很早之前就想学习LaTeX，之前只是看书，看了好长时间并没有什么收获，效率不高。七天前开始结合一个具体任务（中期报告）来做幻灯片，中间有三天没有做，真正花在其上的时间是三天半至四天，这四天因为是任务驱动，需要什么学什么，遇到什么问题搜索什么，哪个命令不懂查哪个，所以进步特别快，收获非常大。记起老师说的，现阶段的学习不再是抱着一本书系统性的学习，太耗费时间、精力，且效率低，很不一定能用到。而是要求你结合问题去学习，要求你能看到问题，知道如何去解决。从提出到解决问题的过程中去学习，搞明白知识，能做出点东西来。
附我做的幻灯片的LaTeX源码 （2.9版LaTeX）。(直接复制粘贴不能用，里面有些内容在往博客上粘贴时格式变了，所以，要借鉴的话一点点往LaTeX粘贴吧，基本上两个百分号行之间是一个幻灯片的内容)
\documentclass[cjk]{beamer}
\usepackage{CJK}
\usepackage{amsmath}
\usepackage{mathdots}
\usepackage{graphicx}
\usepackage{float}
\usepackage{multirow}
\usetheme{Warsaw}
\begin{document}
\begin{CJK*}{GBK}{kai}
\title{********************************}
\author{指导老师\ ***\\ 报告人\ **}
%\date{\today}
\frame{\titlepage}
%\frame{\frametitle{目录}\tableofcontents}
%\section{背景介绍}
%\section{现有恒星大气参数估计方案}
%\section{课题研究内容及其设计}
%\section{已完成的研究工作及结果}
%\section{存在的问题及其解决方案}
%\section{后期拟完成的研究工作}
\begin{itemize}[]
\item背景介绍
\item现有恒星大气参数估计方案
\item课题研究内容及其设计
\item恒星光谱数据和对应恒星大气物理参数
\\ 原始光谱数据详细信息
\\ 数据预处理
\item特征提取
\\ 前向传播过程
\\ 反向传播过程
\\ 算法伪代码
\item回归预测分析
\item评价指标
\\ 平均绝对误差 \ MAE
\\ 标准差 \ SD
\item对比试验
\\ 稀疏自编码 \ VS\ 主成分分析
\\ SVR \ VS \ 线性树 \ 回归树 \ 神经网络
\end{itemize}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{背景介绍}
恒星发出的光包含星体自身的温度$T_{eff}$、星体表面重力加速度$log \ g$、化学元素丰富度$[Fe/H]$信息，科学家通过对天文望远镜采集来的恒星光谱数据分析恒星目前的温度、重力加速度、化学元素丰富度，确定恒星的年龄，进而探索宇宙的历史。
\\ 传统的恒星参数估计方法包括\ 线指数法\ ，模板匹配法。它们物理意义明确，适合分析小量恒星光谱数据的情况。
\\ 随着GAIA，SLOAN和郭守敬望远镜（LAMOST）等大型巡天计划的相继实施，我们正在高速获取大量恒星光谱数据。传统恒星参数估计方法已不能适应处理如此庞大的数据量，直接从光谱中估计大气参数变得非常必要。特别是，恒星有效温度（Teff）、重力加速度（logged）与化学丰度（Fe/H）等物理参数的自动估计成为相关研究中的一个热点。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{现有恒星大气参数估计方案}
\begin{itemize}[]
\item线指数法；
\item模板匹配法；
\item统计估计法；
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{现有恒星大气参数估计方案}
线指数法：\\
优点：物理意义强\\
局限性：是在实测光谱噪声畸变影响下谱线准确提取难以实现 \\
模板匹配法：\\
优点：准确，目前使用最多的方法\\
局限性：高度依赖模板库，模板库是通过某个物理模型生成，物理模型往往存在不同适用范围，该局限性导致相应的参数估计在有些情况下不理想
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{统计估计法}
统计估计法\ 即使用统计回归方法对恒星物理参数进行估计，这类方法假定对问题背后物理模型不甚明了，相关信息在观测数据中，这类方法在当前光谱数据以雪崩之势增长情况下显得尤为重要。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{课题研究内容及其设计}
本课题通过利用深度学习领域中的一种特征提取方法（自编码）和支持向量回归的组合，来解决现有方案中存在的不足。主要分为以下三个步骤：
\begin{itemize}[]
\item（1）对所使用数据的分析和对所使用数据的预处理，确保下一步使用自编码进行特征提取的实施。
\item（2）特征提取问题。构建三层稀疏自编码神经网络，令输出层神经元数量等于输入层神经元数量，限制隐层神经元的数量，使用梯度下降法进行训练，训练结束，隐层神经元的激活输出即为我们要提取的光谱数据特征。
\item（3）回归问题。利用支持向量回归进行恒星大气物理参数估计。
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{恒星光谱数据和对应恒星大气物理参数}
第七次发布的斯隆数据中的20000条SDSS／SEGUE观测恒星光谱和它们之前计算出的对应物理参数。
\begin{equation}
\left[
\begin{array}{cccc}
a_{11} & a_{12} & \dots & a_{1*3821} \\
a_{21}& a_{22} & \dots & a_{2*3821} \\
\vdots & \vdots & \ddots &\vdots \\
a_{20000*1} & a_{20000*2} & \dots & a_{20000*3821} \\
\end{array}
\right]
\end{equation}
\section{恒星大气物理参数}
\begin{equation}
\left[
\begin{array}{ccc}
b_{11} & b_{12} & b_{13} \\
b_{21} & b_{22} & b_{23} \\
\vdots & \vdots & \vdots \\
