80 56.86 59.51 67.57 82.73 (0.83) (0.00, 2) (0.00, 2) (0.00, 4) (0.00, 102) (0.93, 4) (5.83, 2) (2.19, 102) (0.0001) (1, $-$1, 0.6) Colon 54.84 54.84 54.84 56.45 64.19 59.52 67.06 85.95 (0.00) (0.00, 2) (0.00, 2) (0.00, 2) (0.68, 62) (6.99, 32) (4.19, 32) (3.69, 8) (0.0001) (0.001, $-$0.8, 1) 为进一步对比几种降维方法在不同维数下的聚类准确率, 分别选取目标维数2, 4, 8, 16, 32, $\cdots$执行各种降维算法, 各种降维算法在不同维数下的聚类准确率如图 5所示.从图 5可以看出SNP-ELM及其余6种降维算法将6个数据集投影到相同维数的特征空间时, SNP-ELM的聚类准确率都是最高的.而对于SNP-ELM算法, 除Prostate和Prostate0两个数据集, 在其他4个基因数据集上都在8维处得到最高的聚类准确率.
图 5 将6个数据集映射到不同维度特征空间时的聚类准确率Fig. 5 Clustering accuracy on six gene expression data in different dimensions3) 参数分析
SNP-ELM模型有3个参数$\lambda, \delta$和$\eta$, 其中$\lambda$为正则参数. $\delta$和$\eta$为权重系数, 分别表示近邻重构系数和稀疏重构系数的重要性.本节讨论不同参数对实验结果的影响, 由前面的实验结果可知将基因表达数据降到8维时能够得到较高的聚类准确率, 因此在进行参数分析时我们固定维数为8.根据3个参数在SNP-ELM中的不同作用, 将其分为两组分别进行分析, 正则参数$\lambda$单独分析, 权重系数$\delta$和$\eta$一起分析.其中, $\lambda$的取值范围为$\{10^{-4}, 10^{-3}, \cdots, 10^4\}$, $\delta$和$\eta$的取值范围为$[-1, 1]$, 取值步长为0.2.
图 6给出$\delta=\eta=-0.2$时, SNP-ELM降维的聚类准确率随参数$\lambda$不同取值的变化情况.从图 6可以看出, 除了Leukema2在$\lambda=10^{-4}$时聚类准确率达到最高, 其余5个基因表达数据均在$\lambda=10^{-3}$时聚类准确率达到最高.这说明对高维基因数据而言, $\lambda$取较小值时本文方法能达到较好效果.
图 6 聚类准确率随参数λ的变化情况 $(\delta=\eta=-0.2) $Fig. 6 Variation of accuracy with respect of parameters $ \lambda (\delta=\eta=-0.2))$图 7给出$\lambda=0.001$时, 不同$\delta$和$\eta$取值下的聚类准确率.从图 7可以看出当$\delta$ 取值自$[-0.6, -0.2]$, $\eta$取值自时, 对高维基因表达数据而言SNP-ELM算法可以取得较高的聚类准确率.
图 7 不同$\delta$和$\eta$取值下的聚类准确率$(\lambda=0.001)$Fig. 7 ariation of accuracy with respect of parameters $\delta $ and $ \eta(\lambda=0.001)$4. 结论
目前, ELM模型主要用于有监督分类或回归问题, 本文则对ELM模型推广到无监督降维问题进行了进一步研究, 提出基于稀疏和近邻结构保持的极限学习机降维算法SNP-ELM. SNP-ELM通过模型优化求解计算近邻表示系数, 具有一定的数据自适应性, 实验结果表明SNP-ELM算法在Wine数据和基因表达数据集上性能优于其他对比方法.从研究中我们可以得到以下2个结论: 1)对Wine数据、高维基因表示数据降维时, 同时考虑稀疏结构和近邻结构比只考虑单一结构更有效; 2)基于ELM的非线性降维方法在Wine数据和基因表达数据上优于线性降维方法.
