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摘要: 深度学习是一门依赖于数据的科学, 传统深度学习方法假定在平衡数据集上训练模型, 然而, 现实世界中大规模数据集通常表现出长尾分布现象, 样本数量众多的少量头部类主导模型训练, 而大量尾部类样本数量过少, 难以得到充分学习. 近年来, 长尾学习掀起学术界的研究热潮, 涌现出大量先进的工作. 本文综合梳理和分析了近年来发表在高水平会议或期刊上的文献, 对长尾学习进行全面的综述. 具体而言, 根据深度学习模型设计流程, 将图像识别领域的长尾学习算法分为丰富样本数量与语义信息的优化样本空间方法, 关注特征提取器、分类器、logits和损失函数这四个基本组成部分的优化模型方法以及通过引入帮助模型训练的辅助任务, 在多个空间共同优化长尾学习模型的辅助任务学习3大类, 并根据提出的分类方法综合对比分析每类长尾学习方法的优缺点. 然后, 进一步将基于样本数量的狭义长尾学习概念推广至多尺度广义长尾学习. 此外, 本文对文本数据、语音数据等其它数据形式下的长尾学习算法进行简要评述. 最后, 讨论了目前长尾学习面临的可解释性较差、数据质量较低等挑战, 并展望了如多模态长尾学习、半监督长尾学习等未来具有潜力的发展方向.Abstract: Deep learning is a science that depends on data. Traditional deep learning methods unrealistically assume that the training models are on balanced datasets. In real-world large-scale datasets, a long-tailed distribution often occurs, with a few head classes having many samples dominating model training, while many tail classes have too few samples to be adequately learned. In recent years, the long-tailed learning has set off a research upsurge in academic circles. In this paper, we synthesize and analyze the literature published in high-level conferences or journals to provide a comprehensive survey of long-tailed learning. Specifically, we categorize long-tailed learning algorithms in the field of image recognition according to the design process of deep learning models into three main types: optimizing the sample space by enriching the quantity and semantic information of samples, optimizing the model by focusing on the four fundamental components of feature extractor, classifier, logits, and loss function, and auxiliary task learning, which involves introducing auxiliary tasks to aid model training and jointly optimizing long-tailed learning models across multiple spaces. Additionally, a comprehensive comparative analysis of the strengths and weaknesses of each category is conducted based on the proposed classification method. We further extend the concept of narrow long-tail learning based on the number of samples to multi-scale generalized long-tailed learning. In addition, we briefly review long-tailed learning algorithms in other data forms such as text data. Finally, we discussed the current challenges faced by long-tailed learning, such as poor interpretability and low data quality, and explored promising future directions such as multimodal long-tailed learning and semi-supervised long-tailed learning.
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肺癌是世界范围内发病率和死亡率最高的疾病之一, 占所有癌症病发症的18 %左右[1].美国癌症社区统计显示, 80 %到85 %的肺癌为非小细胞肺癌[2].在该亚型中, 大多数病人会发生淋巴结转移, 在手术中需对转移的淋巴结进行清扫, 现阶段通常以穿刺活检的方式确定淋巴结的转移情况.因此, 以非侵入性的方式确定淋巴结的转移情况对临床治疗具有一定的指导意义[3-5].然而, 基本的诊断方法在无创淋巴结转移的预测上存在很大挑战.
影像组学是针对医学影像的兴起的热门方法, 指通过定量医学影像来描述肿瘤的异质性, 构造大量纹理图像特征, 对临床问题进行分析决策[6-7].利用先进机器学习方法实现的影像组学已经大大提高了肿瘤良恶性的预测准确性[8].研究表明, 通过客观定量的描述影像信息, 并结合临床经验, 对肿瘤进行术前预测及预后分析, 将对临床产生更好的指导价值[9].
