From 65e6f9f6cd5d47998ee20d1c031d25a2b24e9375 Mon Sep 17 00:00:00 2001 From: Tan Date: Wed, 14 Nov 2018 20:17:44 +0800 Subject: [PATCH] =?UTF-8?q?=E5=85=A8=E5=B1=80=E6=9B=B4=E6=96=B0=E7=9B=AE?= =?UTF-8?q?=E5=BD=95=EF=BC=8C=E5=8F=8A=E6=9C=89=E4=BA=9B=E6=A0=BC=E5=BC=8F?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- ch02_机器学习基础/第二章_机器学习基础.md | 247 +++++++------- ch03_深度学习基础/第三章_深度学习基础.pdf | Bin 0 -> 3762225 bytes ...络(CNN)(修改版).md => 第五章 卷积神经网络(CNN).md} | 20 +- .../第六章_循环神经网络(RNN).md | 4 + .../第七章_生成对抗网络(GAN).md | 38 ++- ch08_目标检测/第八章_目标检测.md | 40 ++- ch09_图像分割/第九章_图像分割.md | 17 +- ch10_强化学习/第十章_强化学习.md | 9 +- ch11_迁移学习/第十一章_迁移学习.md | 6 +- .../第十二章_网络搭建及训练.md | 7 +- ch13_优化算法/第十三章_优化算法.md | 4 + ch14_超参数调整/第十四章_超参数调整.md | 4 + .../第十五章_异构运算、GPU及框架选型.md | 32 +- ch16_自然语言处理(NLP)/第十六章_NLP.md | 4 + .../第十七章_模型压缩、加速及移动端部署.md | 14 +- .../第十八章_后端架构选型、离线及实时计算.md | 8 +- chap05/img/img1.png | Bin 699253 -> 0 bytes chap05/img/img10.png | Bin 33890 -> 0 bytes chap05/img/img11.png | Bin 25817 -> 0 bytes chap05/img/img12.png | Bin 27636 -> 0 bytes chap05/img/img13.png | Bin 30118 -> 0 bytes chap05/img/img14.png | Bin 10951 -> 0 bytes chap05/img/img17.png | Bin 50416 -> 0 bytes chap05/img/img18.png | Bin 68144 -> 0 bytes chap05/img/img19.png | Bin 81122 -> 0 bytes chap05/img/img2.png | Bin 20750 -> 0 bytes chap05/img/img20.png | Bin 132407 -> 0 bytes chap05/img/img21.png | Bin 97163 -> 0 bytes chap05/img/img24.png | Bin 78461 -> 0 bytes chap05/img/img28.png | Bin 182744 -> 0 bytes chap05/img/img3.png | Bin 56646 -> 0 bytes chap05/img/img4.png | Bin 155430 -> 0 bytes chap05/img/img5.png | Bin 81509 -> 0 bytes chap05/img/img6.png | Bin 70387 -> 0 bytes chap05/img/img62.png | Bin 27312 -> 0 bytes chap05/img/img63.png | Bin 206649 -> 0 bytes chap05/img/img64.png | Bin 267429 -> 0 bytes chap05/img/img66.png | Bin 514612 -> 0 bytes chap05/img/img7.png | Bin 47323 -> 0 bytes chap05/img/img8.png | Bin 42161 -> 0 bytes chap05/img/img9.png | Bin 21412 -> 0 bytes chap05/read | 5 - .../第五章 卷积神经网络(CNN)(修改版).md | 315 ------------------ 43 files changed, 255 insertions(+), 519 deletions(-) create mode 100644 ch03_深度学习基础/第三章_深度学习基础.pdf rename ch05_卷积神经网络(CNN)/{第五章 卷积神经网络(CNN)(修改版).md => 第五章 卷积神经网络(CNN).md} (99%) delete mode 100644 chap05/img/img1.png delete mode 100644 chap05/img/img10.png delete mode 100644 chap05/img/img11.png delete mode 100644 chap05/img/img12.png delete mode 100644 chap05/img/img13.png delete mode 100644 chap05/img/img14.png delete mode 100644 chap05/img/img17.png delete mode 100644 chap05/img/img18.png delete mode 100644 chap05/img/img19.png delete mode 100644 chap05/img/img2.png delete mode 100644 chap05/img/img20.png delete mode 100644 chap05/img/img21.png delete mode 100644 chap05/img/img24.png delete mode 100644 chap05/img/img28.png delete mode 100644 chap05/img/img3.png delete mode 100644 chap05/img/img4.png delete mode 100644 chap05/img/img5.png delete mode 100644 chap05/img/img6.png delete mode 100644 chap05/img/img62.png delete mode 100644 chap05/img/img63.png delete mode 100644 chap05/img/img64.png delete mode 100644 chap05/img/img66.png delete mode 100644 chap05/img/img7.png delete mode 100644 chap05/img/img8.png delete mode 100644 chap05/img/img9.png delete mode 100644 chap05/read delete mode 100644 chap05/第五章 卷积神经网络(CNN)(修改版).md diff --git a/ch02_机器学习基础/第二章_机器学习基础.md b/ch02_机器学习基础/第二章_机器学习基础.md index 053b054..523e68e 100644 --- a/ch02_机器学习基础/第二章_机器学习基础.md +++ b/ch02_机器学习基础/第二章_机器学习基础.md @@ -1,5 +1,3 @@ -### - [TOC] @@ -84,7 +82,7 @@ 下面这张图就是一个神经网络系统,它由很多层组成。输入层负责接收信息,比如一只猫的图片。输出层是计算机对这个输入信息的判断结果,它是不是猫。隐藏层就是对输入信息的传递和加工处理。 ![](./img/ch2/2.6/1.png) -## 2.12 理解局部最优与全局最优 +## 2.7 理解局部最优与全局最优 笑谈局部最优和全局最优 @@ -97,9 +95,9 @@ 2. 函数局部最小点是那种它的函数值小于或等于附近点的点。但是有可能大于较远距离的点。 3. 全局最小点是那种它的函数值小于或等于所有的可行点。 -## 2.7 分类算法 +## 2.8 分类算法 -### 2.7 常用分类算法的优缺点? +### 2.8.1 常用分类算法的优缺点? |算法|优点|缺点| |:-|:-|:-| @@ -111,12 +109,12 @@ |Neural Network 神经网络|1)分类准确率高。2)并行处理能力强。3)分布式存储和学习能力强。4)鲁棒性较强,不易受噪声影响。|1)需要大量参数(网络拓扑、阀值、阈值)。2)结果难以解释。3)训练时间过长。| |Adaboosting|1)adaboost是一种有很高精度的分类器。2)可以使用各种方法构建子分类器,Adaboost算法提供的是框架。3)当使用简单分类器时,计算出的结果是可以理解的。而且弱分类器构造极其简单。4)简单,不用做特征筛选。5)不用担心overfitting。|对outlier比较敏感| -### 2.8 正确率能很好的评估分类算法吗? +### 2.8.2 正确率能很好的评估分类算法吗? 不同算法有不同特点,在不同数据集上有不同的表现效果,根据特定的任务选择不同的算法。如何评价分类算法的好坏,要做具体任务具体分析。对于决策树,主要用正确率去评估,但是其他算法,只用正确率能很好的评估吗? 答案是否定的。 正确率确实是一个很直观很好的评价指标,但是有时候正确率高并不能完全代表一个算法就好。比如对某个地区进行地震预测,地震分类属性分为0:不发生地震、1发生地震。我们都知道,不发生的概率是极大的,对于分类器而言,如果分类器不加思考,对每一个测试样例的类别都划分为0,达到99%的正确率,但是,问题来了,如果真的发生地震时,这个分类器毫无察觉,那带来的后果将是巨大的。很显然,99%正确率的分类器并不是我们想要的。出现这种现象的原因主要是数据分布不均衡,类别为1的数据太少,错分了类别1但达到了很高的正确率缺忽视了研究者本身最为关注的情况。 -### 2.9 分类算法的评估方法? +### 2.8.3 分类算法的评估方法? 1. **几个常用的术语** 这里首先介绍几个*常见*的 模型评价术语,现在假设我们的分类目标只有两类,计为正例(positive)和负例(negative)分别是: 1) True positives(TP): 被正确地划分为正例的个数,即实际为正例且被分类器划分为正例的实例数(样本数); @@ -157,13 +155,13 @@ References [1] 李航. 统计学习方法[M]. 北京:清华大学出版社,2012. -### 2.10 什么样的分类器是最好的? +### 2.8.4 什么样的分类器是最好的? 对某一个任务,某个具体的分类器不可能同时满足或提高所有上面介绍的指标。 如果一个分类器能正确分对所有的实例,那么各项指标都已经达到最优,但这样的分类器往往不存在。比如之前说的地震预测,既然不能百分百预测地震的发生,但实际情况中能容忍一定程度的误报。假设在1000次预测中,共有5次预测发生了地震,真实情况中有一次发生了地震,其他4次则为误报。正确率由原来的999/1000=99.9下降为996/10000=99.6。召回率由0/1=0%上升为1/1=100%。对此解释为,虽然预测失误了4次,但真的地震发生前,分类器能预测对,没有错过,这样的分类器实际意义更为重大,正是我们想要的。在这种情况下,在一定正确率前提下,要求分类器的召回率尽量高。 -## 2.13 逻辑回归 +## 2.9 逻辑回归 -### 2.13 理解逻辑回归 +### 2.9.1 理解逻辑回归 **回归划分**: 广义线性模型家族里,依据因变量不同,可以有如下划分: @@ -180,13 +178,13 @@ Logistic回归的因变量可以是二分类的,也可以是多分类的,但 4. 仅能用于线性问题。只有当目标和特征是线性关系时,才能用逻辑回归。在应用逻辑回归时注意两点:一是当知道模型是非线性时,不适用逻辑回归;二是当使用逻辑回归时,应注意选择和目标为线性关系的特征。 5. 各特征之间不需要满足条件独立假设,但各个特征的贡献独立计算。 -### 2.14 逻辑回归与朴素贝叶斯有什么区别? +### 2.9.2 逻辑回归与朴素贝叶斯有什么区别? 1. 逻辑回归时生成模型,朴素贝叶斯是判别模型,所以生成和判别的所有区别它们都有。 2. 朴素贝叶斯属于贝叶斯,逻辑回归是最大似然,两种概率哲学间的区别。 3. 朴素贝叶斯需要独立假设。 4. 逻辑回归需要求特征参数间是线性的。 -### 2.15 线性回归与逻辑回归的区别?(贡献者:黄钦建-华南理工大学) +### 2.9.3线性回归与逻辑回归的区别?