a_{20000*1} & a_{20000*2} & a_{20000*3} \\
\end{array}
\right]
\end{equation}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{所用原始光谱的详细信息}
所使用的光谱的有效温度Teff的跨度范围是$[4088,9704]K$，表面重力加速度log g的跨度范围是$[1.015000,4.998000]dex$,化学丰度［Fe/H] 的跨度范围是$[－3.497000,0.268000]dex$。 \\
光自身所具有的多普勒效应造成了光谱谱线的红移，我们首先去除光谱红移，使光谱波长统一于静止波长之下，然后截取相同波段的光谱数据进行物理参数估计。所以，基于SSPP提供的此前估计的径向速度，所有的观测恒星光谱被移动到了零径向速度，截取共同波段范围：$[3.5808, 3.9640]$, 并按照分辨率0.0001对光谱进行线性差值采样。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{数据预处理}
\begin{equation}
Str={ (x^i ,y_i ) ,i=1 ,2 , . . . ,N }
\end{equation}
\begin{itemize}
\item 1.使用logTeff取代Teff减小动态范围，更好的表达光谱数据的不确定性
\item 2.使用逐样本归一化的方式把数据归一化到[0,1]之间，表达式可以表示为：
\begin{equation}
x_j^i=(x_j^i-x_{min}^i)/(x_{max}^i-x_{min}^i)
\end{equation}
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{特征提取}
\begin{figure}[H]
\centering
\includegraphics[height=16cm,width=13cm]{autoencoder1.pdf}
\caption{Endpoint detection}
\end {figure}
%\centering{}\includegraphics[width=12cm]{autoencoder.pdf}\caption{Caption here}
%\centering{}\includegraphics[width=3in]{fig1.eps}\caption{Caption here}
%\end{figure}
%\begin{small}
%\begin{equation}
%\begin{aligned}
%\resizebox{.9\hsize}{!}{$J(W,b)=\frac 1m \sum_{i=1}^m\frac 12\Vert h_{w,b}(x^{(i)})-y^i\Vert^2+\frac \lambda2 %\sum_{l=1}^{n_l-1} \sum_{i=1}^{S_l} \sum_{j=1}^{S_l+1} (W_{ij}^{(l)})^2+\beta \sum_{j=1}^{s_2}[\rho \log \frac \rho %\rho\hat+(1-\rho)]$}%\log %\frac{1-\rho}{1-\rho\hat}]
%\end{aligned}
%\end{equation}
%\end{small}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{前向传播过程}
%\begin{small}
\begin{gather}
z^{(2)}=f(w^{(1)}x+b^{(1)}) \notag \\
a^{(2)}=f(z^{(2)}) \notag \\
z^{(3)}=w^{(2)}a^{(2)}+b^{(2)} \notag \\
h_{w,b}(x)=a^{(3)}=f(z^{(3)}) \notag
\end{gather}
%\end{small}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{反向传播过程}
\begin{itemize}[]
\item 1 进行前馈传到计算，得到$L_{2}$,$L_{3},....$的激活值。
\item 2 对于第$n_{l}$层（输出层）的每个输出单元$i$ ，我们根据以下公式计算残差 $$\delta^{(n_l)}=-(y-a^{(n_l)})\cdot f^{'}(z^{(n_l)})$$
\item 3 对于$ l=n_l-1,n_l-2,n_l-3,...,2 $ 的各层，计算：
$$\delta^{(l)}=((W^{(l)})^T \delta^{(l+1)})\cdot f^{'}(z^{(l)})$$
\item 4 计算最终需要的偏导数值：
$$ \nabla_{W^{(l)}}J(W,b;x,y)= \delta^{(l+1)}(a^{(l)})^T,$$
$$ \nabla_{b^{(l)}}J(W,b;x,y)= \delta^{(l+1)}.$$
\end{itemize}
\begin{equation}
%\begin{aligned}
\resizebox{.9\hsize}{!}{$J(W,b)=\frac 1m \sum_{i=1}^m\frac 12\Vert h_{w,b}(x^{(i)})-y^i\Vert^2+\frac \lambda2 \sum_{l=1}^{n_l-1} \sum_{i=1}^{S_l} \sum_{j=1}^{S_l+1} (W_{ij}^{(l)})^2+\beta \sum_{j=1}^{s_2}[\rho \log \frac \rho \rho\hat+(1-\rho)\log \frac {1-\rho}{1-\hat{\rho}}]$}%\log %\frac{1-\rho}{1-\rho\hat}]
%\end{aligned}
\end{equation}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{伪代码}
\framesubtitle{实现批量梯度下降法的一次迭代}
\begin{itemize}[]
\item 1.对于所有l,令$ \Delta W^{(l)}:=0,\Delta b^{(l)}:=0 $ (设置全零矩阵或全零向量)
\item 2.对于$i=1$到$ m $,
\\ a.使用反向传播算法$ \nabla_{W^{(l)}}J(W,b;x,y)$ 和 $\nabla_{b^{(l)}}J(W,b;x,y)$.