本文采用影像组学的方法来解决非小细胞肺癌淋巴结转移预测的问题.通过利用套索逻辑斯特回归(Lasso logistics regression, LLR)[10]模型得出基本的非小细胞肺癌淋巴结的转移预测概率, 并把组学模型的预测概率作为独立的生物标志物, 与患者的临床特征一起构建多元Logistics预测模型并绘制个性化诺模图, 在临床决策中的起重要参考作用.
1. 材料和方法
1.1 病人数据
我们收集了广东省人民医院2007年5月至2014年6月期间的717例肺癌病例.这些病人在签署知情同意书后, 自愿提供自己的信息作为研究使用.为了充分利用收集到的数据对非小细胞肺癌淋巴结转移预测, 即对$N1-N3$与$N0$进行有效区分, 我们对收集的数据设置了三个入组标准: 1)年龄大于等于18周岁, 此时的肺部已经发育完全, 消除一定的干扰因素; 2)病理诊断为非小细胞肺癌无其他疾病干扰, 并有完整的CT (Computed tomography)增强图像及个人基本信息; 3)有可利用的术前病理组织活检分级用于确定N分期.经筛选, 共564例病例符合进行肺癌淋巴结转移预测研究的要求(如图 1).
为了得到有价值的结果, 考虑到数据的分配问题, 为了保证客观性, 防止挑数据的现象出现, 在数据分配上, 训练集与测试集将按照时间进行划分, 并以2013年1月为划分点.得到训练集: 400例, 其中, 243例正样本$N1-N3$, 157例负样本$N0$; 测试集: 164例, 其中, 93例正样本, 71例负样本.
1.2 病灶分割
在进行特征提取工作前, 首先要对肿瘤病灶进行分割.医学图像分割的金标准是需要有经验的医生进行手动勾画的结果.但手动分割无法保证每次的分割结果完全一致, 且耗时耗力, 尤其是在数据量很大的情况下.因此, 手动分割不是最理想的做法.在本文中, 使用的自动图像分割算法为基于雪橇的自动区域生长分割算法[11], 该算法首先选定最大切片层的种子点, 这时一般情况下最大切片为中间层的切片, 然后估计肿瘤的大小即直径, 作为一个输入参数, 再自动进行区域生长得到每个切片的肿瘤如图 2(a1), (b1), 之后我们进行雪橇滑动到邻接的上下两个切面, 进行分割, 这样重复上述的区域生长即滑动切片, 最终分割得到多个切片的的肿瘤区域, 我们将肿瘤切面层进行组合, 得到三维肿瘤如图 2(a2), (b2).
1.3 特征的提取与筛选
利用影像组学处理方法, 从分割得到的肿瘤区域中总共提取出386个特征.这些特征可分为四组:三维形状特征, 表面纹理特征, Gabor特征和小波特征[12-13].形状特征通过肿瘤体积、表面积、体积面积比等特征描述肿瘤在空间和平面上的信息.纹理特征通过统计三维不同方向上像素的规律, 通过不同的分布规律来表示肿瘤的异质性. Gabor特征指根据特定方向, 特定尺度筛选出来的纹理信息.
小波特征是指原图像经过小波变换滤波器后的纹理特征.在模式识别范畴中, 高维特征会增加计算复杂度, 此外, 高维的特征往往存在冗余性, 容易造成模型过拟合.因此, 本位通过特征筛选方法首先对所有特征进行降维处理.
本文采用$L$1正则化Lasso进行特征筛选, 对于简单线性回归模型定义为:
$$ \begin{equation} f(x)=\sum\limits_{j=1}^p {w^jx^j} =w^\mathrm{T}x \end{equation} $$ (1) 其中, $x$表示样本, $w$表示要拟合的参数, $p$表示特征的维数.
要进行参数$w$学习, 应用二次损失来表示目标函数, 即:
$$ \begin{equation} J(w)=\frac{1}{n}\sum\limits_{i=1}^n{(y_i-f(x_i)})^2= \frac{1}{n}\vert\vert\ {{y}-Xw\vert\vert}^2 \end{equation} $$ (2) 其中, $X$是数据矩阵, $X=(x_1 , \cdots, x_n)^\mathrm{T}\in {\bf R}^{n\times p}$, ${y}$是由标签组成的列向量, ${y}=(y_1, \cdots, y_n )^\mathrm{T}$.
