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<h1 class="entry-title"><a href="https://kingx.me/detect-apt-through-user-behavior.html" rel="bookmark" title="基于行为相似性度量检测APT活动">基于行为相似性度量检测APT活动</a></h1>
<h2><span class="entry-date date published"><time datetime="2017-12-04T00:00:00-05:00">December 04, 2017, KINGX</time></span></h2>
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<span class="entry-tags" style="color:red;font-size:13px;margin-bottom: 0px;">「声明：本博客中涉及到的相关漏洞均为官方已经公开并修复的漏洞，涉及到的安全技术也仅用于企业安全建设和安全对抗研究。本文仅限业内技术研究与讨论，严禁用于非法用途，否则产生的一切后果自行承担。」</span>
<h2 id="1-概述">1. 概述</h2>
<p>在基于大数据的安全防御建设中，为了从数据挖掘出异常行为，通常我们需要计算不同个体之间的差异，从而通过相似性和类别来判定异常行为和正常行为，找出偏离用户行为基线的异常点。数据科学中有很多常用的”距离“、”相似性“的计算方法。我们可以根据数据特性而采用不同的度量方法。比如：</p>
<ul>
<li>空间：欧氏距离</li>
<li>路径：曼哈顿距离</li>
<li>国际象棋国王：切比雪夫距离</li>
</ul>
<p>以上三种的统一形式: 闵可夫斯基距离</p>
<ul>
<li>加权：标准化欧氏距离</li>
<li>排除量纲和依存：马氏距离</li>
<li>向量差距：夹角余弦</li>
<li>编码差别：汉明距离</li>
<li>集合近似度：杰卡德类似系数与距离</li>
<li>相关：相关系数与相关距离</li>
</ul>
<p>定义一个距离函数，需要满足几个准则：</p>
<ol>
<li>仅到自己的距离为零</li>
<li>距离非负</li>
<li>三角形法则，两边之和大于第三边</li>
</ol>
<h2 id="2-余弦相似度向量内积">2. 余弦相似度（向量内积）</h2>
<p>适合高维度向量vectors的相似度计算。两个向量的Cosine距离就是这两个向量之间的夹角。
Cosine值越接近0表示夹角越大，越接近于1表示夹角越小。</p>
<p>http://www.cnblogs.com/chaosimple/p/3160839.html</p>
<p>余弦相似度，又称为余弦相似性，是通过计算两个向量的夹角余弦值来评估他们的相似度。余弦相似度将向量根据坐标值，绘制到向量空间中，如最常见的二维空间。</p>
<p>将向量根据坐标值，绘制到向量空间中。如最常见的二维空间。
求得他们的夹角，并得出夹角对应的余弦值，此余弦值就可以用来表征，这两个向量的相似性。夹角越小，余弦值越接近于1，它们的方向更加吻合，则越相似。</p>
<h3 id="计算方法">计算方法</h3>
<p>假设两个向量，a向量是(x1,x2,x3…) b向量是 (y1,y2,y3…)</p>
<p>假设a向量是（x1, y1,…），b向量是(x2, y2,…)</p>
<p>x1<em>x2+y1</em>y2+……/更号(x1^2+y1^2…)+更号(x2^2+y2^2…)</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="kn">from</span> <span class="nn">scipy.spatial.distance</span> <span class="kn">import</span> <span class="n">cosine</span>
<span class="n">cosine_value</span> <span class="o">=</span> <span class="mi">1</span><span class="o">-</span><span class="n">cosine</span><span class="p">(</span><span class="n">p</span><span class="p">,</span><span class="n">q</span><span class="p">)</span>
</code></pre></div></div>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code><span class="c1">#-*-coding:utf-8-*-
</span><span class="k">def</span> <span class="nf">cos</span><span class="p">(</span><span class="n">vector1</span><span class="p">,</span><span class="n">vector2</span><span class="p">):</span>
<span class="n">dot_product</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">;</span>
<span class="n">normA</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">;</span>
<span class="n">normB</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">;</span>
<span class="k">for</span> <span class="n">a</span><span class="p">,</span><span class="n">b</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">vector1</span><span class="p">,</span><span class="n">vector2</span><span class="p">):</span>
<span class="n">dot_product</span> <span class="o">+=</span> <span class="n">a</span><span class="o">*</span><span class="n">b</span>
<span class="n">normA</span> <span class="o">+=</span> <span class="n">a</span><span class="o">**</span><span class="mi">2</span>
<span class="n">normB</span> <span class="o">+=</span> <span class="n">b</span><span class="o">**</span><span class="mi">2</span>
<span class="k">if</span> <span class="n">normA</span> <span class="o">==</span> <span class="mf">0.0</span> <span class="ow">or</span> <span class="n">normB</span><span class="o">==</span><span class="mf">0.0</span><span class="p">:</span>
<span class="k">return</span> <span class="bp">None</span>
<span class="k">else</span><span class="p">:</span>
<span class="k">return</span> <span class="n">dot_product</span> <span class="o">/</span> <span class="p">((</span><span class="n">normA</span><span class="o">*</span><span class="n">normB</span><span class="p">)</span><span class="o">**</span><span class="mf">0.5</span><span class="p">)</span>
