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<a href="/2018/08/Computer-Vision-01/" class="thumbnail">
<span style="background-image:url(/images/Computer_Vision.jpg)" alt="计算机视觉（一）：图像表示与梯度" class="thumbnail-image"></span>
<span class="comment-counter">
<i class="fa fa-comments-o"></i>
<span class="disqus-comment-count" data-disqus-identifier="" data-disqus-url="https://haosutopia.github.io/2018/08/Computer-Vision-01/">0</span>
</span>
</a>
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<div class="category">
<a class="article-category-link" href="/categories/%E8%AE%A1%E7%AE%97%E6%9C%BA%E8%A7%86%E8%A7%89/">计算机视觉</a>
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<div class="date"><time datetime="2018-08-08T19:13:45.000Z" itemprop="datePublished">2018-08-09</time></div>
</div>
<h1 class="article-title" itemprop="name">
<a href="/2018/08/Computer-Vision-01/">计算机视觉（一）：图像表示与梯度</a>
</h1>
<p class="article-excerpt">
  计算机视觉，顾名思义就是使计算机能够像人眼一样“看”东西的科学。一张图片，人可以将它抽象并快速提取其中的有效信息。而对于计算机来说，图片就是一个特殊的矩阵，需要通过一系列算法来得到相关信息。本次学习材料主要是TUM Computer Vision课堂内容以及一些相关论文。
图像表示  首先介绍一下图像的基本知识。图像一般可分为彩色图和灰度图：彩色图每个点
</p>
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</article>
<article class="article article-summary">
<div class="article-summary-inner">
<a href="/2018/06/Decision-Tree-01/" class="thumbnail">
<span style="background-image:url(/images/Decision_Tree.png)" alt="决策树" class="thumbnail-image"></span>
<span class="comment-counter">
<i class="fa fa-comments-o"></i>
<span class="disqus-comment-count" data-disqus-identifier="" data-disqus-url="https://haosutopia.github.io/2018/06/Decision-Tree-01/">0</span>
</span>
</a>
<div class="article-meta">
<div class="category">
<a class="article-category-link" href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/">机器学习</a>
</div>
<div class="date"><time datetime="2018-05-31T20:56:03.000Z" itemprop="datePublished">2018-06-01</time></div>
</div>
<h1 class="article-title" itemprop="name">
<a href="/2018/06/Decision-Tree-01/">决策树</a>
</h1>
<p class="article-excerpt">
  机器学习中使用最多的算法莫过于神经网络与树形算法了，而树形算法的基础就是决策树（Decision Tree）。决策树是一种基本的分类与回归方法，相对于神经网络这种黑箱，决策树容易理解，并且运行速度快。但由于其结构较为简单，故预测能力有限，无法与强监督学习模型相提并论，需要进一步的优化。
概述  决策树的思想与我们在日常生活中进行判断或决策的过程类似。下面
</p>
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<a href="/2018/04/K-Means-01/" class="thumbnail">
<span style="background-image:url(/images/K_Means.png)" alt="K-Means聚类算法" class="thumbnail-image"></span>
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<a class="article-category-link" href="/categories/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0/">机器学习</a>
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<div class="date"><time datetime="2018-04-15T13:27:06.000Z" itemprop="datePublished">2018-04-15</time></div>
</div>
<h1 class="article-title" itemprop="name">
<a href="/2018/04/K-Means-01/">K-Means聚类算法</a>
</h1>
<p class="article-excerpt">
  K-Means聚类算法（k-means clustering algorithm）是一种无监督学习算法。它可以通过多次迭代，将一系列无标记的数据根据它们的特征分布划分为$k$个子集，使得子集内部元素之间的相异度尽可能低，而不同子集元素相异度尽可能高。我们称这样的子集为簇（cluster），而将数据划分为簇的过程称为聚类。
算法思想  假设我们有一组无标记
</p>
</div>
</article>
<article class="article article-summary">
<div class="article-summary-inner">
<a href="/2018/04/RSVP-07/" class="thumbnail">
<span style="background-image:url(/images/RSVP.png)" alt="分布参数系统控制（七）：边界输入" class="thumbnail-image"></span>
<span class="comment-counter">
<i class="fa fa-comments-o"></i>
<span class="disqus-comment-count" data-disqus-identifier="" data-disqus-url="https://haosutopia.github.io/2018/04/RSVP-07/">0</span>
</span>
</a>
<div class="article-meta">
<div class="category">
<a class="article-category-link" href="/categories/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AE%BA/">控制理论</a><i class="icon fa fa-angle-right"></i><a class="article-category-link" href="/categories/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AE%BA/%E5%88%86%E5%B8%83%E5%8F%82%E6%95%B0%E7%B3%BB%E7%BB%9F%E6%8E%A7%E5%88%B6/">分布参数系统控制</a>
</div>