式(2)的解析解为:
$$ \begin{equation} \hat{w}=(X^\mathrm{T}X)^{-1}X^\mathrm{T}{y} \end{equation} $$ (3) 然而, 若$p\gg n$, 即特征维数远远大于数据个数, 矩阵$X^\mathrm{T}X$将不是满秩的, 此时无解.
通过Lasso正则化, 得到目标函数:
$$ \begin{equation} J_L(w)=\frac{1}{n} \vert\vert{y}-Xw\vert\vert^2+\lambda\vert\vert w\vert\vert _1 \end{equation} $$ (4) 目标函数最小化等价为:
$$ \begin{equation} \mathop {\min }\limits_w \frac{1}{n} \vert\vert{y}-Xw\vert\vert^2, \, \, \, \, \, \, \, \mathrm{s.t.}\, \, \vert \vert w\vert \vert _1 \le C \end{equation} $$ (5) 为了使部分特征排除, 本文采用$L$1正则方法进行压缩.二维情况下, 在$\mbox{(}w^1, w^2)$平面上可画出目标函数的等高线, 取值范围则为平面上半径为$C$的$L$1范数圆, 等高线与$L$1范数圆的交点为最优解. $L$1范数圆和每个坐标轴相交的地方都有"角''出现, 因此在角的位置将产生稀疏性.而在维数更高的情况下, 等高线与L1范数球的交点除角点之外还可能产生在很多边的轮廓线上, 同样也会产生稀疏性.对于式(5), 本位采用近似梯度下降(Proximal gradient descent)[14]算法进行参数$w$的迭代求解, 所构造的最小化函数为$Jl=\{g(w)+R(w)\}$.在每次迭代中, $Jl(w)$的近似计算方法如下:
$$ \begin{align} J_L (w^t+d)&\approx \tilde {J}_{w^t} (d)=g(w^t)+\nabla g(w^t)^\mathrm{T}d\, +\nonumber\\ &\frac{1} {2d^\mathrm{T}(\frac{I }{ \alpha })d}+R(w^t+d)=\nonumber\\ &g(w^t)+\nabla g(w^t)^\mathrm{T}d+\frac{{d^\mathrm{T}d} } {2\alpha } +\nonumber\\ &R(w^t+d) \end{align} $$ (6) 更新迭代$w^{(t+1)}\leftarrow w^t+\mathrm{argmin}_d \tilde {J}_{(w^t)} (d)$, 由于$R(w)$整体不可导, 因而利用子可导引理得:
$$ \begin{align} w^{(t+1)}&=w^t+\mathop {\mathrm{argmin}} \nabla g(w^t)d^\mathrm{T}d\, +\nonumber\\ &\frac{d^\mathrm{T}d}{2\alpha }+\lambda \vert \vert w^t+d\vert \vert _1=\nonumber\\ &\mathrm{argmin}\frac{1 }{ 2}\vert \vert u-(w^t-\alpha \nabla g(w^t))\vert \vert ^2+\nonumber\\ &\lambda \alpha \vert \vert u\vert \vert _1 \end{align} $$ (7) 其中, $S$是软阈值算子, 定义如下:
$$ \begin{equation} S(a, z)=\left\{\begin{array}{ll} a-z, &a>z \\ a+z, &a<-z \\ 0, &a\in [-z, z] \\ \end{array}\right. \end{equation} $$ (8) 整个迭代求解过程为:
输入.数据$X\in {\bf R}^{n\times p}, {y}\in {\bf R}^n$, 初始化$w^{(0)}$.
输出.参数$w^\ast ={\rm argmin}_w\textstyle{1 \over n}\vert \vert Xw-{y}\vert \vert ^2+\\ \lambda \vert\vert w\vert \vert _1 $.