(贡献者:黄钦建-华南理工大学) 线性回归的样本的输出,都是连续值,$ y\in (-\infty ,+\infty )$,而逻辑回归中$y\in (0,1)$,只能取0和1。 @@ -223,14 +221,14 @@ $\theta ^{T}x=0$就相当于是1类和0类的决策边界: 1. 拟合函数和预测函数什么关系呢?其实就是将拟合函数做了一个逻辑函数的转换,转换后使得$y^{(i)} \in (0,1)$; 2. 最小二乘和最大似然估计可以相互替代吗?回答当然是不行了。我们来看看两者依仗的原理:最大似然估计是计算使得数据出现的可能性最大的参数,依仗的自然是Probability。而最小二乘是计算误差损失。 -## 2.16 代价函数 +## 2.10 代价函数 -### 2.16 为什么需要代价函数? +### 2.10.1 为什么需要代价函数? 1. 为了得到训练逻辑回归模型的参数,需要一个代价函数,通过训练代价函数来得到参数。 2. 用于找到最优解的目的函数。 -### 2.17 代价函数作用原理 +### 2.10.2 代价函数作用原理 在回归问题中,通过代价函数来求解最优解,常用的是平方误差代价函数。有如下假设函数: $$ h(x) = A + Bx @@ -252,11 +250,11 @@ $$ ![](./img/ch2/2.16/2.png) -### 2.18 为什么代价函数要非负? +### 2.10.3 为什么代价函数要非负? 目标函数存在一个下界,在优化过程当中,如果优化算法能够使目标函数不断减小,根据单调有界准则,这个优化算法就能证明是收敛有效的。 只要设计的目标函数有下界,基本上都可以,代价函数非负更为方便。 -### 2.19 常见代价函数? +### 2.10.4 常见代价函数? 1. **二次代价函数(quadratic cost)**: $$ J = \frac{1}{2n}\sum_x\Vert y(x)-a^L(x)\Vert^2 @@ -301,7 +299,7 @@ $$ 与sigmoid搭配使用的交叉熵函数:`tf.nn.sigmoid_cross_entropy_with_logits()`。 与softmax搭配使用的交叉熵函数:`tf.nn.softmax_cross_entropy_with_logits()`。 -### 2.20 为什么用交叉熵代替二次代价函数 +### 2.10.5 为什么用交叉熵代替二次代价函数 1. **为什么不用二次方代价函数** 由2.18节可知,权值$w$和偏置$b$的偏导数为$\frac{\delta J}{\delta w}=(a-y)\delta'(z)x$,$\frac{\delta J}{\delta b}=(a-y)\delta'(z)$, 偏导数受激活函数的导数影响,sigmoid函数导数在输出接近0和1时非常小,会导致一些实例在刚开始训练时学习得非常慢。 @@ -313,14 +311,14 @@ $$ $$ 由以上公式可知,权重学习的速度受到$\delta{(z)}-y$影响,更大的误差,就有更快的学习速度,避免了二次代价函数方程中因$\delta'{(z)}$导致的学习缓慢的情况。 -## 2.21 损失函数 +## 2.11 损失函数 -### 2.21 什么是损失函数? +### 2.11.1 什么是损失函数? 损失函数(Loss function)又叫做误差函数,用来衡量算法的运行情况,估量模型的预测值 与真实值 的不一致程度,是一个非负实值函数,通常使用 来表示,损失函数越小,模型的鲁棒性就越好。 损失函数是经验风险函数的核心部分,也是结构风险函数重要组成部分。 -### 2.22 常见的损失函数 +### 2.11.2 常见的损失函数 机器学习通过对算法中的目标函数进行不断求解优化,得到最终想要的结果。分类和回归问题中,通常使用损失函数或代价函数作为目标函数。 损失函数用来评价预测值和真实值不一样的程度。通常损失函数越好,模型的性能也越好。 损失函数可分为经验风险损失函数和结构风险损失函数。经验风险损失函数指预测结果和实际结果的差别,结构风险损失函数是在经验风险损失函数上加上正则项。 @@ -389,7 +387,7 @@ $$ $$ 其中$l(wx_i+by_i)$是Hinge损失函数,$\Vert w^2\Vert$可看做为正则化项。 -### 2.23 逻辑回归为什么使用对数损失函数? +### 2.11.3 逻辑回归为什么使用对数损失函数? 假设逻辑回归模型 TODO 假设逻辑回归模型的概率分布是伯努利分布,其概率质量函数为 @@ -404,7 +402,7 @@ TODO TODO 由此可看出,对数损失函数与极大似然估计的对数似然函数本质上是相同的。所以逻辑回归直接采用对数损失函数。 -### 2.24 对数损失函数是如何度量损失的? +### 2.11.4 对数损失函数是如何度量损失的? 举例: 高斯分布中,我们需要确定均值 和标注差 。 如何确定这两个参数?最大似然估计是比较常用的方法。最大似然的目标是找到一些参数值,这些参数值对应的分布可以最大化观测到数据的概率。 @@ -425,9 +423,9 @@ TODO TODO 同理,可计算TODO。 -## 2.25 梯度下降 +## 2.12 梯度下降 -### 2.25 机器学习中为什么需要梯度下降? +### 2.12.1 机器学习中为什么需要梯度下降? 1. 梯度下降是迭代法的一种,可以用于求解最小二乘问题。 2. 在求解机器学习算法的模型参数,即无约束优化问题时,主要有梯度下降法(Gradient Descent)和最小二乘法。 @@ -435,7 +433,7 @@ TODO 4. 如果我们需要求解损失函数的最大值,可通过梯度上升法来迭代。梯度下降法和梯度上升法可相互转换。 5. 在机器学习中,梯度下降法主要有随机梯度下降法和批量梯度下降法。 -### 2.26 梯度下降法缺点? +### 2.12.2 梯度下降法缺点? 1. 靠近极小值时收敛速度减慢。 2. 直线搜索时可能会产生一些问题。 3. 可能会“之字形”地下降。 @@ -445,7 +443,7 @@ TODO 2. 梯度的方向是最大方向导数的方向; 3. 梯度的值是最大方向导数的值。 -### 2.27 梯度下降法直观理解? +### 2.12.3 梯度下降法直观理解? 梯度下降法经典图示: ![](./img/ch2/2.25/1.png) @@ -463,7 +461,7 @@ TODO d)判断是否需要终止,如否,返回a); 3. 得到全局最优解或者接近全局最优解。 -### 2.28 梯度下降法算法描述? +### 2.12.4 梯度下降法算法描述? 1. 确定优化模型的假设函数及损失函数。 举例,对于线性回归,假设函数为: TODO @@ -494,7 +492,7 @@ TODO TODO 由此,可看出,当前位置的梯度方向由所有样本决定,上式中TODO的目的是为了便于理解。 -### 2.29 如何对梯度下降法进行调优? +### 2.12.5 如何对梯度下降法进行调优? 实际使用梯度下降法时,各项参数指标不能一步就达到理想状态,对梯度下降法调优主要体现在以下几个方面: 1. **算法迭代步长$\alpha$选择。** 在算法参数初始化时,有时根据经验将步长 初始化为1。实际取值取决于数据样本。可以从大到小,多取一些值,分别运行算法看迭代效果,如果损失函数在变小,则取值有效。如果取值无效,说明要增大步长。但步长太大,有时会导致迭代速度过快,错过最优解。步长太小,迭代速度慢,算法运行时间长。 @@ -503,7 +501,7 @@ TODO 3. **标准化处理。** 由于样本不同,特征取值范围也不同,导致迭代速度慢。为了减少特征取值的影响,可对特征数据标准化,使新期望为0,新方差为1,可节省算法运行时间。 -### 2.30 随机梯度和批量梯度区别? +### 2.12.7 随机梯度和批量梯度区别? 随机梯度下降和批量梯度下降是两种主要梯度下降法,其目的是增加某些限制来加速运算求解。 引入随机梯度下降法与mini-batch梯度下降法是为了应对大数据量的计算而实现一种快速的求解。 下面通过介绍两种梯度下降法的求解思路,对其进行比较。 @@ -553,7 +551,7 @@ d) 收敛速度来说,随机梯度下降法一次迭代一个样本,导致 对于总数为$m$个样本的数据,根据样本的数据,选取其中的$n(1< n< m)$个子样本来迭代。其参数$\theta$按梯度方向更新$\theta_i$公式如下: TODO -### 2.31 各种梯度下降法性能比较 +### 2.12.8 各种梯度下降法性能比较 下表简单对比随机梯度下降(SGD)、批量梯度下降(BGD)、小批量梯度下降(mini-batch GD)、和online GD的区别,主要区别在于如何选取训练数据: ||BGD|SGD|Mini-batch GD|Online GD| |:-:|:-:|:-:|:-:|:-:|:-:| @@ -569,7 +567,7 @@ Online GD于mini-batch GD/SGD的区别在于,所有训练数据只用一次, Online GD在互联网领域用的较多,比如搜索广告的点击率(CTR)预估模型,网民的点击行为会随着时间改变。用普通的BGD算法(每天更新一次)一方面耗时较长(需要对所有历史数据重新训练);另一方面,无法及时反馈用户的点击行为迁移。而Online GD算法可以实时的依据网民的点击行为进行迁移。 -## 2.32 计算图的导数计算图解? +## 2.13 计算图的导数计算图解? ​ 计算图导数计算是反向传播,利用链式法则和隐式函数求导。 ​ 假设TODO在点TODO处偏导连续,TODO是关于TODO的函数,在TODO点可导,求TODO在TODO点的导数。 @@ -594,9 +592,9 @@ $$ $$ -## 2.33 线性判别分析(LDA) +## 2.14 线性判别分析(LDA) -### 2.33 线性判别分析(LDA)思想总结 +### 2.14.1 线性判别分析(LDA)思想总结 线性判别分析(Linear Discriminant Analysis,LDA)是一种经典的降维方法。 @@ -608,7 +606,7 @@ LDA分类思想简单总结如下: 3. 对数据进行分类时,将其投影到同样的这条直线上,再根据投影点的位置来确定样本的类别。 如果用一句话概括LDA思想,即“投影后类内方差最小,类间方差最大”。 -### 2.34 图解LDA核心思想 +### 2.14.2 图解LDA核心思想 假设有红、蓝两类数据,这些数据特征均为二维,如下图所示。我们的目标是将这些数据投影到一维,让每一类相近的数据的投影点尽可能接近,不同类别数据尽可能远,即图中红色和蓝色数据中心之间的距离尽可能大。 ![](./img/ch2/2.29/1.png) @@ -623,7 +621,7 @@ LDA分类思想简单总结如下: 以上例子是基于数据是二维的,分类后的投影是一条直线。如果原始数据是多维的,则投影后的分类面是一低维的超平面。 -### 2.35 二类LDA算法原理? +### 2.14.3 二类LDA算法原理? 输入:数据集TODO,其中样本TODO是n维向量,TODO,TODO降维后的目标维度TODO。定义 TODO为第TODO类样本个数; @@ -648,7 +646,7 @@ LDA的目标是让两类别的数据中心间的距离TODO尽量大,与此同 根据广义瑞利商的性质,矩阵TODO的最大特征值为TODO的最大值,矩阵TODO的最大特征值对应的特征向量即为TODO。 -### 2.36 LDA算法流程总结? +### 2.14.4 LDA算法流程总结? LDA算法降维流程如下: 输入:数据集TODO,其中样本TODO是n维向量,TODO,降维后的目标维度TODO。 @@ -664,7 +662,7 @@ LDA算法降维流程如下: 6. 转化样本集的每个样本,得到新样本 。 7. 输出新样本集 -### 2.37 LDA和PCA区别? +### 2.14.5 LDA和PCA区别? |异同点|LDA|PCA| |:-:|:-|:-| |相同点|1. 两者均可以对数据进行降维;2. 两者在降维时均使用了矩阵特征分解的思想;3. 两者都假设数据符合高斯分布;| @@ -674,15 +672,15 @@ LDA算法降维流程如下: ||选择分类性能最好的投影方向|选择样本点投影具有最大方差的方向| ||更明确,更能反映样本间差异|目的较为模糊| -### 2.38 LDA优缺点? +### 2.14.6 LDA优缺点? |优缺点|简要说明| |:-:|:-| |优点|1. 可以使用类别的先验知识;2. 以标签,类别衡量差异性的有监督降维方式,相对于PCA的模糊性,其目的更明确,更能反映样本间的差异;| |缺点|1. LDA不适合对非高斯分布样本进行降维;2. LDA降维最多降到k-1维;3. LDA在样本分类信息依赖方差而不是均值时,降维效果不好;4. LDA可能过度拟合数据。| -## 2.39 主成分分析(PCA) +## 2.15 主成分分析(PCA) -### 2.39 主成分分析(PCA)思想总结 +### 2.15.1 主成分分析(PCA)思想总结 1. PCA就是将高维的数据通过线性变换投影到低维空间上去。 2. 投影思想:找出最能够代表原始数据的投影方法。被PCA降掉的那些维度只能是那些噪声或是冗余的数据。 @@ -694,7 +692,7 @@ LDA算法降维流程如下: 协方差矩阵度量的是维度与维度之间的关系,而非样本与样本之间。 7. 之所以对角化,因为对角化之后非对角上的元素都是0,达到去噪声的目的。对角化后的协方差矩阵,对角线上较小的新方差对应的就是那些该去掉的维度。所以我们只取那些含有较大能量(特征值)的维度,其余的就舍掉,即去冗余。 -### 2.40 图解PCA核心思想 +### 2.15.2 图解PCA核心思想 PCA可解决训练数据中存在数据特征过多或特征累赘的问题。核心思想是将m维特征映射到n维(n < m),这n维形成主元,是重构出来最能代表原始数据的正交特征。 假设数据集是m个n维,$(x^{(1)}, x^{(2)}, \cdots, x^{(m)})$。如果n=2,需要降维到$n'=1$,现在想找到某一维度方向代表这两个维度的数据。下图有$u_1, u_2$两个向量方向,但是哪个向量才是我们所想要的,可以更好代表原始数据集的呢? @@ -709,7 +707,7 @@ PCA可解决训练数据中存在数据特征过多或特征累赘的问题。 1. 样本点到这个超平面的距离足够近。 2. 样本点在这个超平面上的投影能尽可能的分开。 -### 2.41 PCA算法推理 +### 2.15.3 PCA算法推理 下面以基于最小投影距离为评价指标推理: 假设数据集是m个n维,TODO,且数据进行了中心化。经过投影变换得到新坐标为TODO,其中TODO是标准正交基,即TODO,TODO。经过降维后,新坐标为TODO,其中TODO是降维后的目标维数。样本点TODO在新坐标系下的投影为TODO,其中TODO是TODO在低维坐标系里第j维的坐标。如果用TODO去恢复TODO,则得到的恢复数据为TODO,其中TODO为标准正交基组成的矩阵。 @@ -730,7 +728,7 @@ TODO 基于最大投影方差的推导,这里就不再赘述,有兴趣的同仁可自行查阅资料。 -### 2.42 PCA算法流程总结 +### 2.15.4 PCA算法流程总结 输入:TODO维样本集TODO,目标降维的维数TODO。 输出:降维后的新样本集TODO。 @@ -745,13 +743,13 @@ TODO 7. 得到输出矩阵TODO。 *注*:在降维时,有时不明确目标维数,而是指定降维到的主成分比重阈值TODO。假设TODO个特征值为TODO,则TODO可从TODO得到。 -### 2.43 PCA算法主要优缺点 +### 2.15.5 PCA算法主要优缺点 |优缺点|简要说明| |:-:|:-| |优点|1. 仅仅需要以方差衡量信息量,不受数据集以外的因素影响。 2.各主成分之间正交,可消除原始数据成分间的相互影响的因素。3. 计算方法简单,主要运算是特征值分解,易于实现。| |缺点|1.主成分各个特征维度的含义具有一定的模糊性,不如原始样本特征的解释性强。2. 方差小的非主成分也可能含有对样本差异的重要信息,因降维丢弃可能对后续数据处理有影响。| -### 2.44 降维的必要性及目的 +### 2.15.6 降维的必要性及目的 **降维的必要性**: 1. 多重共线性--预测变量之间相互关联。多重共线性会导致解空间的不稳定,从而可能导致结果的不连贯。 2. 高维空间本身具有稀疏性。一维正态分布有68%的值落于正负标准差之间,而在十维空间上只有0.02%。 @@ -766,7 +764,7 @@ TODO 5. 去除数据噪声。 6. 降低算法运算开销。 -### 2.45 KPCA与PCA的区别? +### 2.15.7 KPCA与PCA的区别? 应用PCA算法的前提是假设存在一个线性的超平面,进而投影。那如果数据不是线性的呢?该怎么办?这时候就需要KPCA,数据集从TODO维映射到线性可分的高维TODO,然后再从TODO维降维到一个低维度TODO。 KPCA用到了核函数思想,使用了核函数的主成分分析一般称为核主成分分析(Kernelized PCA, 简称KPCA)。 @@ -778,8 +776,8 @@ TODO其映射为TODO 通过在高维空间进行协方差矩阵的特征值分解,然后用和PCA一样的方法进行降维。由于KPCA需要核函数的运算,因此它的计算量要比PCA大很多。 -## 2.46 模型评估 -### 2.46.1 模型评估常用方法? +## 2.16 模型评估 +### 2.16.1 模型评估常用方法? 一般情况来说,单一评分标准无法完全评估一个机器学习模型。只用good和bad偏离真实场景去评估某个模型,都是一种欠妥的评估方式。下面介绍常用的分类模型和回归模型评估方法。 **分类模型常用评估方法:** @@ -803,7 +801,11 @@ TODO其映射为TODO |Absolute Error (MAE, RAE)|绝对误差|from sklearn.metrics import mean_absolute_error, median_absolute_error| |R-Squared|R平方值|from sklearn.metrics import r2_score| -### 2.47.1 机器学习中的Bias(偏差),Error(误差),和Variance(方差)有什么区别和联系?(贡献者:黄钦建-华南理工大学) +### 2.16.2 机器学习中的Bias,Error和Variance有什么区别和联系? + +**(贡献者:黄钦建-华南理工大学)** + +Bias(偏差),Error(误差),和Variance(方差) **对于Bias:** @@ -821,14 +823,14 @@ TODO其映射为TODO > > 训练误差大,测试误差大→ 升VC维 -### 2.47.1 经验误差与泛化误差 +### 2.16.3 经验误差与泛化误差 误差(error):一般地,我们把学习器的实际预测输出与样本的真是输出之间的差异称为“误差” 经验误差(empirical error):也叫训练误差(training error)。模型在训练集上的误差。 泛化误差(generalization error):模型在新样本集(测试集)上的误差称为“泛化误差”。 -### 2.47.2 图解欠拟合、过拟合 +### 2.16.4 图解欠拟合、过拟合 根据不同的坐标方式,欠拟合与过拟合图解不同。 1. **横轴为训练样本数量,纵轴为误差** @@ -862,7 +864,7 @@ TODO其映射为TODO 模型正常:模型复杂程度控制在点B处为最优。 -### 2.47.3 如何解决过拟合与欠拟合? +### 2.16.5 如何解决过拟合与欠拟合? **如何解决欠拟合:** 1. 添加其他特征项。组合、泛化、相关性、上下文特征、平台特征等特征是特征添加的重要手段,有时候特征项不够会导致模型欠拟合。 2. 添加多项式特征。例如将线性模型添加二次项或三次项使模型泛化能力更强。例如,FM模型、FFM模型,其实就是线性模型,增加了二阶多项式,保证了模型一定的拟合程度。 @@ -883,12 +885,12 @@ TODO其映射为TODO 欠拟合和过拟合这些方法,需要根据实际问题,实际模型,进行选择。 -### 2.47.4 交叉验证的主要作用? +### 2.16.6 交叉验证的主要作用? 为了得到更为稳健可靠的模型,对模型的泛化误差进行评估,得到模型泛化误差的近似值。当有多个模型可以选择时,我们通常选择“泛化误差”最小的模型。 交叉验证的方法有许多种,但是最常用的是:留一交叉验证、k折交叉验证 -### 2.47.5 k折交叉验证? +### 2.16.7 k折交叉验证? 1. 将含有N个样本的数据集,分成K份,每份含有N/K个样本。选择其中1份作为测试集,另外K-1份作为训练集,测试集就有K种情况。 2. 在每种情况中,用训练集训练模型,用测试集测试模型,计算模型的泛化误差。 3. 交叉验证重复K次,每份验证一次,平均K次的结果或者使用其它结合方式,最终得到一个单一估测,得到模型最终的泛化误差。 @@ -898,7 +900,7 @@ TODO其映射为TODO 2. 训练集中样本数量要足够多,一般至少大于总样本数的50%。 3. 训练集和测试集必须从完整的数据集中均匀取样。均匀取样的目的是希望减少训练集、测试集与原数据集之间的偏差。当样本数量足够多时,通过随机取样,便可以实现均匀取样的效果。 -### 2.47.6 混淆矩阵 +### 2.16.8 混淆矩阵 第一种混淆矩阵 |真实情况T or F|预测为正例1,P|预测为负例0,N| |:-:|:-|:-| @@ -911,11 +913,11 @@ TODO其映射为TODO |预测为正例1,P|TP(预测为1,实际为1)|FP(预测为1,实际为0)| |预测为负例0,N|FN(预测为0,实际为1)|TN(预测为0,实际也为0)| -### 2.47.7 错误率及精度 +### 2.16.9 错误率及精度 1. 错误率(Error Rate):分类错误的样本数占样本总数的比例。 2. 精度(accuracy):分类正确的样本数占样本总数的比例。 -### 2.47.8 查准率与查全率 +### 2.16.10 查准率与查全率 将算法预测的结果分成四种情况: 1. 正确肯定(True Positive,TP):预测为真,实际为真 2. 正确否定(True Negative,TN):预测为假,实际为假 @@ -934,7 +936,7 @@ TODO其映射为TODO **理解**:正确预测为阳性的数量占总样本中阳性数量的比例。 例,在所有实际上有恶性肿瘤的病人中,成功预测有恶性肿瘤的病人的百分比,越高越好。 -### 2.47.9 ROC与AUC +### 2.16.11 ROC与AUC ROC全称是“受试者工作特征”(Receiver Operating Characteristic)。 ROC曲线的面积就是AUC(Area Under the Curve)。 @@ -957,7 +959,7 @@ TODO, TODO, 经过以上分析,ROC曲线越接近左上角,该分类器的性能越好。 ROC曲线所覆盖的面积称为AUC(Area Under Curve),可以更直观的判断学习器的性能,AUC越大则性能越好。 -### 2.47.10 如何画ROC曲线? +### 2.16.12 如何画ROC曲线? http://blog.csdn.net/zdy0_2004/article/details/44948511 下图是一个示例,图中共有20个测试样本,“Class”一栏表示每个测试样本真正的标签(p表示正样本,n表示负样本),“Score”表示每个测试样本属于正样本的概率。 @@ -969,7 +971,7 @@ http://blog.csdn.net/zdy0_2004/article/details/44948511 ![](./img/ch2/2.40.11/1.jpg) -### 2.47.11 如何计算TPR,FPR? +### 2.16.13 如何计算TPR,FPR? 1、分析数据 y_true = [0, 0, 1, 1]; scores = [0.1, 0.4, 0.35, 0.8]; @@ -1034,18 +1036,18 @@ TPR = TP/(TP+FN) = 0.5; FPR = FP/(TN+FP) = 0; 4、根据TPR、FPR值,以FPR为横轴,TPR为纵轴画图。 -### 2.47.12 如何计算Auc? +### 2.16.14 如何计算Auc? a.将坐标点按照横着FPR排序 b.计算第i个坐标点和第i+1个坐标点的间距 dx; c.获取第i(或者i+1)个坐标点的纵坐标y; d.计算面积微元ds = ydx; e.对面积微元进行累加,得到AUC。 -### 2.47.13 为什么使用Roc和Auc评价分类器? +### 2.16.15 为什么使用Roc和Auc评价分类器? 模型有很多评估方法,为什么还要使用ROC和AUC呢? 因为ROC曲线有个很好的特性:当测试集中的正负样本的分布变换的时候,ROC曲线能够保持不变。在实际的数据集中经常会出现样本类不平衡,即正负样本比例差距较大,而且测试数据中的正负样本也可能随着时间变化。 -### 2.47.14 直观理解AUC +### 2.16.17 直观理解AUC http://blog.csdn.net/cherrylvlei/article/details/52958720 AUC是ROC右下方的曲线面积。下图展现了三种AUC的值: @@ -1055,7 +1057,7 @@ AUC是衡量二分类模型优劣的一种评价指标,表示正例排在负 因为一般在分类模型中,预测结果都是以概率的形式表现,如果要计算准确率,通常都会手动设置一个阈值来将对应的概率转化成类别,这个阈值也就很大程度上影响了模型准确率的计算。 我们不妨举一个极端的例子:一个二类分类问题一共10个样本,其中9个样本为正例,1个样本为负例,在全部判正的情况下准确率将高达90%,而这并不是我们希望的结果,尤其是在这个负例样本得分还是最高的情况下,模型的性能本应极差,从准确率上看却适得其反。而AUC能很好描述模型整体性能的高低。这种情况下,模型的AUC值将等于0(当然,通过取反可以解决小于50%的情况,不过这是另一回事了)。 -### 2.47.15 代价敏感错误率与代价曲线 +### 2.16.18 代价敏感错误率与代价曲线 http://blog.csdn.net/cug_lzt/article/details/78295140 @@ -1099,14 +1101,14 @@ $Cost_{norm}=\frac{FNR*p*Cost_{01}+FNR*(1-p)*Cost_{10}}{p*Cost_{01}+(1-p)*Cost_{ ![](./img/ch2/2-3.png) -### 2.40.17 模型有哪些比较检验方法 +### 2.16.19 模型有哪些比较检验方法 http://wenwen.sogou.com/z/q721171854.htm 正确性分析:模型稳定性分析,稳健性分析,收敛性分析,变化趋势分析,极值分析等。 有效性分析:误差分析,参数敏感性分析,模型对比检验等。 有用性分析:关键数据求解,极值点,拐点,变化趋势分析,用数据验证动态模拟等。 高效性分析:时空复杂度分析与现有进行比较等。 -### 2.40.18 偏差与方差 +### 2.16.20 偏差与方差 http://blog.csdn.net/zhihua_oba/article/details/78684257 方差公式为: @@ -1130,7 +1132,7 @@ generalization error=bias+variance。 偏差大,会造成模型欠拟合; 方差大,会造成模型过拟合。 -### 2.40.19为什么使用标准差? +### 2.16.21为什么使用标准差? 标准差公式为: $S_{N}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(x_{i}-\bar{x})^{2}}$ @@ -1143,14 +1145,14 @@ $S_{N}=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^{2}}$ 2、表示离散程度的数字单位与样本数据的单位一致,更方便做后续的分析运算。 3、在样本数据大致符合正态分布的情况下,标准差具有方便估算的特性:66.7%的数据点落在平均值前后1个标准差的范围内、95%的数据点落在平均值前后2个标准差的范围内,而99%的数据点将会落在平均值前后3个标准差的范围内。 -### 2.40.20 点估计思想 +### 2.16.22点估计思想 点估计:用实际样本的一个指标来估计总体的一个指标的一种估计方法。 点估计举例:比如说,我们想要了解中国人的平均身高,那么在大街上随便找了一个人,通过测量这个人的身高来估计中国人的平均身高水平;或者在淘宝上买东西的时候随便一次买到假货就说淘宝上都是假货等;这些都属于点估计。 点估计主要思想:在样本数据中得到一个指标,通过这个指标来估计总体指标;比如我们用样本均数来估计总体均数,样本均数就是我们要找到的指标。 -### 2.40.21 点估计优良性原则? +### 2.16.23 点估计优良性原则? 获取样本均数指标相对来说比较简单,但是并不是总体的所有指标都很容易在样本中得到,比如说总体的标准差用样本的哪个指标来估计呢? 优良性准则有两大类:一类是小样本准则,即在样本大小固定时的优良性准则;另一类是大样本准则,即在样本大小趋于无穷时的优良性准则。最重要的小样本优良性准则是无偏性及与此相关的一致最小方差无偏计。 @@ -1169,7 +1171,7 @@ $S_{N}=\sqrt{\frac{1}{N-1}\sum_{i=1}^{N}(x_{i}-\bar{x})^{2}}$ 要明白一个原则:计算样本的任何分布、均数、标准差都是没有任何意义的,如果样本的这种计算不能反映总体的某种特性。 -### 2.40.22点估计、区间估计、中心极限定理之间的联系? +### 2.16.24 点估计、区间估计、中心极限定理之间的联系? https://www.zhihu.com/question/21871331#answer-4090464 点估计:是用样本统计量来估计总体参数,因为样本统计量为数轴上某一点值,估计的结果也以一个点的数值表示,所以称为点估计。 @@ -1186,13 +1188,13 @@ https://www.zhihu.com/question/21871331#answer-4090464 不同点:点估计只提供单一的估计值,而区间估计基于点估计还提供误差界限,给出了置信区间,受置信度的影响。 -### 2.40.23 类别不平衡产生原因? +### 2.16.25 类别不平衡产生原因? 类别不平衡(class-imbalance)是指分类任务中不同类别的训练样例数目差别很大的情况。 产生原因: 通常分类学习算法都会假设不同类别的训练样例数目基本相同。如果不同类别的训练样例数目差别很大,则会影响学习结果,测试结果变差。例如二分类问题中有998个反例,正例有2个,那学习方法只需返回一个永远将新样本预测为反例的分类器,就能达到99.8%的精度;然而这样的分类器没有价值。 -### 2.40.24 常见的类别不平衡问题解决方法 +### 2.16.26 常见的类别不平衡问题解决方法 http://blog.csdn.net/u013829973/article/details/77675147   防止类别不平衡对学习造成的影响,在构建分类模型之前,需要对分类不平衡性问题进行处理。主要解决方法有: @@ -1238,12 +1240,12 @@ ADASYN:根据学习难度的不同,对不同的少数类别的样本使用 对问题进行分析与挖掘,将问题划分成多个更小的问题,看这些小问题是否更容易解决。 -## 2.41 决策树 +## 2.17 决策树 -### 2.41.1 决策树的基本原理 +### 2.17.1 决策树的基本原理 决策树是一种分而治之(Divide and Conquer)的决策过程。一个困难的预测问题, 通过树的分支节点, 被划分成两个或多个较为简单的子集,从结构上划分为不同的子问题。将依规则分割数据集的过程不断递归下去(Recursive Partitioning)。随着树的深度不断增加,分支节点的子集越来越小,所需要提的问题数也逐渐简化。当分支节点的深度或者问题的简单程度满足一定的停止规则(Stopping Rule)时, 该分支节点会停止劈分,此为自上而下的停止阈值(Cutoff Threshold)法;有些决策树也使用自下而上的剪枝(Pruning)法。 -### 2.41.2 决策树的三要素? +### 2.17.2 决策树的三要素? 一棵决策树的生成过程主要分为以下3个部分: 特征选择:从训练数据中众多的特征中选择一个特征作为当前节点的分裂标准,如何选择特征有着很多不同量化评估标准标准,从而衍生出不同的决策树算法。 @@ -1251,11 +1253,11 @@ ADASYN:根据学习难度的不同,对不同的少数类别的样本使用 决策树生成:根据选择的特征评估标准,从上至下递归地生成子节点,直到数据集不可分则停止决策树停止生长。树结构来说,递归结构是最容易理解的方式。 剪枝:决策树容易过拟合,一般来需要剪枝,缩小树结构规模、缓解过拟合。剪枝技术有预剪枝和后剪枝两种。 -### 2.41.3 决策树学习基本算法 +### 2.17.3 决策树学习基本算法 ![](./img/ch2/2-5.png) -### 2.41.4 决策树算法优缺点 +### 2.17.4 决策树算法优缺点 决策树算法的优点: @@ -1289,7 +1291,7 @@ ADASYN:根据学习难度的不同,对不同的少数类别的样本使用 6、对于各类别样本数量不一致的数据,在决策树当中,信息增益的结果偏向于那些具有更多数值的特征。 -### 2.40.5熵的概念以及理解 +### 2.17.5熵的概念以及理解 熵:度量随机变量的不确定性。 @@ -1300,7 +1302,7 @@ $H(X)=-\sum_{i=1}^{n}p_{i}log_{2}p_{i}$ 对于样本集合 ,假设样本有k个类别,每个类别的概率为$\frac{|C_{k}|}{|D|}$,其中$|C_{k}|}{|D|$为类别为k的样本个数,$|D|$为样本总数。样本集合D的熵为: $H(D)=-\sum_{k=1}^{k}\frac{|C_{k}|}{|D|}log_{2}\frac{|C_{k}|}{|D|}$ -### 2.40.6 信息增益的理解 +### 2.17.6 信息增益的理解 定义:以某特征划分数据集前后的熵的差值。 熵可以表示样本集合的不确定性,熵越大,样本的不确定性就越大。因此可以使用划分前后集合熵的差值来衡量使用当前特征对于样本集合D划分效果的好坏。 假设划分前样本集合D的熵为H(D)。使用某个特征A划分数据集D,计算划分后的数据子集的熵为H(D|A)。 @@ -1321,7 +1323,7 @@ $g(D,A)=H(D)-H(D|A)$ 惩罚参数:数据集D以特征A作为随机变量的熵的倒数。 -### 2.40.7 剪枝处理的作用及策略? +### 2.17.7 剪枝处理的作用及策略? 剪枝处理是决策树学习算法用来解决过拟合的一种办法。 在决策树算法中,为了尽可能正确分类训练样本, 节点划分过程不断重复, 有时候会造成决策树分支过多,以至于将训练样本集自身特点当作泛化特点, 而导致过拟合。 因此可以采用剪枝处理来去掉一些分支来降低过拟合的风险。 @@ -1332,9 +1334,9 @@ $g(D,A)=H(D)-H(D|A)$ 后剪枝:生成决策树以后,再自下而上对非叶结点进行考察, 若将此节点标记为叶结点可以带来泛化性能提升,则修改之。 -## 2.41 支持向量机 +## 2.18 支持向量机 -### 2.41.1 什么是支持向量机 +### 2.18.1 什么是支持向量机 SVM - Support Vector Machine。支持向量机,其含义是通过支持向量运算的分类器。其中“机”的意思是机器,可以理解为分类器。 什么是支持向量呢?在求解的过程中,会发现只根据部分数据就可以确定分类器,这些数据称为支持向量。 @@ -1343,7 +1345,7 @@ SVM - Support Vector Machine。支持向量机,其含义是通过支持向量 ![](./img/ch2/2-6.png) -### 2.25.2 支持向量机解决的问题? +### 2.18.2 支持向量机解决的问题? https://www.cnblogs.com/steven-yang/p/5658362.html 解决的问题: @@ -1385,7 +1387,7 @@ f(x)=∑ni=1αiyiK(xi,x)+bherexi : training data iyi : label value of training d αα, σσ 和 bb 是训练数据后产生的值。 可以通过调节σσ来匹配维度的大小,σσ越大,维度越低。 -### 2.25.2 核函数作用? +### 2.18.3 核函数作用? 核函数目的:把原坐标系里线性不可分的数据用Kernel投影到另一个空间,尽量使得数据在新的空间里线性可分。 @@ -1399,14 +1401,14 @@ f(x)=∑ni=1αiyiK(xi,x)+bherexi : training data iyi : label value of training d 4)核函数方法可以和不同的算法相结合,形成多种不同的基于核函数技术的方法,且这两部分的设计可以单独进行,并可以为不同的应用选择不同的核函数和算法。 -### 2.25.3 对偶问题 -### 2.25.4 理解支持向量回归 +### 2.18.4 对偶问题 +### 2.18.5 理解支持向量回归 http://blog.csdn.net/liyaohhh/article/details/51077082 -### 2.25.5 理解SVM(核函数) +### 2.18.6 理解SVM(核函数) http://blog.csdn.net/Love_wanling/article/details/69390047 -### 2.25.6 常见的核函数有哪些? +### 2.18.7 常见的核函数有哪些? http://blog.csdn.net/Love_wanling/article/details/69390047 本文将遇到的核函数进行收集整理,分享给大家。 @@ -1464,8 +1466,8 @@ $k(x,y)=tanh(ax^{t}y+c)$ $k(x,y)=1-\frac{\left \| x-y \right \|^{2}}{\left \| x-y \right \|^{2}+c}$ -### 2.25.6 软间隔与正则化 -### 2.25.7 SVM主要特点及缺点? +### 2.18.8 软间隔与正则化 +### 2.18.9 SVM主要特点及缺点? http://www.elecfans.com/emb/fpga/20171118582139_2.html @@ -1486,8 +1488,8 @@ http://www.elecfans.com/emb/fpga/20171118582139_2.html (2) 用SVM解决多分类问题存在困难 经典的支持向量机算法只给出了二类分类的算法,而在数据挖掘的实际应用中,一般要解决多类的分类问题。可以通过多个二类支持向量机的组合来解决。主要有一对多组合模式、一对一组合模式和SVM决策树;再就是通过构造多个分类器的组合来解决。主要原理是克服SVM固有的缺点,结合其他算法的优势,解决多类问题的分类精度。如:与粗集理论结合,形成一种优势互补的多类问题的组合分类器。 -## 2.26 贝叶斯 -### 2.26.1 图解极大似然估计 +## 2.19 贝叶斯 +### 2.19.1 图解极大似然估计 极大似然估计 http://blog.csdn.net/zengxiantao1994/article/details/72787849 @@ -1513,12 +1515,12 @@ $\hat{\theta}=d(x_{1},x_{2},...,x_{N})=d(D)$ $\hat{\theta}(x_{1},x_{2},...,x_{N})$称为极大似然函数估计值。 -### 2.26.2 朴素贝叶斯分类器和一般的贝叶斯分类器有什么区别? -### 2.26.4 朴素与半朴素贝叶斯分类器 -### 2.26.5 贝叶斯网三种典型结构 -### 2.26.6 什么是贝叶斯错误率 -### 2.26.7 什么是贝叶斯最优错误率 -## 2.27 EM算法解决问题及实现流程 +### 2.19.2 朴素贝叶斯分类器和一般的贝叶斯分类器有什么区别? +### 2.19.3 朴素与半朴素贝叶斯分类器 +### 2.19.4 贝叶斯网三种典型结构 +### 2.19.5 什么是贝叶斯错误率 +### 2.19.6 什么是贝叶斯最优错误率 +## 2.20 EM算法解决问题及实现流程 1.EM算法要解决的问题 @@ -1539,8 +1541,7 @@ EM算法解决这个的思路是使用启发式的迭代方法,既然我们无 当然,K-Means算法是比较简单的,实际中的问题往往没有这么简单。上面对EM算法的描述还很粗糙,我们需要用数学的语言精准描述。 - -EM算法流程 +2.EM算法流程 现在我们总结下EM算法的流程。 @@ -1561,7 +1562,9 @@ c) 如果θj+1θj+1已收敛,则算法结束。否则继续回到步骤a)进 输出:模型参数θθ。 -## 2.28 为什么会产生维数灾难? +## 2.21 降维和聚类 + +### 2.21.1 为什么会产生维数灾难? http://blog.csdn.net/chenjianbo88/article/details/52382943 @@ -1617,7 +1620,7 @@ $V(d)=\frac{\pi ^{\frac{d}{2}}}{\Gamma (\frac{d}{2}+1)}0.5^{d}$ 参考资料: [1] Vincent Spruyt. The Curse of Dimensionality in classification. Computer vision for dummies. 2014. [Link] -## 2.29怎样避免维数灾难 +### 2.21.2 怎样避免维数灾难 解决维度灾难问题: @@ -1627,7 +1630,7 @@ $V(d)=\frac{\pi ^{\frac{d}{2}}}{\Gamma (\frac{d}{2}+1)}0.5^{d}$ Lassio缩减系数法、小波分析法、 -## 2.30聚类和降维有什么区别与联系? +### 2.21.3 聚类和降维有什么区别与联系? 聚类用于找寻数据内在的分布结构,既可以作为一个单独的过程,比如异常检测等等。也可作为分类等其他学习任务的前驱过程。聚类是标准的无监督学习。 @@ -1643,21 +1646,7 @@ Lassio缩减系数法、小波分析法、 但是他们虽然都能实现对数据的约减。但是二者适用的对象不同,聚类针对的是数据点,而降维则是对于数据的特征。另外它们着很多种实现方法。聚类中常用的有K-means、层次聚类、基于密度的聚类等;降维中常用的则PCA、Isomap、LLE等。 -## 2.31 GBDT和随机森林的区别 - -GBDT和随机森林的相同点: -1、都是由多棵树组成 -2、最终的结果都是由多棵树一起决定 - -GBDT和随机森林的不同点: -1、组成随机森林的树可以是分类树,也可以是回归树;而GBDT只由回归树组成 -2、组成随机森林的树可以并行生成;而GBDT只能是串行生成 -3、对于最终的输出结果而言,随机森林采用多数投票等;而GBDT则是将所有结果累加起来,或者加权累加起来 -4、随机森林对异常值不敏感,GBDT对异常值非常敏感 -5、随机森林对训练集一视同仁,GBDT是基于权值的弱分类器的集成 -6、随机森林是通过减少模型方差提高性能,GBDT是通过减少模型偏差提高性能 - -## 2.32 四种聚类方法之比较 +### 2.21.4 四种聚类方法之比较 http://www.cnblogs.com/William_Fire/archive/2013/02/09/2909499.html @@ -1709,7 +1698,7 @@ http://www.cnblogs.com/William_Fire/archive/2013/02/09/2909499.html  (3) 重新计算新类与所有类之间的距离;  (4) 重复(2)、(3),直到所有类最后合并成一类。 -## 2.3 SOM聚类算法 +### 2.21.5 SOM聚类算法 SOM神经网络[11]是由芬兰神经网络专家Kohonen教授提出的,该算法假设在输入对象中存在一些拓扑结构或顺序,可以实现从输入空间(n维)到输出平面(2维)的降维映射,其映射具有拓扑特征保持性质,与实际的大脑处理有很强的理论联系。 SOM网络包含输入层和输出层。输入层对应一个高维的输入向量,输出层由一系列组织在2维网格上的有序节点构成,输入节点与输出节点通过权重向量连接。 学习过程中,找到与之距离最短的输出层单元,即获胜单元,对其更新。同时,将邻近区域的权值更新,使输出节点保持输入向量的拓扑特征。 @@ -1722,7 +1711,7 @@ SOM网络包含输入层和输出层。输入层对应一个高维的输入向 (4) 提供新样本、进行训练; (5) 收缩邻域半径、减小学习率、重复,直到小于允许值,输出聚类结果。 -## 2.4 FCM聚类算法 +### 2.21.6 FCM聚类算法 1965年美国加州大学柏克莱分校的扎德教授第一次提出了‘集合’的概念。经过十多年的发展,模糊集合理论渐渐被应用到各个实际应用方面。为克服非此即彼的分类缺点,出现了以模糊集合论为数学基础的聚类分析。用模糊数学的方法进行聚类分析,就是模糊聚类分析[12]。 @@ -1760,7 +1749,21 @@ FCM算法是一种以隶属度来确定每个数据点属于某个聚类程度 $avg=\frac{1}{k}\sum_{i=1}^{k}\frac{m_{i}}{n_{i}}$ -## 2.18 大数据与深度学习之间的关系 +## 2.22 GBDT和随机森林的区别 + +GBDT和随机森林的相同点: +1、都是由多棵树组成 +2、最终的结果都是由多棵树一起决定 + +GBDT和随机森林的不同点: +1、组成随机森林的树可以是分类树,也可以是回归树;而GBDT只由回归树组成 +2、组成随机森林的树可以并行生成;而GBDT只能是串行生成 +3、对于最终的输出结果而言,随机森林采用多数投票等;而GBDT则是将所有结果累加起来,或者加权累加起来 +4、随机森林对异常值不敏感,GBDT对异常值非常敏感 +5、随机森林对训练集一视同仁,GBDT是基于权值的弱分类器的集成 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zK>Y)hD1XyqM!r%Gtf}D)LJ^K?t%m@Nu71!07zV* zf=cWvRRxLL^X5CP>-kyG4J;}&nT+ij$FUvz`R16kb5m{zN`0*6HA>c;$h&P6B~Qw+ zYGUMFIaWg{DQ_bb^6q#1r>jzKh`%#t44LT8Nygd6S&t=&xTn`+K9x2)$;hM0#`x%%^h(0ul0S9~ zSQ-SDS44mBn*A{*gBE5ojvL4_D2v3hw+HCc{KAf99-5?AVi`&=V~w4aZQ$rd(__o6 z$wbvp_KG3EIE5-JL`6#%Qcw2%5a8r|FBBw8mu;XfV_QqU z7wE0aN<#9o-V#Tf-e9Os^t`@+O}07-@HXQy;SU>{6dAn3oM(`?=D)FIMB|3thV~4? ze@>`f%0{lu_Zvq7f`!faPQa;J=GMouWHc^mfJe{I%)nVnR<=pB`rh6|D%l6n1amw_ ucJyEAHFV%zWe0*yoN * 输入层 @@ -158,7 +158,7 @@ http://www.sohu.com/a/159591827_390227 1. 实现信息的跨通道交互和整合。 2. 对卷积核通道数进行降维和升维,减小参数量。 - + 下面详细解释一下: **第一点 实现信息的跨通道交互和整合** 对1×1卷积层的探讨最初是出现在NIN的结构,论文作者的动机是利用MLP代替传统的线性卷积核,从而提高网络的表达能力。文中从跨通道池化的角度进行解释,认为文中提出的MLP其实等价于在传统卷积核后面接cccp层,从而实现多个feature map的线性组合,实现跨通道的信息整合。而查看代码实现,cccp层即等价于1×1卷积层。 @@ -240,7 +240,7 @@ Xception网络由此诞生。我们首先对每一个通道进行各自的卷积 ### 5.14.2 为什么采用宽卷积? 通过将输入边角的值纳入到滑窗中心进行计算,以便损失更少的信息。 - + ## 5.15 在卷积操作后,输出特征图(图像)大小如何计算? 在进行卷积操作时,往往根据需要,我们需设定一些参数。常见的参数有卷积核大小k, 窗口滑动的步长s, 进行填充的像素p, 假设输入特征图大小为Iw*Iw。则由以下公式可计算出输出特征图的大小Ow。 diff --git a/ch06_循环神经网络(RNN)/第六章_循环神经网络(RNN).md b/ch06_循环神经网络(RNN)/第六章_循环神经网络(RNN).md index 7f41126..36e7076 100644 --- a/ch06_循环神经网络(RNN)/第六章_循环神经网络(RNN).md +++ b/ch06_循环神经网络(RNN)/第六章_循环神经网络(RNN).md @@ -1,3 +1,7 @@ +[TOC] + + + # 第六章 循环神经网络(RNN) Markdown Revision 2; diff --git a/ch07_生成对抗网络(GAN)/第七章_生成对抗网络(GAN).md b/ch07_生成对抗网络(GAN)/第七章_生成对抗网络(GAN).md index d558ced..ef12ee5 100644 --- a/ch07_生成对抗网络(GAN)/第七章_生成对抗网络(GAN).md +++ b/ch07_生成对抗网络(GAN)/第七章_生成对抗网络(GAN).md @@ -1,24 +1,28 @@ +[TOC] + + + # 第七章_生成对抗网络(GAN) -## GAN的「生成」的本质是什么? +## 7.1 GAN的「生成」的本质是什么? GAN的形式是:两个网络,G(Generator)和D(Discriminator)。Generator是一个生成图片的网络,它接收一个随机的噪声z,记做G(z)。Discriminator是一个判别网络,判别一张图片是不是“真实的”。它的输入是x,x代表一张图片,输出D(x)代表x为真实图片的概率,如果为1,就代表100%是真实的图片,而输出为0,就代表不可能是真实的图片。 GAN*生成*能力是*学习分布*,引入的latent variable的noise使习得的概率分布进行偏移。因此在训练GAN的时候,latent variable**不能**引入均匀分布(uniform distribution),因为均匀分布的数据的引入并不会改变概率分布。 -## GAN能做数据增广吗? +## 7.2 GAN能做数据增广吗? GAN能够从一个模型引入一个随机数之后「生成」无限的output,用GAN来做数据增广似乎很有吸引力并且是一个极清晰的一个insight。然而,纵观整个GAN的训练过程,Generator习得分布再引入一个Distribution(Gaussian或其他)的噪声以「骗过」Discriminator,并且无论是KL Divergence或是Wasserstein Divergence,本质还是信息衡量的手段(在本章中其余部分介绍),能「骗过」Discriminator的Generator一定是能在引入一个Distribution的噪声的情况下最好的结合已有信息。 训练好的GAN应该能够很好的使用已有的数据的信息(特征或分布),现在问题来了,这些信息本来就包含在数据里面,有必要把信息丢到Generator学习使得的结果加上噪声作为训练模型的输入吗? -## VAE与GAN有什么不同? +## 7.3 VAE与GAN有什么不同? 1. VAE可以直接用在离散型数据。 2. VAE整个训练流程只靠一个假设的loss函数和KL Divergence逼近真实分布。GAN没有假设单个loss函数, 而是让判别器D和生成器G互相博弈,以期得到Nash Equilibrium。 -## 有哪些优秀的GAN? +## 7.4 有哪些优秀的GAN? -### DCGAN +### 7.4.1 DCGAN -### WGAN/WGAN-GP +### 7.4.2 WGAN/WGAN-GP WGAN及其延伸是被讨论的最多的部分,原文连发两文,第一篇(Towards principled methods for training generative adversarial networks)非常solid的提了一堆的数学,一作Arjovsky克朗所的数学能力果然一个打十几个。