<div class="date"><time datetime="2018-04-12T22:39:55.000Z" itemprop="datePublished">2018-04-13</time></div>
</div>
<h1 class="article-title" itemprop="name">
<a href="/2018/04/RSVP-07/">分布参数系统控制（七）：边界输入</a>
</h1>
<p class="article-excerpt">
  分布参数系统的输入可以分为点输入、分布式输入和边界输入。之前的章节我们讨论的都是分布式输入，此时输入分布在定义域的某个区间。而若输入$u(t)$定义在边界，则称为边界输入（Randeingriff），此时系统方程会有所不同，相应的计算方法也会有差别。因此本文讨论边界输入以及它在反馈控制中的应用。
边界输入系统方程  分布式输入中，输入$u(t)$在系统状
</p>
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</article>
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<a href="/2018/04/RSVP-06/" class="thumbnail">
<span style="background-image:url(/images/RSVP.png)" alt="分布参数系统控制（六）：反馈控制" class="thumbnail-image"></span>
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<div class="date"><time datetime="2018-04-10T22:19:02.000Z" itemprop="datePublished">2018-04-11</time></div>
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<h1 class="article-title" itemprop="name">
<a href="/2018/04/RSVP-06/">分布参数系统控制（六）：反馈控制</a>
</h1>
<p class="article-excerpt">
  在控制理论中，稳定性始终是一个系统最基本的要求，之后一切的控制都要建立在系统稳定的基础上。与集总参数系统控制类似，我们可以通过增加反馈使系统达到稳定状态，并满足一定特性。分布参数系统状态方程如下：
\dot{x}(t)={\cal A}x(t)\tag{1}指数稳定  首先我们给出分布参数系统的指数稳定（Exponentielle Stabilität
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<a href="/2018/03/RSVP-05/" class="thumbnail">
<span style="background-image:url(/images/RSVP.png)" alt="分布参数系统控制（五）：模型近似" class="thumbnail-image"></span>
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<div class="date"><time datetime="2018-03-24T19:19:41.000Z" itemprop="datePublished">2018-03-25</time></div>
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<h1 class="article-title" itemprop="name">
<a href="/2018/03/RSVP-05/">分布参数系统控制（五）：模型近似</a>
</h1>
<p class="article-excerpt">
  分布参数系统是个无限维的系统，在第一章节所提到的early-lumping控制中，我们先将系统过程近似为集总参数系统，再使用现代控制方法对系统进行分析控制。本文将阐述模型近似的过程及相关注意事项。
模型近似  分布参数系统状态方程如下：
\begin{eqnarray}
\dot{x}(t)&=&\mathcal{A}x(t)+\mathcal{B}u
</p>
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<div class="date"><time datetime="2018-03-21T00:35:21.000Z" itemprop="datePublished">2018-03-21</time></div>
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<a href="/2018/03/RSVP-04/">分布参数系统控制（四）：解的存在唯一性</a>
</h1>
<p class="article-excerpt">
  在求解微分方程的初值问题时，我们通常要考虑解的存在唯一性，以及解受初始条件的影响。一般来说，我们希望问题的解存在且唯一，并且连续地取决于初始条件（通常无法准确得知状态变量初始值，导致实际应用中会产生一定的偏差。因此我们希望当初始值$x(0)$微小变化时，$x(t)$的变化足够小）。我们称这样的问题为适定性问题（wohlgestelltes Problem）。 &e
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<div class="date"><time datetime="2018-03-16T20:51:52.000Z" itemprop="datePublished">2018-03-17</time></div>
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<a href="/2018/03/SVM-04/">支持向量机（四）</a>
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<p class="article-excerpt">
  到目前为止，我们把SVM优化问题化为了更容易解决的对偶问题，并且使用核函数及正则化来改善它的特性。现在我们只需解决这个对偶问题就可以得到最优间隔分类器，可以说是“万事具备，只欠东风”了。我们先将第三章节得到的对偶问题搬运过来：
\begin{eqnarray}
\max_{\alpha}\ &&\theta_{\cal{D}}(\alpha)=\sum_{i=1}^m\a
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<div class="date"><time datetime="2018-03-15T20:42:35.000Z" itemprop="datePublished">2018-03-16</time></div>
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<a href="/2018/03/SVM-03/">支持向量机（三）</a>
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  支持向量机的强大不止在于它能在特征空间找到合适的超平面将正负样本分开并保持最大间隔，通过引入核函数，它还能在更高维，甚至无限维空间中对样本进行分离，以此来解决非线性的问题。
核特征映射  在之前的推导中，我们使用的一直是样本的原始特征$x$，并通过线性平面$w^Tx+b$进行分割。但如果样本是线性不可分的，我们就需要先将特征映射到更高维空间，再分离正负样
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<div class="date"><time datetime="2018-03-14T20:37:57.000Z" itemprop="datePublished">2018-03-15</time></div>
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<a href="/2018/03/SVM-02/">支持向量机（二）</a>
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<p class="article-excerpt">
  上一章节我们将SVM的目标转换为了一个带不等式约束条件的优化问题，现在我们的目标就是解决这个优化问题。在此我们先将SVM及最优间隔分类器放一放，来看看一般约束优化问题的求解方法。
约束优化问题等式约束优化问题  等式优化问题一般描述如下：
\begin{split}
\min_x\ &f(x)\\
{\rm s.t.}\ &h_i(x)=0,\ i=1
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