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表 1 多视角步态库
Table 1 Databases for multiview gait
库名 建立机构 样本容量 具体角度 示例 USF[3] 南佛罗里达大学 122人, 1 870序列(地面、鞋子、负重和时间) 在摄像机前(左右两个)绕椭圆路线行走 
CASIA-A[13] 中国科学院自动化研究所 20人×3视角× 4序列= 240 3个(侧面的3个点) 
CASIA-B[14] 中国科学院自动化研究所 124人× 11视角× (8正常+2背包+ 2外套) = 13 640 11个($180^{\circ}$每间隔$18^{\circ}$度一个视角) 
HID-UMD[15] 马里兰大学 1: 25人× 4个视角= 100 正面(走向、走出)、侧面(向左、向右) 
2: 55人× 4 (2视角) = 220 T形路径(正面、侧面) 
CMU MoBo[16] 卡耐基梅隆大学 25人× 6视角× (3速度+1抱球+ 1上坡) = 600 6个($360^{\circ}$圆周每$60^{\circ}$一个视角) 
OU-ISIR Treadmill[17] 大阪大学 168人 25个(12个方位角× 2个倾斜角度+1个俯视) 
OU-ISIR LP[18] 大阪大学 4 007人 8个(2摄像机$\times $ 4个侧面角度) 
SZU RBG-D[19] 深圳大学 99人× 2视角× 4序列= 792 $90^{\circ}$和$30^{\circ} \sim 60^{\circ}$之间的一个角度 
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表 2 类能量图构造方法与性能分析
Table 2 The construction methods and performances analysis of class energy image
表 3 CASIA-B数据集上现有步态识别方法的准确率对比
Table 3 Recognition accuracy of existing approaches on CASIA-B datasets
方法 识别率(%) $54^{\circ}$ $72^{\circ}$ $90^{\circ}$ $108^{\circ}$ $126^{\circ}$ 3D模型局部能量图投影[31] 86.1 98.1 - 92.3 90.4 下肢姿态重构[47] 74.4 72.6 86.5 69.2 67.4 聚类AGI +SRML[48] 68.3 92.7 - 93.4 70.3 聚类EDI +IT2FKNN[49] 72.2 94.8 - 95.3 74.9 GEI+CCA[53] 52.0 94.6 - 93.8 78.3 C3A[55] 86.6 98.7 - 95.4 86.0 GEI+TSVD[59] 53.7 81.8 - 86.3 45.7 低秩GEI+SVD[61] 42.5 86.2 - 88.3 49.8 JSL[68] 71.4 91.7 - 90.5 73.6 KCDML[75] 76.7 94.3 - 88.1 88.4 GEI+SPAE[88] 82.3 94.4 96.0 96.0 86.3
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表 4 现有多视角步态识别方法
Table 4 Existing approaches for multiview gait recognition
模板 方法 实现途径 优点 缺点 三维模板 建立三维步态模型 利用多摄像机对人体结构或人体运动进行3D建模[22, 27-35] 更准确地表达人体各个部位的物理空间; 能够降低遮挡等因素的负面影响. 需要全可控的多摄像机协作的识别环境; 摄像机平衡视角和建模计算复杂. 提取视角不变性特征 提取局部特征[44-47]; 聚类图像估计视角[48, 49]; 其他[38, 51]. 直接提取不随着角度而改变的步态特征进行身份识别, 避免轮廓差异; 思路直观, 计算简单, 易于理解和实现. 仅仅适用于视角变化有限的情况下; 易受到遮挡因素或服饰变化的破坏. 二维图像或视频序列特征 学习不同视角下的映射或投影关系 典范相关分析(CCA)[53-57]; 视角转换模型(VTM)[58-65]; 其他(LDA、CML、MPCA与核扩展等)[66-77]. 投影到子空间中获得步态的视角不变特征, 减小同一行人不同视角下的类内方差; 具有相对较高的识别精度. 步态图像转换成向量后维数常高达上万维, 计算量很大; 视角变化较大时效果不理想; CCA和CML类的方法仅能利用两个视角间的互补信息, 处理N个视角时要重复N次来学习N对特征映射; VTM方法在进行模型构建和视角转化时容易造成噪声传播, 致使识别性能退化. 基于深度神经网络 CNN[80-86]与AutoEncoder[88] 无图像的预处理过程; 有效提取步态特征; 具有相对较高的识别精度. 需要大量数据用于训练; 卷积神经网络缺乏对时间序列信号的记忆功能; 基于自动编码的VTM也有在转化时容易造成噪声传播使识别性能退化的问题.