后来给了第二篇Wasserstein GAN,可以说直接给结果了,和第一篇相比,第二篇更加好接受。 @@ -53,42 +57,42 @@ $$JS(P_1||P_2)=\frac{1}{2}KL(P_1||\frac{P_1+P_2}{2})$$ **如何理解Wasserstein距离?** Wasserstein距离与optimal transport有一些关系,并且从数学上想很好的理解需要一定的测度论的知识。 -### condition GAN +### 7.4.3 condition GAN -### InfoGAN +### 7.4.4 InfoGAN 通过最大化互信息(c,c’)来生成同类别的样本。 $$L^{infoGAN}_{D,Q}=L^{GAN}_D-\lambda L_1(c,c')$$ $$L^{infoGAN}_{G}=L^{GAN}_G-\lambda L_1(c,c')$$ -### CycleGAN +### 7.4.5 CycleGAN **CycleGAN与DualGAN之间的区别** -### StarGAN +### 7.4.6 StarGAN 目前Image-to-Image Translation做的最好的GAN。 -## Self-Attention GAN +### 7.4.7 Self-Attention GAN -## GAN训练有什么难点? +## 7.5 GAN训练有什么难点? 由于GAN的收敛要求**两个网络(D&G)同时达到一个均衡**, -## GAN与强化学习中的AC网络有何区别? +## 7.6 GAN与强化学习中的AC网络有何区别? 强化学习中的AC网络也是Dual Network,似乎从某个角度上理解可以为一个GAN。但是GAN本身 -## GAN的可创新的点 +## 7.7 GAN的可创新的点 GAN是一种半监督学习模型,对训练集不需要太多有标签的数据。 -## 如何训练GAN? +## 7.8 如何训练GAN? 判别器D在GAN训练中是比生成器G更强的网络 Instance Norm比Batch Norm的效果要更好。 使用逆卷积来生成图片会比用全连接层效果好,全连接层会有较多的噪点,逆卷积层效果清晰。 -## GAN如何解决NLP问题 +## 7.9 GAN如何解决NLP问题 GAN只适用于连续型数据的生成,对于离散型数据效果不佳,因此假如NLP方法直接应用的是character-wise的方案,Gradient based的GAN是无法将梯度Back propagation(BP)给生成网络的,因此从训练结果上看,GAN中G的表现长期被D压着打。 -## Reference +## 7.10 Reference ### DCGAN部分: ### WGAN部分: diff --git a/ch08_目标检测/第八章_目标检测.md b/ch08_目标检测/第八章_目标检测.md index 72fba4f..e693405 100644 --- a/ch08_目标检测/第八章_目标检测.md +++ b/ch08_目标检测/第八章_目标检测.md @@ -1,3 +1,7 @@ +[TOC] + + + # 第八章 目标检测 **目标检测负责人:** @@ -63,13 +67,13 @@ ![](./img/ch8/8.1.1.png) 图8.1.1 滑动窗口示意图(从右向左,从上至下) - + 采用滑动窗口从图像中剪切相应的图像块。由于很多分类器只能采用固定大小的图像块,因此这些图像块大多是原始图像块经过变形转换得到的。尽管如此,这样的操作并不影响分类的准确率,因为分类器可以处理变形后的图像块。 ![](./img/ch8/8.1.2.png) 图8.1.2 将图像转换成固定尺寸的图像 - + 经过变形后的图像块被输入到CNN分类器中,用来提取出4096维特征。之后,使用SVM分类器识别该图像的类别,并且采用线性回归输出该图像的边界框。 ![](./img/ch8/8.1.3.png) @@ -303,7 +307,7 @@ TODO 图7.4.2 ##### (1)Unified Detection YOLO将输入图像划分为S×S的栅格,每个栅格负责检测中心落在该栅格中的物体,如下图所示: - + 图7.4.3 每一个栅格预测B个bounding boxes,以及这些bounding boxes的confidence scores。这个confidence scores反映了模型对于这个栅格的预测:该栅格是否含有物体,以及这个box的坐标预测的有多准。如果这个栅格中不存在一个object,则confidence score应该为0;否则的话,confidence score则为predicted bounding box与ground truth box之间的IOU(intersection over union)。YOLO对每个bounding box有5个predictions:x, y, w, h, and confidence。坐标x,y代表了预测的bounding box的中心与栅格边界的相对值。坐标w,h代表了预测的bounding box的width、height相对于整幅图像width,height的比例。confidence就是预测的bounding box和ground truth box的IOU值。 @@ -326,9 +330,9 @@ TODO ##### (2)Network Design YOLO检测网络包括24个卷积层和2个全连接层,如图所示: - + 图7.4.11 - + 图7.4.12 其中,卷积层用来提取图像特征,全连接层用来预测图像位置和类别概率值。YOLO网络借鉴了GoogLeNet分类网络结构。不同的是,YOLO未使用inception module,而是使用1×1卷积层(此处1x1卷积层的存在是为了跨通道信息整合)3×3卷积层进行简单替代。 @@ -337,14 +341,14 @@ TODO ##### (4)损失函数 损失函数的设计目标就是让坐标(x,y,w,h),confidence,classification这个三个方面达到很好的平衡。简单的全部采用了sum-squared error loss来做这件事会有以下不足:(1)8维的localization error和20维的classification error同等重要显然是不合理的;(2)如果一些栅格中没有object(一幅图中这种栅格很多),那么就会将这些栅格中的bounding box的confidence置为0,相比于较少的有object的栅格,这些不包含物体的栅格对梯度更新的贡献会远大于包含物体的栅格对梯度更新的贡献,这会导致网络不稳定甚至发散。 - + 图7.4.13 解决方案如下:更重视8维的坐标预测,给这些损失前面赋予更大的loss weight,记为λcoord,在pascal VOC训练中取5(上图蓝色框)。对没有object的bbox的confidence loss,赋予小的loss weight,记为λnoobj,在pascal VOC训练中取0.5(上图橙色框)。有object的bbox的confidence loss(上图红色框)和类别的loss(上图紫色框)的loss weight正常取1。 对不同大小的bbox预测中,相比于大bbox预测偏一点,小box预测偏相同的尺寸对IOU的影响更大。而sum-square error loss中对同样的偏移loss是一样。为了缓和这个问题,作者用了一个巧妙的办法,就是将box的width和height取平方根代替原本的height和width。在YOLO中,每个栅格预测多个bounding box,但在网络模型的训练中,希望每一个物体最后由一个bounding box predictor来负责预测。因此,当前哪一个predictor预测的bounding box与ground truth box的IOU最大,这个predictor就负责predict object。这会使得每个predictor可以专门的负责特定的物体检测。随着训练的进行,每一个predictor对特定的物体尺寸、长宽比的物体的类别的预测会越来越好。 图7.4.14神经网络输出后的检测流程 - + 图7.4.15 ##### (5)非极大值抑制 @@ -371,7 +375,7 @@ TODO 图7.4.18 #### 8.3.2.2 YOLOv2 YOLOv2相比YOLOv1做了很多方面的改进,这也使得YOLOv2的mAP有显著的提升,并且YOLOv2的速度依然很快,保持着自己作为one-stage方法的优势,YOLOv2和Faster R-CNN,SSD等模型的对比如图7.4.19所示。 - + 图7.4.19 YOLOv2与其它模型在VOC 2007数据集上的效果对比 YOLOv1虽然检测速度很快,但是在检测精度上却不如R-CNN系检测方法,YOLOv1在物体定位方面(localization)不够准确,并且召回率(recall)较低。YOLOv2共提出了几种改进策略来提升YOLO模型的定位准确度和召回率,从而提高mAP,YOLOv2在改进中遵循一个原则:保持检测速度,这也是YOLO模型的一大优势。YOLOv2的改进策略如图7.4.20所示,可以看出,大部分的改进方法都可以比较显著提升模型的mAP。 ##### YOLOv2改进策略 @@ -386,16 +390,16 @@ TODO ##### (3)Convolutional With Anchor Boxes 之前的YOLO利用全连接层的数据完成边框的预测,导致丢失较多的空间信息,定位不准。作者在这一版本中借鉴了Faster R-CNN中的anchor思想,回顾一下,anchor是RNP网络中的一个关键步骤,说的是在卷积特征图上进行滑窗操作,每一个中心可以预测9种不同大小的建议框。 - + 图7.4.21 为了引入anchor boxes来预测bounding boxes,作者在网络中果断去掉了全连接层。剩下的具体怎么操作呢? 首先,作者去掉了后面的一个池化层以确保输出的卷积特征图有更高的分辨率。然后,通过缩减网络,让图片输入分辨率为416×416,这一步的目的是为了让后面产生的卷积特征图宽高都为奇数,这样就可以产生一个center cell。作者观察到,大物体通常占据了图像的中间位置,就可以只用中心的一个cell来预测这些物体的位置,否则就要用中间的4个cell来进行预测,这个技巧可稍稍提升效率。最后,YOLOv2使用了卷积层降采样(factor为32),使得输入卷积网络的416×416图片最终得到13×13的卷积特征图(416/32=13)。加入了anchor boxes后,可以预料到的结果是召回率上升,准确率下降。我们来计算一下,假设每个cell预测9个建议框,那么总共会预测13×13×9=1521个boxes,而之前的网络仅仅预测7×7×2=98个boxes。具体数据为:没有anchor boxes,模型recall为81%,mAP为69.5%;加入anchor boxes,模型recall为88%,mAP为69.2%。这样看来,准确率只有小幅度的下降,而召回率则提升了7%,说明可以通过进一步的工作来加强准确率,的确有改进空间。 ##### (4)Dimension Clusters(维度聚类) 作者在使用anchor的时候遇到了两个问题,第一个是anchor boxes的宽高维度往往是精选的先验框(hand-picked priors),虽说在训练过程中网络也会学习调整boxes的宽高维度,最终得到准确的bounding boxes。但是,如果一开始就选择了更好的、更有代表性的先验boxes维度,那么网络就更容易学到准确的预测位置。和以前的精选boxes维度不同,作者使用了K-means聚类方法类训练bounding boxes,可以自动找到更好的boxes宽高维度。传统的K-means聚类方法使用的是欧氏距离函数,也就意味着较大的boxes会比较小的boxes产生更多的error,聚类结果可能会偏离。为此,作者采用的评判标准是IOU得分(也就是boxes之间的交集除以并集),这样的话,error就和box的尺度无关了,最终的距离函数为: - + 作者通过改进的K-means对训练集中的boxes进行了聚类,判别标准是平均IOU得分,聚类结果如下图: - + 图7.4.22数据集VOC和COCO上的边界框聚类分析结果 可以看到,平衡复杂度和IOU之后,最终得到k值为5,意味着作者选择了5种大小的box维度来进行定位预测,这与手动精选的box维度不同。结果中扁长的框较少,而瘦高的框更多(这符合行人的特征),这种结论如不通过聚类实验恐怕是发现不了的。当然,作者也做了实验来对比两种策略的优劣,如下图,使用聚类方法,仅仅5种boxes的召回率就和Faster R-CNN的9种相当。说明K-means方法的引入使得生成的boxes更具有代表性,为后面的检测任务提供了便利。 表7.4.1 @@ -408,13 +412,13 @@ TODO ##### (6)Direct location prediction 前面讲到,YOLOv2借鉴RPN网络使用anchor boxes来预测边界框相对先验框的offsets。