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AdaBoost作为一个高精度的自适应分类模型,在结构上与神经网络相似,由于不需要做特征筛选,该模型适用于信号特征提取困难的弱光信号。AdaBoost算法是若干个基分类器的带权加性模型,加权组合一系列基分类器,共同决策出结果。在每轮迭代中,根据当前基分类器结果调整样本权重,增大误分类样本权重,使其在下一轮迭代中受到更多关注, 直到达到预期的误差或指定的基分类器迭代次数。由于AdaBoost算法表现优良,已广泛应用于模型预测[20]、目标识别[21]、人脸检测[22]等领域。
传统AdaBoost的基分类器有简单多数投票、加权投票等多种组合方法。仅由错误率构成的对数函数计算而来的基分类器系数不足以反映基分类器性能,计算基分类器系数时需要考虑多种因素。
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AdaBoost算法的基分类器系数αq决定着此基分类器在最终决策中的话语权。αq反映了基分类器的分类效果,在计算αq时,本文中加入对分类正确样本权重分布的考虑。
传统的AdaBoost算法计算系数公式如下:
$ \alpha_q=\frac{1}{2} \ln \left(\frac{1-e_q}{e_q}\right) $
(1) 式中,eq表示第q次分类中错误分类的样本权重和。
本文中对基分类器系数计算公式重新定义为:
$ \alpha_q=\frac{1}{2} \ln \left(\frac{1-e_q}{e_q}\right)+\kappa \exp \left(c_q\right) $
(2) 式中,κ为常数,cq表示第q个基分类器正确分类样本权重和,如下式:
$ c_q=\sum\limits_{G_q\left(\bar{y}_i\right)=z_i} d_q(i) $
(3) 式中,dq(i)为第q次分类第i个样本的样本权重,Gq(yi)表示第q个基分类器,yi为第i个经过样本权重调整后的待分类样本,zi是第i个待分类样本的类别标签。
从(2)式中可以看出,改进后的αq与错误分类样本分布状态eq和正确分类样本分布状态cq都息息相关。cq反映了正确分类样本分布状态,αq决定着此基分类器在最终决策中的重要性。cq较大时,意味着正确分类的样本数量较多,αq随着cq增加而增加,即增加基分类器分类性能优良的αq,表示此基分类器在最终决策中话语权较大。(2)式克服了AdaBoost算法的αq仅与eq有关,而与正确分类样本分布状态cq无关的不足,能避免因产生冗余和无用基分类器而浪费系统资源和时间开销,从而提升系统性能。本文作者提出改进的AdaBoost基分类器系数αq的算法, 记为W-AdaBoost。
由于AdaBoost算法是一种带权加性模型,算法将训练Q次基分类器,故应当选取计算复杂度小的基分类器进行集成。KNN分类算法简单有效、计算复杂度较低,本文中采用KNN为基分类器。基于KNN的改进AdaBoost算法流程如图 1所示。图中, H(yi)为最终强分类器。
基于KNN的W-AdaBoost算法的具体步骤如下:
(1) 步骤1。给定训练集:将部分MPPC探测信号作为训练集标记为$S=\left\{\left(\hat{y}_1, z_1\right), \left(\hat{y}_2, z_2\right), \cdots, \left(\hat{y}_i, z_i\right)\right.$, $\left.\cdots, \left(\hat{y}_K, z_K\right)\right\}, \hat{y}_i$是实测样本,对于OOK调制信号的检测即为二分类问题,zi是类别标签,zi∈{-1, +1},K表示样本个数。
(2) 步骤2。初始化样本权重:对训练样本集设置相等的初始权重,即d1(i)=1/K; i=1, 2, …, K。
(3) 步骤3。循环q=1, 2, …, Q,Q代表基分类器个数:首先对于第q个基分类器,根据上轮结果对样本集dq(i)进行调整,得到新的带权样本集记为Sq=$\left\{\left(\bar{y}_{q, 1}, z_1\right), \left(\bar{y}_{q, 2}, z_2\right), \cdots, \left(\bar{y}_{q, i}, z_i\right), \cdots, \left(\bar{y}_{q, K}, z_K\right)\right\}, \bar{y}_{q, i}$表示第q次迭代的第i个待分类样本, $G_q\left(\bar{y}_i\right)=z_i$表示分类器将yi分类为zi,本文中最近邻值设为1。
$ G_q\left(\bar{y}_i\right)=\operatorname{argmin}\left\|\hat{y}_{q, i}-\bar{y}_i\right\|_2 $
(4) 式中,$\left\|\hat{y}_{q, i}-\bar{y}_i\right\|_2$表示$\hat{y}_{q, i}$与$\bar{y}_i$之间的欧氏距离,argmin函数表示使$\left\|\hat{y}_{q, i}-\bar{y}_i\right\|_2$取最小值时$\bar{y}_i$的取值,$\hat{y}_{q, i}$表示第q次迭代中第i个训练样本; 其次针对Gq(yi)计算加权错误率eq:
$ e_q=\sum\limits_{G_q\left(\bar{y}_i\right) \neq z_i} d_q(i) $
(5) 然后针对Gq(yi)使用(3)式计算正确分类样本权重和cq; 接着使用(2)式计算基于错误和正确分类样本权重的基分类器Gq(yi)的权重系数αq; 最后更新样本权重:
$ d_{q+1}(i)=\frac{d_q(i) \exp \left[-\alpha_q z_i G_q\left(\bar{y}_i\right)\right]}{Z_q} $