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[1] Phillips P J. Human identification technical challenges. In: Proceedings of the 2002 International Conference on Image Processing. New York, USA: IEEE, 2002. I-49-I-52 [2] Tariq M, Shah M A. Review of model-free gait recognition in biometrie systems. In: Proceedings of the 23rd International Conference on Automation and Computing. Huddersfield, UK: IEEE, 2017. 1-7 [3] Sarkar S, Phillips P J, Liu Z, Vega, I R, Grother P, Bowyer K W. The humanID gait challenge problem:data sets, performance, and analysis. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(2):162-177 doi: 10.1109/TPAMI.2005.39 [4] Liu Z, Sarkar S. Effect of silhouette quality on hard problems in gait recognition. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2005, 35(2):170-183 doi: 10.1109/TSMCB.2004.842251 [5] Kale A, Sundaresan A, Rajagopalan A N, Cuntoor N P, Roy-Chowdhury A K, Kruger V, et al. Identification of humans using gait. IEEE Transactions on Image Processing, 2004, 13(9):1163-1173 doi: 10.1109/TIP.2004.832865 [6] Masood H, Farooq H. A proposed framework for vision based gait biometric system against spoofing attacks. In: Proceedings of the 2017 International Conference on Communication, Computing and Digital Systems. Islamabad, Pakistan: IEEE, 2017. 357-362 [7] Arseneau S, Cooperstock J R. Real-time image segmentation for action recognition. In: Proceedings of the 1999 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing. British Columbia, Canada: IEEE, 1999. 86-89 [8] Verlekar T T, Correia P L, Soares L D. View-invariant gait recognition system using a gait energy image decomposition method. IET Biometrics, 2017, 6(4):299-306 doi: 10.1049/iet-bmt.2016.0118 [9] Niyogi S A, Adelson E H. Analyzing gait with spatiotemporal surfaces. In: Proceedings of the 1994 IEEE Workshop on Motion of Non-Rigid and Articulated Objects. Texas, USA: IEEE, 1994. 64-69 [10] 王科俊, 侯本博.步态识别综述.中国图象图形学报, 2007, 12(7):1152-1160 doi: 10.3969/j.issn.1006-8961.2007.07.002Wang Ke-Jun, Hou Ben-Bo. A survey of gait recognition. Journal of Image and Graphics, 2007, 12(7):1152-1160 doi: 10.3969/j.issn.1006-8961.2007.07.002 [11] Sugandhi K, Wahid F F, Raju G. Feature extraction methods for human gait recognition——a survey. In: Proceedings of the 2017 Advances in Computing and Data Sciences. Communications in Computer and Information Science, vol. 721. Singapore: Springer, 2017. 377-385 [12] Lv Z W, Xing X L, Wang K J, Guan D H. Class energy image analysis for video sensor-based gait recognition:a review. Sensors, 2015, 15(1):932-964 [13] Wang L, Tan T N, Ning H Z, Hu W M. Silhouette analysis-based gait recognition for human identification. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(12):1505-1518 doi: 10.1109/TPAMI.2003.1251144 [14] Yu S Q, Tan D L, Tan T N. A framework for evaluating the effect of view angle, clothing and carrying condition on gait recognition. In: Proceedings of 18th International Conference on Pattern Recognition. Hong Kong, China: IEEE, 2006. 441-444 [15] Chalidabhongse T, Kruger V, Chellappa R. The UMD Database for Human Identification at a Distance, Technical Report, University of Maryland, USA, 2001 [16] Gross R, Shi J B. The CMU Motion of Body (MoBo) Database, Technical Report CMU-RI-TR-01-18, Carnegie Mellon University, USA, 2001 [17] Makihara Y, Mannami H, Yagi Y. Gait analysis of gender and age using a large-scale multi-view gait database computer vision. In: Proceedings of Asian Conference on Computer Vision. Queenstown, New Zealand: ACM, 2010. 440-451 [18] Iwama H, Okumura M, Makihara Y, Yagi Y. The OU-ISIR gait database comprising the large population dataset and performance evaluation of gait recognition. IEEE Transactions on Information Forensics and Security, 2012, 7(5):1511-1521 doi: 10.1109/TIFS.2012.2204253 [19] Yu S Q, Wang Q, Huang Y Z. A large RGB-D gait dataset and the baseline algorithm. In: Biometric Recognition. Lecture Notes in Computer Science, vol. 8232. Cham: Springer, 2013. 