\\ b.计算$ \Delta W^{(l)}:=\Delta W^{(l)}+\nabla_{W^{(l)}J(W,b;x,y)} $.
\\ c.计算$ \Delta b^{(l)}:=\Delta b^{(l)}+\nabla_{b^{(l)}J(W,b;x,y)} $.
\item 3.更新权重参数：
\\ $ W^{(l)} = W^{(l)}- \alpha[(\frac 1m \Delta W^{(l)})+\lambda W^{(l)}] $
\\ $ b^{(l)} = b^{(l)}- \alpha[(\frac 1m \Delta b^{(l)}] $
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{回归问题}
实际天文光谱数据采集、前期处理难度比较大，光谱中存在天光残余量，光谱信号存在微小畸变，这增加了恒星大气物理参数测量的难度。\\ 支持向量机引入了∈-损失函数，对光谱畸变的容忍性比较好，因此我们采用支持向量回归算法来建立恒星光谱和大气参数的映射关系。\\ 支持向量回归基于结构风险最小化标准，结合经验主义误差和模型复杂度计算，自我们提取的光谱特征组成的训练集中学习估计模型。多方面研究显示，我们生成的估计模型具有很好的泛化能力。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{公式}
\begin{block}{平均绝对误差}
\begin{equation}
MAE=\frac 1M\sum_{m=1}^M\vert e_m \vert
\end{equation}
\end{block}
\begin{block}{标准差}
\begin{equation}
SD=\sqrt{\frac 1M\sum_{m=1}^M(e_m-\bar{e})^2}
\end{equation}
\end{block}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{样本使用稀疏自编码SVR方法进行恒星大气物理参数估计，比较提取不同维数特征对应的参数log Teff ,log g 和[Fe/H] 的估计误差}
\centerline{\includegraphics[height=20cm,width=13cm]{fig1.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{样本使用SVR（PCA）方法进行恒星大气物理参数估计，比较提取不同维数特征下对应的参数log Teff ,log g和[Fe/H]的估计误差}
\centerline{\includegraphics[height=20cm,width=13cm]{fig2.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{稀疏自编码\ VS \ PCA}
\centerline{\includegraphics[height=17cm,width=13cm]{fig3.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SVR \ 回归树 \ 线性回归 \ 反向传播神经网络}
\centerline{\includegraphics[height=17cm,width=13cm]{fig4.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ 稀疏自编码回归树方案}
\centerline{\includegraphics[height=21cm,width=15cm]{fig6.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ 稀疏自编码线性回归方案}
\centerline{\includegraphics[height=21cm,width=15cm]{fig7.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ 稀疏自编码三层神经网络方案}
\centerline{\includegraphics[height=21cm,width=15cm]{fig8.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{ 稀疏自编码SVR方案}
\centerline{\includegraphics[height=21cm,width=15cm]{fig9.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{稀疏自编码回归树\ 稀疏自编码线性回归\ 稀疏自编码反向传播神经网络\ 稀疏自编码SVR }
\centerline{\includegraphics[height=5cm,width=13cm]{fig5.pdf}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{结论}
提出了基于稀疏自编码SVR的大气物理参数测量的新方法。此方法适用于高维大样本的光谱物理参数的测量。采用该模型对Sloan Digtal Sky Survey(SDSS)采集来的光谱数据进行测量，获得了非常好的实验结果。
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\huge 谢谢! \\ %Q \& A
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{xiaojiebiaoti}
% \frame{
%\frametitle{列表环境}
%\begin{itemize}[]
%\item第一项；
%\item第二项；
%\item第三项。
%\end{itemize}
%}
% \frame{\frametitle{幻灯片测试}\pause
% 我的第一张幻灯片。
% }
\end{CJK*}
\end{document}