边界框的实际中心位置 ,需要根据预测的坐标偏移值 ,先验框的尺度 以及中心坐标 (特征图每个位置的中心点)来计算: - + 但是上面的公式是无约束的,预测的边界框很容易向任何方向偏移,如当 时边界框将向右偏移先验框的一个宽度大小,而当 时边界框将向左偏移先验框的一个宽度大小,因此每个位置预测的边界框可以落在图片任何位置,这导致模型的不稳定性,在训练时需要很长时间来预测出正确的offsets。所以,YOLOv2弃用了这种预测方式,而是沿用YOLOv1的方法,就是预测边界框中心点相对于对应cell左上角位置的相对偏移值,为了将边界框中心点约束在当前cell中,使用sigmoid函数处理偏移值,这样预测的偏移值在(0,1)范围内(每个cell的尺度看做1)。总结来看,根据边界框预测的4个offsets: ,可以按如下公式计算出边界框实际位置和大小: - + 其中为 为cell的左上角坐标,如图5所示,在计算时每个cell的尺度为1,所以当前cell的左上角坐标为(1,1)。由于sigmoid函数的处理,边界框的中心位置会约束在当前cell内部,防止偏移过多。而 和 是先验框的宽度与长度,前面说过它们的值也是相对于特征图大小的,在特征图中每个cell的长和宽均为1。这里记特征图的大小为 (在文中是(13,13)),这样我们可以将边界框相对于整张图片的位置和大小计算出来(4个值均在0和1之间): - + 如果再将上面的4个值分别乘以图片的宽度和长度(像素点值)就可以得到边界框的最终位置和大小了。这就是YOLOv2边界框的整个解码过程。约束了边界框的位置预测值使得模型更容易稳定训练,结合聚类分析得到先验框与这种预测方法,YOLOv2的mAP值提升了约5%。 - + 图7.4.23边界框位置与大小的计算示例图 ##### (7)Fine-Grained Features @@ -423,7 +427,7 @@ TODO ##### (8)Multi-Scale Training 由于YOLOv2模型中只有卷积层和池化层,所以YOLOv2的输入可以不限于416*416大小的图片。为了增强模型的鲁棒性,YOLOv2采用了多尺度输入训练策略,具体来说就是在训练过程中每间隔一定的iterations之后改变模型的输入图片大小。由于YOLOv2的下采样总步长为32,输入图片大小选择一系列为32倍数的值:输入图片最小为320*320,此时对应的特征图大小为10*10(不是奇数了,确实有点尴尬),而输入图片最大为608*608,对应的特征图大小为19*19,在训练过程,每隔10个iterations随机选择一种输入图片大小,然后只需要修改对最后检测层的处理就可以重新训练。 - + 图7.4.24 Multi-Scale Training 采用Multi-Scale Training策略,YOLOv2可以适应不同大小的图片,并且预测出很好的结果。在测试时,YOLOv2可以采用不同大小的图片作为输入,在VOC 2007数据集上的效果如下图所示。可以看到采用较小分辨率时,YOLOv2的mAP值略低,但是速度更快,而采用高分辨输入时,mAP值更高,但是速度略有下降,对于544*544,mAP高达78.6%。注意,这只是测试时输入图片大小不同,而实际上用的是同一个模型(采用Multi-Scale Training训练)。 @@ -440,7 +444,7 @@ TODO #### 8.3.2.3 YOLO9000 YOLO9000是在YOLOv2的基础上提出的一种可以检测超过9000个类别的模型,其主要贡献点在于提出了一种分类和检测的联合训练策略。众多周知,检测数据集的标注要比分类数据集打标签繁琐的多,所以ImageNet分类数据集比VOC等检测数据集高出几个数量级。在YOLO中,边界框的预测其实并不依赖于物体的标签,所以YOLO可以实现在分类和检测数据集上的联合训练。对于检测数据集,可以用来学习预测物体的边界框、置信度以及为物体分类,而对于分类数据集可以仅用来学习分类,但是其可以大大扩充模型所能检测的物体种类。 作者选择在COCO和ImageNet数据集上进行联合训练,但是遇到的第一问题是两者的类别并不是完全互斥的,比如"Norfolk terrier"明显属于"dog",所以作者提出了一种层级分类方法(Hierarchical classification),主要思路是根据各个类别之间的从属关系(根据WordNet)建立一种树结构WordTree,结合COCO和ImageNet建立的WordTree如下图所示: - + 图7.4.26 基于COCO和ImageNet数据集建立的WordTree WordTree中的根节点为"physical object",每个节点的子节点都属于同一子类,可以对它们进行softmax处理。在给出某个类别的预测概率时,需要找到其所在的位置,遍历这个path,然后计算path上各个节点的概率之积。 @@ -449,7 +453,7 @@ TODO #### 8.3.2.4 YOLOv3 YOLOv3在Pascal TitanX上处理608x608图像速度达到20FPS,在COCO test-dev上mAP@0.5达到57.9%,与RetinaNet(FocalLoss论文所提出的单阶段网络)的结果相近,并且速度快4倍。YOLOv3的模型比之前的模型复杂了不少,可以通过改变模型结构的大小来权衡速度与精度。速度对比如下: - + 图7.4.28 性能对比图 YOLOv3在实现相同准确度下要显著地比其它检测方法快。时间都是在采用M40或TitanX等相同GPU下测量的。 简而言之,YOLOv3的先验检测(Prior detection)系统将分类器或定位器重新用于执行检测任务。他们将模型应用于图像的多个位置和尺度。而那些评分较高的区域就可以视为检测结果。此外,相对于其它目标检测方法,我们使用了完全不同的方法。我们将一个单神经网络应用于整张图像,该网络将图像划分为不同的区域,因而预测每一块区域的边界框和概率,这些边界框会通过预测的概率加权。我们的模型相比于基于分类器的系统有一些优势。它在测试时会查看整个图像,所以它的预测利用了图像中的全局信息。与需要数千张单一目标图像的R-CNN不同,它通过单一网络评估进行预测。这令YOLOv3非常快,一般它比R-CNN快1000倍、比Fast R-CNN快100倍。 diff --git a/ch09_图像分割/第九章_图像分割.md b/ch09_图像分割/第九章_图像分割.md index 883e90f..db446e8 100644 --- a/ch09_图像分割/第九章_图像分割.md +++ b/ch09_图像分割/第九章_图像分割.md @@ -1,10 +1,13 @@ -######################################################### -### 深度学习500问-第九章 图像分割(md版本) + + +[TOC] + 作者:scutan90 编辑者:shw2018(UESTC_孙洪卫_硕,Wechat:sunhwee) 提交:2018.10.25 更新:2018.10.31 -######################################################### + +###### # **第九章 图像分割** @@ -223,7 +226,7 @@ learning rate:0.001。    (4) 最后再经过两次反卷积操作,生成特征图,再用两个1X1的卷积做分类得到最后的两张heatmap,例如第一张表示的是第一类的得分,第二张表示第二类的得分heatmap,然后作为softmax函数的输入,算出概率比较大的softmax类,选择它作为输入给交叉熵进行反向传播训练。 -## 下面是U-Net模型的代码实现:(贡献者:黄钦建-华南理工大学) +下面是U-Net模型的代码实现:(贡献者:黄钦建-华南理工大学) ``` def get_unet(): @@ -367,7 +370,7 @@ RefineNet block的作用就是把不同resolution level的feature map进行融    Residual convolution unit就是普通的去除了BN的residual unit; - +    Multi-resolution fusion是先对多输入的feature map都用一个卷积层进行adaptation(都化到最小的feature map的shape),再上采样再做element-wise的相加。注意如果是像RefineNet-4那样的单输入block这一部分就直接pass了; @@ -636,7 +639,7 @@ UC Berkeley的Deepak Pathak使用了一个具有图像级别标记的训练数 $$ \underset{\theta ,P}{minimize}\qquad D(P(X)||Q(X|\theta ))\\ subject\to\qquad A\overrightarrow{P} \geqslant \overrightarrow{b},\sum_{X}^{ }P(X)=1 -$$ +$$    其中的线性限制条件来自于训练数据上的标记,例如一幅图像中前景类别像素个数期望值的上界或者下界(物体大小)、某个类别的像素个数在某图像中为0,或者至少为1等。该目标函数可以转化为为一个loss function,然后通过SGD进行训练。 @@ -656,7 +659,7 @@ Google的George Papandreou 和UCLA的Liang-Chieh Chen等在DeepLab的基础上 $$ P\left ( x,y,z;\theta \right ) = P\left ( x \right )\left (\prod_{m=1}^{M} P\left ( y_m|x;\theta \right )\right )P\left ( z|y \right ) -$$ +$$    这篇论文是通过EM算法来学习模型的参数$\theta$,具体推导过程可参考原论文。 ![](./img/ch9/figure_9.9_7.png) diff --git a/ch10_强化学习/第十章_强化学习.md b/ch10_强化学习/第十章_强化学习.md index c31f051..32d460e 100644 --- a/ch10_强化学习/第十章_强化学习.md +++ b/ch10_强化学习/第十章_强化学习.md @@ -1,4 +1,9 @@ +[TOC] + + + # 第十章 强化学习 + ## 10.1强化学习的主要特点? 其他许多机器学习算法中学习器都是学得怎样做,而RL是在尝试的过程中学习到在特定的情境下选择哪种行动可以得到最大的回报。在很多场景中,当前的行动不仅会影响当前的rewards,还会影响之后的状态和一系列的rewards。RL最重要的3个特定在于: (1) 基本是以一种闭环的形式; @@ -13,7 +18,7 @@ 小孩就是 agent,他试图通过采取行动(即行走)来操纵环境(行走的表面),并且从一个状态转变到另一个状态(即他走的每一步),当他完成任务的子任务(即走了几步)时,孩子得到奖励(给巧克力吃),并且当他不能走路时,就不会给巧克力。 ![](./img/ch10/10-1.png) - + 上图中agent代表自身,如果是自动驾驶,agent就是车;如果你玩游戏它就是你当前控制的游戏角色,如马里奥,马里奥往前走时环境就一直在发生变化,有小怪物或者障碍物出现,它需要通过跳跃来进行躲避,就是要做action(如向前走和跳起的动作);无人驾驶的action就是车左转、右转或刹车等等,它无时无刻都在与环境产生交互,action会反馈给环境,进而改变环境,如果自动驾驶的车行驶目标是100米,它向前开了10米,那环境就发生了变化,所以每次产生action都会导致环境改变,环境的改变会反馈给自身(agent),就是这样的一个循环;反馈又两种方式:1、做的好(reward)即正反馈,2、做得不好(punishment惩罚)即负反馈。Agent可能做得好,也可能做的不好,环境始终都会给它反馈,agent会尽量去做对自身有利的决策,通过反反复复这样的一个循环,agent会越来越做的好,就像孩子在成长过程中会逐渐明辨是非,这就是强化学习。 ## 10.2强化学习应用实例 (1)Manufacturing @@ -91,7 +96,7 @@ exploitation 会尝试过去经验中最有效的行为。 强化学习不需要监督信号,可以在模型未知的环境中平衡探索和利用, 其主要算法有蒙特卡罗强化学习, 时间差分(temporal difference: TD)学习, 策略梯度等。典型的深度强化学习算法特点及性能比较如下图所示: ![](./img/ch10/10-4.png) - + 除了上述深度强化学习算法,还有深度迁移强化学习、分层深度强化学习、深度记忆强化学习以及多智能体强化学习等算法。 ## 10.5深度迁移强化学习算法 传统深度强化学习算法每次只能解决一种游戏任务, 无法在一次训练中完成多种任务. 迁移学习和强化学习的结合也是深度强化学习的一种主要思路。 