417-424 [20] Seely R D, Samangooei S, Lee M, Carter J N, Nixon M S. The University of Southampton Multi-Biometric Tunnel and introducing a novel 3D gait dataset. In: Proceedings of IEEE 2nd International Conference on Biometrics: Theory, Applications and Systems. Virginia USA: IEEE, 2008. 1-6 [21] Anguelov D, Koller D, Pang H C, Srinivasan P, Thrun S. Recovering articulated object models from 3D range data. In: Proceedings of the 20th Conference on Uncertainty in Artificial Intelligence. Banff, Canada: ACM, 2004. 18-26 [22] López-Fernández D, Madrid-Cuevas F J, Carmona-Poyato A, Muñoz-Salinas R, Medina-Carnicer R. A new approach for multi-view gait recognition on unconstrained paths. Journal of Visual Communication and Image Representation, 2016, 38:396-406 doi: 10.1016/j.jvcir.2016.03.020 [23] Hofmann M, Sural S, Rigoll G. Gait recognition in the presence of occlusion: a new dataset and baseline algorithms. In: Proceedings of the 19th International Conference in Central Europe Computer Graphics, Visualization and Computer Vision. Plzen, Czech Republic: Václav Skala UNION Agency, 2011. 99-104 [24] Cho C W, Chao W H, Lin S H, Chen Y Y. A vision-based analysis system for gait recognition in patients with Parkinson's disease. Expert Systems with Applications, 2009, 36(3):7033-7039 doi: 10.1016/j.eswa.2008.08.076 [25] Stevenage S V, Nixon M S, Vince K. Visual analysis of gait as a cue to identity. Applied Cognitive Psychology, 1999, 13(6):513-526 doi: 10.1002/(ISSN)1099-0720 [26] Lai D T H, Begg R K, Palaniswami M. Computational intelligence in gait research:a perspective on current applications and future challenges. IEEE Transactions on Information Technology in Biomedicine, 2009, 13(5):687-702 doi: 10.1109/TITB.2009.2022913 [27] Shakhnarovich G, Lee L, Darrell T. Integrated face and gait recognition from multiple views. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition. Hawaii, USA: IEEE, 2001. 439-446 [28] Bodor R, Drenner A, Fehr D, Masoud O, Papanikolopoulos N. View-independent human motion classification using image-based reconstruction. Image and Vision Computing, 2009, 27(8):1194-1206 doi: 10.1016/j.imavis.2008.11.008 [29] Zhang Z H, Troje N F. View-independent person identification from human gait. Neurocomputing, 2005, 69(1-3):250-256 doi: 10.1016/j.neucom.2005.06.002 [30] Tang J, Luo J, Tjahjadi T, Gao Y. 2.5D multi-view gait recognition based on point cloud registration. Sensors, 2014, 14(4):6124-6143 doi: 10.3390/s140406124 [31] Tang J, Luo J, Tjahjadi T, Guo F. Robust arbitrary-view gait recognition based on 3D partial similarity matching. IEEE Transactions on Image Processing, 2017, 26(1):7-22 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=db1c9453b08e2468c550f2b43633a9b4 [32] Zhao G Y, Liu G Y, Li H, Pietikinen M. 3D gait recognition using multiple cameras. In: Proceedings of the 7th International Conference on Automatic Face and Gesture Recognition. Southampton, UK: IEEE, 2006. 529-534 [33] Deng M Q, Wang C, Chen Q F. Human gait recognition based on deterministic learning through multiple views fusion. Pattern Recognition Letters, 2016, 78:56-63 doi: 10.1016/j.patrec.2016.04.004 [34] Deng M Q, Wang C, Cheng F J, Zeng W. Fusion of spatial-temporal and kinematic features for gait recognition with deterministic learning. Pattern Recognition, 2017, 67:186-200 doi: 10.1016/j.patcog.2017.02.014 [35] Iwashita Y, Ogawara K, Kurazume R. Identification of people walking along curved trajectories. Pattern Recognition Letters, 2014, 48:60-69 doi: 10.1016/j.patrec.2014.04.004 [36] Bobick A F, Davis J W. The recognition of human movement using temporal templates. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2001, 23(3):257-267 doi: 10.1109/34.910878 [37] Han J, Bhanu B. Individual recognition using gait energy image. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(2):316-323 doi: 10.1109/TPAMI.2006.38 [38] Lam T H W, Lee R S T. A new representation for human gait recognition: motion silhouettes image (MSI). In: Advances in Biometrics. Lecture Notes in Computer Science, vol. 3832. Berlin, Heidelberg: Springer-Verlag, 2005. 612-618 [39] Liu J Y, Zheng N N. Gait history image: a novel temporal template for gait recognition. In: Proceedings of the 2007 IEEE International Conference on Multimedia and Expo. Beijing, China: IEEE, 2007. 663-666 [40] Zhang E H, Zhao Y W, Xiong W. Active energy image plus 2DLPP for gait recognition. Signal Processing, 2010, 90(7):2295-2302 doi: 10.1016/j.sigpro.2010.01.024 [41] Bashir K, Xiang T, Gong S G. Gait recognition without subject cooperation. Pattern Recognition Letters, 2010, 31(13):2052-2060 doi: 10.1016/j.patrec.2010.05.027 [42] Chen C H, Liang J M, Zhu X C. Gait recognition based on improved dynamic Bayesian networks. Pattern Recognition, 2011, 44(4):988-995 doi: 10.1016/j.patcog.2010.10.021 [43] Wang C, Zhang J P, Wang L, Pu J, Yuan X R. Human identification using temporal information preserving gait template. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2012, 34(11):2164-2176 doi: 10.1109/TPAMI.2011.260 [44] Jean F, Albu A B, Bergevin R. Towards view-invariant gait modeling:computing view-normalized body part trajectories. Pattern Recognition, 2009, 42(11):2936-2949 doi: 10.1016/j.patcog.2009.05.006 [45] Ng H, Tan W H, Abdullah J, Tong H L. Development of vision based multiview gait recognition system with MMUGait database. The Scientific World Journal, 2014, 2014:Article ID 376569 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Doaj000003705025 [46] 彭彰, 吴晓娟, 杨军.基于肢体长度参数的多视角步态识别算法.自动化学报, 2007, 33(2):210-213 http://www.aas.net.cn/CN/abstract/abstract13832.shtmlPeng Zhang, Wu Xiao-Juan, Yang Jun. A multi-view method for gait recognition based on the length of body's parts. Acta Automatica Sinica, 2007, 33(2):210-213 http://www.aas.net.cn/CN/abstract/abstract13832.shtml [47] Goffredo M, Bouchrika I, Carter J N, Nixon M S. Self-calibrating view-invariant gait biometrics. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2010, 40(4):997-1008 doi: 10.1109/TSMCB.2009.2031091 [48] Lu J W, Wang G, Moulin P. Human identity and gender recognition from gait sequences with arbitrary walking directions. IEEE Transactions on Information Forensics and Security, 2014, 9(1):51-61 doi: 10.1109/TIFS.2013.2291969 [49] Darwish S M. Design of adaptive biometric gait recognition algorithm with free walking directions. IET Biometrics, 2017, 6(2):53-60 doi: 10.1049/iet-bmt.2015.0082 [50] Ma Q Y, Wang S K, Nie D D, Qiu J F. Gait recognition at a distance based on energy deviation image. In: Proceedings of the 1st International Conference on Bioinformatics and Biomedical Engineering. Wuhan, China: IEEE, 2007. 621-624 [51] Kale A, Chowdhury A K R, Chellappa R. Towards a view invariant gait recognition algorithm. In: Proceedings of the IEEE Conference on Advanced Video and Signal Based Surveillance. Miami, Florida, USA: IEEE, 2003. 143-150 [52] Hotelling H. Relations between two sets of variates. Biometrika, 1936, 28(3-4):321-377 doi: 10.1093/biomet/28.3-4.321 [53] Bashir K, Xiang T, Gong S G. Cross-view gait recognition using correlation strength. In: Proceedings of the British Machine Vision Conference. Aberystwyth, UK: BMVA Press, 2010. 109.1-109.11 [54] Hu H F. Multiview gait recognition based on patch distribution features and uncorrelated multilinear sparse local discriminant canonical correlation analysis. IEEE Transactions on Circuits and Systems for Video Technology, 2014, 24(4):617-630 doi: 10.1109/TCSVT.2013.2280098 [55] Xing X L, Wang K J, Yan T, Lv Z W. Complete canonical correlation analysis with application to multi-view gait recognition. Pattern Recognition, 2016, 50:107-117 doi: 10.1016/j.patcog.2015.08.011 [56] Wang K J, Yan T. An improved kernelized discriminative canonical correlation analysis and its application to gait recognition. In: Proceedings of the 10th World Congress on Intelligent Control and Automation. Beijing, China: IEEE, 2012. 