1) 初始化循环次数$t = 0$;
2) 计算梯度$\nabla g=X^\mathrm{T}(Xw-{y})$;
3) 选择一个步长大小$\alpha ^t$;
4) 更新$w\leftarrow S(w-\alpha ^tg, \alpha ^t\lambda )$;
5) 判断是否收敛或者达到最大迭代次数, 未收敛$t\leftarrow t+1$, 并循环2)$\sim$5)步.
通过上述迭代计算, 最终得到最优参数, 而参数大小位于软区间中的, 将被置为零, 即被稀疏掉.
1.4 建立淋巴结转移影像组学标签与预测模型
本文使用LLR对组学特征进行降维并建模, 并使用10折交叉验证, 提高模型的泛化能力, 流程如图 3所示.
将本文使用的影像组学模型的预测概率(Radscore)作为独立的生物标志物, 并与临床指标中显著的特征结合构建多元Logistics模型, 绘制个性化预测的诺模图, 最后通过校正曲线来观察预测模型的偏移情况.
2. 结果
2.1 数据单因素分析结果
我们分别在训练集和验证集上计算各个临床指标与淋巴结转移的单因素P值, 计算方式为卡方检验, 结果见表 1, 发现吸烟与否和EGFR (Epidermal growth factor receptor)基因突变状态与淋巴结转移显著相关.
表 1 训练集和测试集病人的基本情况Table 1 Basic information of patients in the training set and test set基本项 训练集($N=400$) $P$值 测试集($N=164$) $P$值 性别 男 144 (36 %) 0.896 78 (47.6 %) 0.585 女 256 (64 %) 86 (52.4 %) 吸烟 是 126 (31.5 %) 0.030* 45 (27.4 %) 0.081 否 274 (68.5 %) 119 (72.6 %) EGFR 缺失 36 (9 %) 4 (2.4 %) 突变 138 (34.5 %) $ < $0.001* 67 (40.9 %) 0.112 正常 226 (56.5 %) 93 (56.7 %) 2.2 淋巴结转移影像组学标签
影像组学得分是每个病人最后通过模型预测后的输出值, 随着特征数的动态变化, 模型输出的AUC (Area under curve)值也随之变化, 如图 4所示, 使用R语言的Glmnet库可获得模型的参数$\lambda $的变化图.图中直观显示了参数$\lambda $的变化对模型性能的影响, 这次实验中模型选择了3个变量.如图 5所示, 横坐标表示$\lambda $的变化, 纵坐标表示变量的系数变化, 当$\lambda $逐渐变大时, 变量的系数逐渐减少为零, 表示变量选择的过程, 当$\lambda $越大表示模型的压缩程度越大.
图 4 $\lambda $与变量数目对应走势Fig. 4 The trend of the parameters and the number of variables通过套索回归方法, 自动的将变量压缩为3个, 其性能从图 4中也可发现, 模型的AUC值为最佳, 最终的特征如表 2所示. $V0$为截距项; $V179$为横向小波分解90度共生矩阵Contrast特征; $V230$为横向小波分解90度共生矩阵Entropy特征.
表 2 Lasso选择得到的参数Table 2 Parameters selected by LassoLasso选择的参数 含义 数值 $P$值 $V0$ 截距项 2.079115 $V179$ 横向小波分解90度共生矩阵Contrast特征(Contrast_2_90) 0.0000087 < 0.001*** $V230$ 横向小波分解90度共生矩阵Entropy特征(Entropy_3_180) $-$3.573315 < 0.001*** $V591$ 表面积与体积的比例(Surface to volume ratio) $-$1.411426 < 0.001*** $V591$为表面积与体积的比例; 将三个组学特征与$N$分期进行单因素分析, 其$P$值都是小于0.05, 表示与淋巴结转移有显著相关性.根据Lasso选择后的三个变量建立Logistics模型并计算出Rad-score, 详见式(9).并且同时建立SVM (Support vector machine)模型.