diff --git a/ch11_迁移学习/第十一章_迁移学习.md b/ch11_迁移学习/第十一章_迁移学习.md index b39c05d..125835e 100644 --- a/ch11_迁移学习/第十一章_迁移学习.md +++ b/ch11_迁移学习/第十一章_迁移学习.md @@ -1,4 +1,8 @@ -# 第十章 迁移学习 +[TOC] + + + +# 第十章 迁移学习 ## 10.1 什么是迁移学习? 1. 找到目标问题的相似性,迁移学习任务就是从相似性出发,将旧领域(domain)学习过的模型应用在新领域上。 diff --git a/ch12_网络搭建及训练/第十二章_网络搭建及训练.md b/ch12_网络搭建及训练/第十二章_网络搭建及训练.md index 0cee9a6..efc896c 100644 --- a/ch12_网络搭建及训练/第十二章_网络搭建及训练.md +++ b/ch12_网络搭建及训练/第十二章_网络搭建及训练.md @@ -1,4 +1,9 @@ +[TOC] + + + # 第十二章 网络搭建及训练。 + ## 10.1 网络搭建有什么原则? ### 10.1.1新手原则。 @@ -35,7 +40,7 @@ AlexNet中用到了一些非常大的卷积核,比如11×11、5×5卷积核, | 2 | 2014 | VGGNet | ILSVRC图像分类亚军 | | 3 | 2014 | GoogLeNet| ILSVRC图像分类冠军 | | 4 | 2015 | ResNet | ILSVRC图像分类冠军 | -| 5 | 2017 | SeNet | ILSVRC图像分类冠军 | +| 5 | 2017 | SeNet | ILSVRC图像分类冠军 | > - 1 AlexNet 论文:[ImageNet Classification with Deep Convolutional Neural Networks](https://papers.nips.cc/paper/4824-imagenet-classification-with-deep-convolutional-neural-networks.pdf) 代码实现:[tensorflow](https://github.com/tensorflow/tensorflow/blob/361a82d73a50a800510674b3aaa20e4845e56434/tensorflow/contrib/slim/python/slim/nets/alexnet.py) diff --git a/ch13_优化算法/第十三章_优化算法.md b/ch13_优化算法/第十三章_优化算法.md index 2cef7b0..88eae7f 100644 --- a/ch13_优化算法/第十三章_优化算法.md +++ b/ch13_优化算法/第十三章_优化算法.md @@ -1,3 +1,7 @@ +[TOC] + + + # 第一十三章 优化算法 diff --git a/ch14_超参数调整/第十四章_超参数调整.md b/ch14_超参数调整/第十四章_超参数调整.md index 97d3c02..d4fef76 100644 --- a/ch14_超参数调整/第十四章_超参数调整.md +++ b/ch14_超参数调整/第十四章_超参数调整.md @@ -1,3 +1,7 @@ +[TOC] + + + # 第十四章 超参数调整 > Markdown Revision 1; diff --git a/ch15_GPU和框架选型/第十五章_异构运算、GPU及框架选型.md b/ch15_GPU和框架选型/第十五章_异构运算、GPU及框架选型.md index eb22484..e11ae30 100644 --- a/ch15_GPU和框架选型/第十五章_异构运算、GPU及框架选型.md +++ b/ch15_GPU和框架选型/第十五章_异构运算、GPU及框架选型.md @@ -1,4 +1,9 @@ +[TOC] + + + # 第十五章 异构计算, GPU和框架选型指南 + 深度学习训练和推理的过程中,会涉及到大量的向量(vector),矩阵(matrix)和张量(tensor)操作,通常需要大量的浮点计算,包括高精度(在训练的时候)和低精度(在推理和部署的时候)。GPU, 作为一种通用可编程的加速器,最初设计是用来进行图形处理和渲染功能,但是从2007年开始,英伟达(NVIDIA)公司提出了第一个可编程通用计算平台(GPGPU),同时提出了CUDA框架,从此开启了GPU用于通用计算的新纪元。此后,不计其数的科研人员和开发者,对各种不同类型的算法用CUDA进行(部分)改写,从而达到几倍到数百倍的加速效果。尤其是在机器学习,特别是深度学习的浪潮来临后,GPU加速已经是各类工具实现的基本底层构架之一。本章里,会简单介绍GPU的基本架构,性能指标,框架选择等等和深度学习相关的内容。 ## 15.1 什么是异构计算? @@ -153,26 +158,26 @@ cuda8.0: sudo sh cuda_8.0.61_375.26_linux.run cuda9.0: sudo sh cuda_9.0.176_384.81_linux.run 之后命令之后下面就是安装步骤,cuda8.0和cuda9.0几乎一致: 1) 首先出现cuda软件的版权说明,可以直接按q键跳过阅读 - + 2) Do you accept the previously read EULA? - accept/decline/quit: **accept** +​ accept/decline/quit: **accept** 3) Install NVIDIA Accelerated Graphics Driver for Linux-x86_64 384.81? - (y)es/(n)o/(q)uit: **no** - +​ (y)es/(n)o/(q)uit: **no** +​ 4) Install the CUDA 9.0 Toolkit? - (y)es/(n)o/(q)uit: **yes** - +​ (y)es/(n)o/(q)uit: **yes** +​ 5) Enter Toolkit Location - [ default is /usr/local/cuda-9.0 ]: 直接按enter键即可 +​ [ default is /usr/local/cuda-9.0 ]: 直接按enter键即可 6) Do you want to install a symbolic link at /usr/local/cuda? - (y)es/(n)o/(q)uit: **yes** +​ (y)es/(n)o/(q)uit: **yes** 7) Install the CUDA 9.0 Samples? - (y)es/(n)o/(q)uit: **yes** - +​ (y)es/(n)o/(q)uit: **yes** +​ 以上步骤基本就是cuda的安装步骤。 @@ -276,7 +281,6 @@ mxnet的最知名的优点就是其对多GPU的支持和扩展性强,其优秀 ### 15.8.6 未来量子计算对于深度学习等AI技术的影响? - ------- @@ -364,7 +368,7 @@ mxnet是dmlc社区推出的深度学习框架,在2017年被亚马逊指定为 (1)tensorRT (2)TVM - - (3)ONNX - + + (3)ONNX + diff --git a/ch16_自然语言处理(NLP)/第十六章_NLP.md b/ch16_自然语言处理(NLP)/第十六章_NLP.md index 36c274c..c597aee 100644 --- a/ch16_自然语言处理(NLP)/第十六章_NLP.md +++ b/ch16_自然语言处理(NLP)/第十六章_NLP.md @@ -1,3 +1,7 @@ +[TOC] + + + # 第十六章 NLP Markdown Revision 1; diff --git a/ch17_模型压缩、加速及移动端部署/第十七章_模型压缩、加速及移动端部署.md b/ch17_模型压缩、加速及移动端部署/第十七章_模型压缩、加速及移动端部署.md index f192ffb..b1584a3 100644 --- a/ch17_模型压缩、加速及移动端部署/第十七章_模型压缩、加速及移动端部署.md +++ b/ch17_模型压缩、加速及移动端部署/第十七章_模型压缩、加速及移动端部署.md @@ -1,10 +1,14 @@ +[TOC] + + + # 第十七章 模型压缩及移动端部署 Markdown Revision 1; Date: 2018/11/4 Editor: 谈继勇 Contact: scutjy2015@163.com - updata:贵州大学硕士张达峰 + updata:贵州大学硕士张达峰 ## 17.1 为什么需要模型压缩和加速? (1)对于在线学习和增量学习等实时应用而言,如何减少含有大量层级及结点的大型神经网络所需要的内存和计算量显得极为重要。 @@ -42,14 +46,14 @@ https://blog.csdn.net/Touch_Dream/article/details/78441332 剪枝操作包括:非结构化剪枝和结构化剪枝。非结构化剪枝是对神经网络中权重较小的权重或者权重矩阵进剔除,然后对整个神经网络进行微调;结构化剪枝是在网络优化目标中加入权重稀疏正则项,使部分权重在训练时趋于0。 优点: - + * 保持模型性能不损失的情况下,减少参数量9-11倍; * 剔除不重要的权重,可以加快计算速度,同时也可以提高模型的泛化能力; 缺点: - + * 非结构化剪枝会增加内存访问成本; * 极度依赖专门的运行库和特殊的运行平台,不具有通用性; @@ -345,9 +349,9 @@ depthwise convolution 和 瓶颈结构增加了 MAC,用了太多的 group, ### 17.7.1 NCNN ncnn (GitHub地址:https://github.com/Tencent/ncnn ) https://cloud.tencent.com/developer/article/1005805 - + 特点: - NCNN其架构设计以手机端运行为主要原则,考虑了手机端的硬件和系统差异以及调用方式。无第三方依赖,跨平台,手机端 CPU 的速度快于目前所有已知的开源框架。基于 ncnn,开发者能够将深度学习算法轻松移植到手机端高效执行,开发出人工智能 APP,将 AI 带到你的指尖。ncnn 目前已在腾讯多款应用中使用,如 QQ,Qzone,微信,天天P图等。 +​ NCNN其架构设计以手机端运行为主要原则,考虑了手机端的硬件和系统差异以及调用方式。无第三方依赖,跨平台,手机端 CPU 的速度快于目前所有已知的开源框架。基于 ncnn,开发者能够将深度学习算法轻松移植到手机端高效执行,开发出人工智能 APP,将 AI 带到你的指尖。ncnn 目前已在腾讯多款应用中使用,如 QQ,Qzone,微信,天天P图等。 功能: 1、NCNN支持卷积神经网络、多分支多输入的复杂网络结构,如主流的 vgg、googlenet、resnet、squeezenet 等。 diff --git a/ch18_后端架构选型、离线及实时计算/第十八章_后端架构选型、离线及实时计算.md b/ch18_后端架构选型、离线及实时计算/第十八章_后端架构选型、离线及实时计算.md index c86f279..9bbd573 100644 --- a/ch18_后端架构选型、离线及实时计算/第十八章_后端架构选型、离线及实时计算.md +++ b/ch18_后端架构选型、离线及实时计算/第十八章_后端架构选型、离线及实时计算.md @@ -1,3 +1,7 @@ +[TOC] + + + # 第十八章_后端架构选型、离线及实时计算 Markdown Revision 1; @@ -279,7 +283,7 @@ Github地址:https://github.com/uber/petastorm ## 18.4 如何进行实时计算? ## 18.5 如何进行离线计算? - + ## 18.6 如何使用分布式框架提高模型训练速度? ## 18.7 深度学习分布式计算框架如何在移动互联网中应用? @@ -311,6 +315,6 @@ Github地址:https://github.com/uber/petastorm 【10】https://yahoo.github.io/TensorFlowOnSpark/# .... - + 未完待续! diff --git a/chap05/img/img1.png b/chap05/img/img1.png deleted file mode 100644 index d4e31d02d3d5ba8bfd4c4088ee660a402bcb709a..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 699253 zcmV(aLI1vqP)Px#1ZP1_K>z@;j|==^1poj532;bRa{vG#)c^n?)d2*Yw4DF||D{PpK~#8N?41Ri 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