4869-4874 [57] Luo C, Xu W J, Zhu C Y. Robust gait recognition based on partitioning and canonical correlation analysis. In: Proceedings of the 2015 IEEE International Conference on Imaging Systems and Techniques. Macau, China: IEEE, 2015. 1-5 [58] Makihara Y, Sagawa R, Mukaigawa Y, Echigo T, Yagi Y. Gait recognition using a view transformation model in the frequency domain. In: Proceedings of European Conference on Computer Vision. Graz, Austria: Springer-Verlag, 2006. 151-163 [59] Kusakunniran W, Wu Q, Li H D, Zhang J. Multiple views gait recognition using view transformation model based on optimized gait energy image. In: Proceedings of the 12th International Conference on Computer Vision Workshops. Kyoto, Japan: IEEE, 2009. 1058-1064 [60] Kusakunniran W, Wu Q, Zhang J, Li H D. Gait recognition under various viewing angles based on correlated motion regression. IEEE Transactions on Circuits and Systems for Video Technology, 2012, 22(6):966-980 doi: 10.1109/TCSVT.2012.2186744 [61] Zheng S, Zhang J G, Huang K Q, He R, Tan T. Robust view transformation model for gait recognition. In: Proceedings of the 18th International Conference on Image Processing. Brussels, Belgium: IEEE, 2011. 2073-2076 [62] Hu M D, Wang Y H, Zhang Z X. Cross-view gait recognition with short probe sequences:from view transformation model to view-independent stance-independent identity vector. International Journal of Pattern Recognition and Artificial Intelligence, 2013, 27(6):1350017 doi: 10.1142/S0218001413500171 [63] Muramatsu D, Shiraishi A, Makihara Y, Uddin M Z, Yagi Y. Gait-based person recognition using arbitrary view transformation model. IEEE Transactions on Image Processing, 2015, 24(1):140-54 doi: 10.1109/TIP.2014.2371335 [64] Muramatsu D, Makihara Y, Yagi Y. Cross-view gait recognition by fusion of multiple transformation consistency measures. IET Biometrics, 2015, 4(2):62-73 doi: 10.1049/iet-bmt.2014.0042 [65] Muramatsu D, Makihara Y, Yagi Y. View transformation model incorporating quality measures for cross-view gait recognition. IEEE Transactions on Cybernetics, 2016, 46(7):1602-1615 doi: 10.1109/TCYB.2015.2452577 [66] Choudhury S D, Tjahjadi T. Robust view-invariant multiscale gait recognition. Pattern Recognition, 2015, 48(3):798-811 doi: 10.1016/j.patcog.2014.09.022 [67] Liu N, Tan Y P. View invariant gait recognition. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing. Texas USA: IEEE, 2010. 1410-1413 [68] Liu N N, Lu J W, Tan Y P. Joint subspace learning for view-invariant gait recognition. IEEE Signal Processing Letters, 2011, 18(7):431-434 doi: 10.1109/LSP.2011.2157143 [69] Shawe-Taylor J, Cristianini N. Properties of kernels. Kernel Methods for Pattern Analysis. Cambridge:Cambridge University Press, 2004. 47-84 [70] Alzate C, Suykens J A K. Multiway spectral clustering with out-of-sample extensions through weighted kernel PCA. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2010, 32(2):335-347 doi: 10.1109/TPAMI.2008.292 [71] Yang J, Frangi A F, Yang J Y, Zhang D, Jin Z. KPCA Plus LDA:a complete kernel Fisher discriminant framework for feature extraction and recognition. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005, 27(2):230-244 doi: 10.1109/TPAMI.2005.33 [72] Connie T, Goh K O M, Teoh A B J. Multi-view gait recognition using a doubly-kernel approach on the Grassmann manifold. Neurocomputing, 2016, 216:534-542 doi: 10.1016/j.neucom.2016.08.002 [73] Xu W J, Luo C, Ji A M, Zhu C Y. Coupled locality preserving projections for cross-view gait recognition. Neurocomputing, 2017, 224:37-44 doi: 10.1016/j.neucom.2016.10.054 [74] Ben X Y, Meng W X, Yan R, Wang K J. An improved biometrics technique based on metric learning approach. Neurocomputing, 2012, 97(1):44-51 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=4492014b0866d51f7d2415c3699c60d8 [75] Ben X Y, Meng W X, Yan R, Wang K J. Kernel coupled distance metric learning for gait recognition and face recognition. Neurocomputing, 2013, 120:577-589 doi: 10.1016/j.neucom.2013.04.012 [76] Wang K J, Xing X L, Yan T, Lv Z W. Couple metric learning based on separable criteria with its application in cross-view gait recognition. In: Proceedings of the Biometric Recognition. Lecture Notes in Computer Science, vol. 8833. Shenyang, China: Springer, 2014. 