NB (Naive Bayesian)模型, 进行训练与预测, LLR模型训练集AUC为0.710, 测试集为0.712, 表现较优; 如表 3所示.将实验中使用的三个机器学习模型的结果进行对比, 可以发现, LLR的实验结果是最好的.
表 3 不同方法对比结果Table 3 Comparison results of different methods方法 训练集(AUC) 测试集(AUC) 召回率 LLR 0.710 0.712 0.75 SVM 0.698 0.654 0.75 NB 0.718 0.681 0.74 $$ \begin{equation} \begin{aligned} &\text{Rad-score}=2.328373+{\rm Contrast}\_2\_90\times\\ &\qquad 0.0000106 -{\rm entropy}\_3\_180\times 3.838207 +\\ &\qquad\text{Maximum 3D diameter}\times 0.0000002 -\\ &\qquad\text{Surface to volume ratio}\times 1.897416 \\ \end{aligned} \end{equation} $$ (9) 2.3 诺模图个性化预测模型
为了体现诺模图的临床意义, 融合Rad-score, 吸烟情况和EGFR基因因素等有意义的变量进行分析, 绘制出个性化预测的诺模图, 如图 7所示.为了给每个病人在最后得到一个得分, 需要将其对应变量的得分进行相加, 然后在概率线找到对应得分的概率, 从而实现非小细胞肺癌淋巴结转移的个性化预测.我们通过一致性指数(Concordance index, $C$-index)对模型进行了衡量, 其对应的$C$-index为0.724.
本文中使用校正曲线来验证诺模图的预测效果, 如图 8所示, 由校正曲线可以看出, 预测结果基本上没有偏离真实标签的结果, 表现良好, 因此, 该模型具有可靠的预测性能[15].
3. 结论
在构建非小细胞肺癌淋巴结转移的预测模型中, 使用LLR筛选组学特征并构建组学标签, 并与显著的临床特征构建多元Logistics模型, 绘制个性化预测的诺模图.其中LLR模型在训练集上的AUC值为0.710, 在测试集上的AUC值为0.712, 利用多元Logistics模型绘制个性化预测的诺模图, 得到模型表现能力$C$-index为0.724 (95 % CI: 0.678 $\sim$ 0.770), 并且在校正曲线上表现良好, 所以个性化预测的诺模图在临床决策上可起重要参考意义.[16].
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图 1 深度长尾学习研究综述组织结构图
Fig. 1 Organizational Structure Diagram of a Survey on Deep Long-Tail Learning Research
图 8 优化样本空间各方法关系示意图
Fig. 8 Diagram of Relationships Among Various Methods for Optimizing Sample Space
图 14 辅助任务学习各方法关系示意图
Fig. 14 Diagram of the Relationships Among Various Methods in Auxiliary Task Learning
图 20 类间样本数量长尾分布与类内属性长尾分布示例图
Fig. 20 Example Diagram of Long-Tail Distribution of Inter-Class Sample Counts and Intra-Class Attributes
表 1 常见长尾数据集基本信息
Table 1 Basic Information of Common Long-Tail Datasets