</code></pre></div></div>
<h2 id="3-欧氏距离">3. 欧氏距离</h2>
<p>只的是在多维空间中两个点之间的真实距离，或者向量的自然长度（即该点到原点的距离）。在数学上也可以成为范数。</p>
<h3 id="计算方法-1">计算方法</h3>
<p>两个向量各个元素的差值的平方求和然后求平方根。</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>dist = numpy.sqrt(numpy.sum(numpy.square(vec1 - vec2)))
或者
dist = numpy.linalg.norm(vec1 - vec2)
</code></pre></div></div>
<h2 id="4-kl散度相对熵-kullback-leibler-divergence">4. KL散度（相对熵） Kullback-Leibler divergence</h2>
<p>KL散度是用来度量使用基于Q的编码来编码来自P的样本平均所需的额外的位元数，是描述两个概率分布P和Q差异的一种方法。测量两个概率分布之间的距离。可以看做是概率分布P到目标概率Q之间距离。一般情况下，P表示数据的真是分布，Q表示数据的理论分布，也可以理解为影响P分布的一种因素。计算公式为：</p>
<table>
<tbody>
<tr>
<td> DKL(P</td>
<td> </td>
<td>Q) =ΣP(i)log(P(i)/Q(i))</td>
</tr>
</tbody>
</table>
<p>KL散度是不对称的，如果希望对称：</p>
<p>Ds(p1, p2) = (D(p1, p2) + D(p2, p1)) / 2</p>
<p><strong>Tips:</strong></p>
<p>KL散度需要满足</p>
<ul>
<li>概率P和Q各自总和均为1</li>
<li>概率P(i)和Q(i)均大于0</li>
</ul>
<p>时才有定义。</p>
<h3 id="计算方法-2">计算方法</h3>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kn">import</span> <span class="nn">scipy.stats</span>
<span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">970.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">]</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">102.0</span><span class="p">,</span><span class="mf">75.625</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">,</span><span class="mf">0.0</span><span class="p">]</span>
<span class="n">KL</span> <span class="o">=</span> <span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">entropy</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
</code></pre></div></div>
<p>scipy.stats.entropy(p, q) 会计算：</p>
<div class="highlighter-rouge"><div class="highlight"><pre class="highlight"><code>S = sum(pk * log(pk / qk), axis=0).
</code></pre></div></div>
<p>除了用函数库之外，也可以自行编程实现计算：</p>
<div class="language-python highlighter-rouge"><div class="highlight"><pre class="highlight"><code> <span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="n">np</span>
<span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">1.001</span><span class="p">,</span><span class="mf">1.0</span><span class="p">,</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">]</span>
<span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000000001</span><span class="p">,</span><span class="mf">0.9</span><span class="p">,</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">,</span><span class="mf">0.00000001</span><span class="p">]</span>
<span class="c1"># 归一化
</span> <span class="n">pa</span> <span class="o">=</span> <span class="n">a</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="nb">sum</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
<span class="n">pb</span> <span class="o">=</span> <span class="n">b</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="nb">sum</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
<span class="n">KL</span> <span class="o">=</span> <span class="mf">0.0</span>
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">10</span><span class="p">):</span>
<span class="n">KL</span> <span class="o">+=</span> <span class="n">pa</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="n">pa</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span> <span class="n">pb</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
<span class="c1"># print(str(px[i]) + ' ' + str(py[i]) + ' ' + str(px[i] * np.log(px[i] / py[i])))
</span> <span class="k">print</span><span class="p">(</span><span class="n">KL</span><span class="p">)</span>
</code></pre></div></div>
<h3 id="适用场景">适用场景</h3>
<p>《【原】浅谈KL散度（相对熵）在用户画像中的应用》https://www.cnblogs.com/charlotte77/p/5392052.html</p>
<h2 id="5-k-s统计作为距离度量">5. K-S统计作为距离度量</h2>
<h2 id="6-检测分布尖峰的变化">6. 检测分布尖峰的变化</h2>
<h2 id="references-使用-anomalize-算法进行异常检测与威胁狩猎">References 使用 Anomalize 算法进行异常检测与威胁狩猎</h2>
<p>https://holisticinfosec.blogspot.com/2018/06/toolsmith-133-anomaly-detection-threat.html</p>
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