(6) 式中, Zq表示归一化因子,即:
$ Z_q=\sum\limits_{i=1}^K d_q(i) \exp \left[-\alpha_q z_i G_q\left(\bar{y}_i\right)\right] $
(7) (4) 步骤4。得到强分类器:
$ H\left(\bar{y}_i\right)=\operatorname{sgn}\left[\sum\limits_{q=1}^Q \alpha_q G_q\left(\bar{y}_i\right)\right] $
(8) 样本权重也随基分类器系数的变化而变化,本文中计算基分类器系数时考虑了正确分类样本分布状态。在下一次迭代中,分类器将更加关注误分类样本,因并未改变AdaBoost算法的传统结构,保证了算法的收敛性。
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本节中将分析在改进基分类器组合系数、优化样本权重更新策略后提高分类性能的原因。对(7)式进行分解,得到Zq与eq的之间的关系式:
$ \begin{aligned} Z_q= & \sqrt{e_q\left(1-e_q\right)} \exp \left[-\kappa \exp \left(c_q\right)\right]+ \\ & \sqrt{e_q\left(1-e_q\right)} \exp \left[\kappa \exp \left(c_q\right)\right] \end{aligned} $
(9) 将(9)式代入(6)式并化简,可得样本权重更新公式如下:
当Gq(yi)=zi时,
$ d_{q+1}(i)=\frac{d_q(i)}{\left\{1+\exp \left[2 \kappa \exp \left(c_q\right)\right]\right\}\left(1-e_q\right)} $
(10) 当Gq(yi)≠zi时,
$ d_{q+1}(i)=\frac{d_q(i)}{\left\{1+\exp \left[2 \kappa \exp \left(c_q\right)\right]\right\} e_q} $
(11) 将传统AdaBoost的基分类器系数记为αq′,样本权重记为dq′(i),则传统AdaBoost算法样本权重更新公式可表示为:
当Gq(yi)=zi时,
$ d_{q+1}^{\prime}(i)=d_q^{\prime}(i) /\left[2\left(1-e_q\right)\right] $
(12) 当Gq(yi)≠zi时
$ d_{q^{+1}}{ }^{\prime}(i)=d_q{ }^{\prime}(i) /\left(2 e_q\right) $
(13) 对改进W-AdaBoost算法和传统AdaBoost算法样本权重更新(10)式和(11)式、(12)式和(13)式:当Gq(yi)=zi时, $1+\exp \left[2 \kappa \exp \left(c_q\right)\right]>2$,可得$\left\{1+\exp \left[2 \kappa \exp \left(c_q\right)\right]\right\}^{-1} < 1 / 2$,故dq′(i)>dq(i); 当Gq(yi)≠ zi时, $1+\exp \left[2 \kappa \exp \left(c_q\right)\right] < 2$,可$\{1+\exp [2 \kappa \times$$\left.\left.\exp \left(c_q\right)\right]\right\}^{-1}>1 / 2$,故dq′(i) < dq(i)。
通过对比可知,改进W-AdaBoost算法使错误分类dq(i)更大,正确分类dq(i)更小,使样本在参与下一轮迭代时尽力纠正基分类器对错误分类样本的分类结果。
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本节中对(2)式的参数κ值的选取进行讨论,若κ值过大,导致AdaBoost算法无法收敛,若κ值过小,使(2)式性能退化到传统基分类器系数的计算方式,影响系统性能。参考文献[23]中证明了AdaBoost算法的误差收敛上界为$\prod\limits_{q=1}^Q Z_q$,改进算法没有改变样本权值的更新过程,故W-AdaBoost算法误差收敛上界没有改变。κ值的选取满足此误差收敛上界限即可, κ取值范围推导如下:
$ \begin{gathered} Z_q=\left(1-e_q\right) \exp \left(-\alpha_q\right)+e_q \exp \left(\alpha_q\right)= \\ \left(1-e_q\right) \exp \left[-\frac{1}{2} \ln \left(\frac{1-e_q}{e_q}\right)-\kappa \exp \left(c_q\right)\right]+ \\ e_q \exp \left[\frac{1}{2} \ln \left(\frac{1-e_q}{e_q}\right)+\kappa \exp \left(c_q\right)\right]= \\ \sqrt{\left(1-e_q\right) e_q}\left\{\exp \left[\kappa \exp \left(c_q\right)\right]+\right. \\ \left.\exp \left[-\kappa \exp \left(c_q\right)\right]\right\}<1 \end{gathered} $
(14) 即:
$ \begin{gathered} \exp \left[\kappa \exp \left(c_q\right)+\exp \left[-\kappa \exp \left(c_q\right)\right]<\right. \\ 1 / \sqrt{\left(1-e_q\right) e_q} \end{gathered} $
(15) κ值需要满足(15)式,解得κ < 1/120时,eq < 0.494,基分类器误差上界需满足Zq < 1,可保证算法的收敛性,但无法准确解出κ的最佳取值,κ的取值合理即可。
综上所述,W-AdaBoost算法在计算αq时,考虑了正确分类样本分布状态,使基分类器将更关注错误分类样本,评价基分类器性能更加全面,故算法分类精度也更高。
基于改进的AdaBoost无线光通信信号检测算法
Signal detection algorithm of wireless optical communication based on the improved AdaBoost
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摘要: 为了提升无线光通信系统接收灵敏度, 采用一种基于改进基分类器系数的AdaBoost弱光信号检测算法, 解决多像素光子计数器(MPPC)在弱光条件下的信号检测问题。该算法采用k最近邻(KNN)为基分类器组建强分类器, 针对传统AdaBoost算法基分类器系数仅与错误率有关而产生冗余的基分类器消耗系统资源的问题, 提出一种基于错误和正确分类样本权重的基分类器系数优化AdaBoost算法(W-AdaBoost), 将信号解调问题转换为分类问题; 并采用波长450 nm半导体激光器、MPPC光电转换器件搭建了无线光通信系统。结果表明, 系统在通信速率为2 Mbit/s、误比特率为3.8×10-3时, 改进的W-AdaBoost-KNN算法较传统AdaBoost-KNN和单一KNN算法, 灵敏度分别提升了1.6 dB和4.8 dB左右。此研究结果说明W-AdaBoost-KNN算法可提高弱光条件下的信号检测效率, 提升无线光通信系统接收灵敏度。
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关键词:
- 光通信 /
- AdaBoost算法 /
- 多像素光子计数器 /
- 集成学习 /
- 信号检测
Abstract: In order to improve the receiving sensitivity of the wireless optical communication system, an AdaBoost weak-light signal detection algorithm based on the improved base classifier coefficient was adopted to solve the signal detection problem of multi-pixel photon counter (MPPC) under weak-light conditions. In this algorithm, k-nearest neighbor (KNN) was used as the base classifier to build a strong classifier. A W-AdaBoost algorithm based on the weights of incorrect and correct classification samples was proposed to solve the problem of that the traditional AdaBoost algorithm's base classifier coefficients are only related to the error rate, which causes redundant base classifiers to consume system resources. The W-AdaBoost algorithm transforms the issue of signal demodulation into classification, a 450 nm semiconductor laser and MPPC photoelectric conversion device are used to build a wireless optical communication system. The experimental results show that the sensitivity of the improved W-AdaBoost-KNN algorithm is about 1.6 dB and 4.8 dB higher than that of the traditional AdaBoost-KNN algorithm and the single KNN algorithm respectively, when the communication rate of the system is 2 Mbit/s and the bit error rate is 3.8×10-3. The research results show that W-AdaBoost-KNN algorithm can improve the signal detection efficiency under weak-light conditions and improve the receiving sensitivity of the wireless optical communication systems. -
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