类型 数据集 类别数量 训练集样本数量 测试集样本数量 最大类样本数量 最小类样本数量 图像分类 CIFAR10-LT[13] 10 50000 10000 5000 5($ \rho$=100), 50($ \rho$=10) 图像分类 CIFAR100-LT[13] 100 50000 10000 500 5($ \rho$=100), 50($ \rho$=10) 目标检测 ImageNet-LT[62] 1000 115846 50000 1280 5 场景识别 Places-LT[62] 365 62500 36500 4980 5 人脸识别 MS1M-LT[62] 74500 (ID)887530 3530 598 1 目标检测 iNaturalist2017[63] 5089 579184 182707 196613 381 目标检测 iNaturalist 2018[63] 8142 437513 24426 127551 19 实例分割 LVIS v0.5[64] 1230 57000 20000 26148 1 实例分割 LVIS v1[64] 1203 100170 19822 50552 1 场景理解 SUN-LT[65] 397 4084 2868 12 2 目标检测 AWA-LT[65] 50 6713 6092 720 2 鸟类识别 CUB-LT[65] 200 2945 2348 43 2或3 图像分类 STL10-LT[66] 10 5000 8000 500 5($ \rho$=100), 50($ \rho$=10) 目标检测 VOC-LT[67] 20 1142 4952 775 4 视频分类 VideoLT[68] 1004 179352 51244 1912 44 
下载: 导出CSV
表 2 长尾图像识别方法比较
Table 2 Comparison of Long-Tail Image Recognition Methods
分类 代表性文献 优点 缺点 优化样本空间 重采样 [1, 2, 56, 80, 70, 82, 30, 169] 简单通用, 理论直观, 易于操作 1)会丢弃大量头部类有效信息
2)重复采样尾部类不能增加有效信息, 并容易引发过拟合
3)易引入其它噪声数据增强 [2, 8, 9, 15, 76, 88, 89, 94, 95] 样本变换法成本较低, 易与其它方法结合, 灵活性较高. 语义增强法丰富尾部样本的语义信息, 生成具有现实意义的新样本 1)样本变换法引入大量新数据, 增加模型训练成本, 且可能生成毫无意义的样本, 鲁棒性较差.
2)语义增强方法需设计专门的模型结构, 操作复杂. 并过于依赖于头部类数据质量, 易给模型带来新的偏置.优化模型空间 优化特征提取器 [107, 108, 109, 111, 112, 170] 有效增强样本上下文语义特征帮助模型学到无偏的特征表示 1)引入大量参数, 占用内存, 降低训练效率
2)可解释性较差优化分类器 [1, 16, 26, 113, 115, 116, 118, 119] 计算开销小, 训练稳定无需设计额外的损失函数或存储单元 1)对超参数和优化器的选择敏感, 试错代价高
2)灵活性较低, 在目标检测与实例分割任务上表现不佳logits调整 [12, 28, 30, 55, 71, 120, 122] 既能优化训练过程, 又能进行事后修正. 计算开销较低, 泛化性能良好, 易与其它方法结合. 1)依赖于数据集的先验分布
2)修正后的边际分布可能不满足期望分布.代价敏感加权损失函数 [11, 12, 54, 72, 127, 129, 133] 操作简单, 易于实现, 计算开销较小, 适应于实际应用场景 1)优化困难, 参数敏感, 难以处理大规模真实场景
2)头尾性能像“跷跷板”, 无法从本质上解决信息缺乏的问题辅助任务学习 解耦学习 [1, 14, 134, 135, 138, 139] 利用大量头部类数据生成泛化能力良好的特征表示能够有效提升模型性能, 且计算成本较低. 1)两阶段方法不利于端到端的模型训练与部署
2)对数据依赖性较强
3)与其它算法结合使用时需重新设计, 实用性不强度量学习 [40, 58, 59, 127, 145, 149, 151] 便于公式化与计算构建一个正样本接近, 负样本远离的特征空间, 优化决策边界. 1)尾部类样本极少的情况下性能很差.
2)依赖于度量损失函数的设计知识蒸馏 [17, 19, 36, 145, 147, 154] 重用模型资源, 充分利用数据集蕴含的知识. 稳定尾部类学习过程 1)计算开销大, 优化成本相对过高, 对超参数敏感
2)易出现师生不匹配问题, 整体性能过于依赖教师模型的学习情况集成学习 [18, 19, 20, 158, 159, 161] 在头部类和尾部类上都能保持良好性能泛化能力良好, 能够处理未知分布的测试集 1)计算和存储负担过大, 框架部署复杂
2)专家之间存在相互影响的情况, 难以有效整合专家层次学习 [23, 24, 25, 162] 对数据间的关系进行多粒度建模, 捕捉类间隐式语义关系有助于头尾知识迁移 1)模型设计复杂, 训练成本较高
2)依赖于高质量数据, 有时需要数据集提供外部信息
3)层次划分步骤对后续训练产生过大影响
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