347-356 [77] Al-Tayyan A, Assaleh K, Shanableh T. Decision-level fusion for single-view gait recognition with various carrying and clothing conditions. Image and Vision Computing, 2017, 61:54-69 doi: 10.1016/j.imavis.2017.02.004 [78] 陈伟宏, 安吉尧, 李仁发, 李万里.深度学习认知计算综述.自动化学报, 2017, 43(11):1886-1897 http://www.aas.net.cn/CN/abstract/abstract19164.shtmlChen Wei-Hong, An Ji-Yao, Li Ren-Fa, Li Wan-Li. Review on deep-learning-based cognitive computing. Acta Automatica Sinica, 2017, 43(11):1886-1897 http://www.aas.net.cn/CN/abstract/abstract19164.shtml [79] LeCun Y, Kavukcuoglu K, Farabet C. Convolutional networks and applications in vision. In: Proceedings of the 2010 IEEE International Symposium on Circuits and Systems. Paris, France: IEEE, 2010. 253-256 [80] Yan C, Zhang B L, Coenen F. Multi-attributes gait identification by convolutional neural networks. In: Proceedings of the 8th International Congress on Image and Signal Processing. Shenyang, China: IEEE, 2015. 642-647 [81] Wu Z F, Huang Y Z, Wang L. Learning representative deep features for image set analysis. IEEE Transactions on Multimedia, 2015, 17(11):1960-1968 doi: 10.1109/TMM.2015.2477681 [82] Zhang C, Liu W, Ma H D, Fu H Y. Siamese neural network based gait recognition for human identification. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing. Shanghai, China: IEEE, 2016. 2832-2836 [83] Tan T N, Wang L, Huang Y Z, Wu Z F. A Gait Recognition Method Based on Depth Learning, CN Patent 201410587758, June 2017 [84] Wu Z F, Huang Y Z, Wang L, Wang X G, Tan T N. A comprehensive study on cross-view gait based human identification with deep CNNs. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2017, 39(2):209-226 doi: 10.1109/TPAMI.2016.2545669 [85] Wolf T, Babaee M, Rigoll G. Multi-view gait recognition using 3D convolutional neural networks. In: Proceedings of the 2016 IEEE International Conference on Image Processing. Arizona USA: IEEE, 2016. 4165-4169 [86] Li C, Min X, Sun S Q, Lin W Q, Tang Z C. DeepGait:a learning deep convolutional representation for view-invariant gait recognition using joint Bayesian. Applied Sciences, 2017, 7(3):210 doi: 10.3390/app7030210 [87] Simonyan K, Zisserman A. Very deep convolutional networks for large-scale image recognition. In: Proceedings of the 2015 International Conference on Pattern Recognition. California, USA: ICPR, 2015. 212-218 [88] Yu S Q, Chen H F, Wang Q, Shen L L, Huang Y Z. Invariant feature extraction for gait recognition using only one uniform model. Neurocomputing, 2017, 239:81-93 doi: 10.1016/j.neucom.2017.02.006 [89] Gers F A, Schraudolph N N, Schmidhuber J. Learning precise timing with LSTM recurrent networks. Journal of Machine Learning Research, 2002, 3:115-143 http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=89ea080d0ed753eb233a54138e933da4 [90] 王坤峰, 苟超, 段艳杰, 林懿伦, 郑心湖, 王飞跃.生成式对抗网络GAN的研究进展与展望.自动化学报, 2017, 43(3):321-332 http://www.aas.net.cn/CN/abstract/abstract19012.shtmlWang Kun-Feng, Gou Chao, Duan Yan-Jie, Lin Yi-Lun, Zheng Xin-Hu, Wang Fei-Yue. Generative adversarial networks:The state of the art and beyond. Acta Automatica Sinica, 2017, 43(3):321-332 http://www.aas.net.cn/CN/abstract/abstract19012.shtml [91] Cao Z, Simon T, Wei S E, Sheikh Y. Realtime multi-person 2D pose estimation using part affinity fields. In: Proceedings of the 2017 IEEE Conference on Computer Vision and Pattern Recognition. Hawaii, USA: CCPR, 2017. 1302-1310 -
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