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knowledge_embedding.html
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knowledge_embedding.html
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<!DOCTYPE html>
<html>
<head>
<title>knowledge_embedding</title>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<link rel="stylesheet" href="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.css"
integrity="sha384-dbVIfZGuN1Yq7/1Ocstc1lUEm+AT+/rCkibIcC/OmWo5f0EA48Vf8CytHzGrSwbQ" crossorigin="anonymous">
<!-- The loading of KaTeX is deferred to speed up page rendering -->
<script defer src="https://cdn.jsdelivr.net/npm/[email protected]/dist/katex.min.js"
integrity="sha384-2BKqo+exmr9su6dir+qCw08N2ZKRucY4PrGQPPWU1A7FtlCGjmEGFqXCv5nyM5Ij"
crossorigin="anonymous"></script>
<!-- To automatically render math in text elements, include the auto-render extension: -->
<script defer src="https://cdn.jsdelivr.net/npm/[email protected]/dist/contrib/auto-render.min.js"
integrity="sha384-kWPLUVMOks5AQFrykwIup5lo0m3iMkkHrD0uJ4H5cjeGihAutqP0yW0J6dpFiVkI" crossorigin="anonymous"
onload="renderMathInElement(document.body);"></script>
<style>
/**
* prism.js Github theme based on GitHub's theme.
* @author Sam Clarke
*/
code[class*="language-"],
pre[class*="language-"] {
color: #333;
background: none;
font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace;
text-align: left;
white-space: pre;
word-spacing: normal;
word-break: normal;
word-wrap: normal;
line-height: 1.4;
-moz-tab-size: 8;
-o-tab-size: 8;
tab-size: 8;
-webkit-hyphens: none;
-moz-hyphens: none;
-ms-hyphens: none;
hyphens: none;
}
/* Code blocks */
pre[class*="language-"] {
padding: .8em;
overflow: auto;
/* border: 1px solid #ddd; */
border-radius: 3px;
/* background: #fff; */
background: #f5f5f5;
}
/* Inline code */
:not(pre)>code[class*="language-"] {
padding: .1em;
border-radius: .3em;
white-space: normal;
background: #f5f5f5;
}
.token.comment,
.token.blockquote {
color: #969896;
}
.token.cdata {
color: #183691;
}
.token.doctype,
.token.punctuation,
.token.variable,
.token.macro.property {
color: #333;
}
.token.operator,
.token.important,
.token.keyword,
.token.rule,
.token.builtin {
color: #a71d5d;
}
.token.string,
.token.url,
.token.regex,
.token.attr-value {
color: #183691;
}
.token.property,
.token.number,
.token.boolean,
.token.entity,
.token.atrule,
.token.constant,
.token.symbol,
.token.command,
.token.code {
color: #0086b3;
}
.token.tag,
.token.selector,
.token.prolog {
color: #63a35c;
}
.token.function,
.token.namespace,
.token.pseudo-element,
.token.class,
.token.class-name,
.token.pseudo-class,
.token.id,
.token.url-reference .token.variable,
.token.attr-name {
color: #795da3;
}
.token.entity {
cursor: help;
}
.token.title,
.token.title .token.punctuation {
font-weight: bold;
color: #1d3e81;
}
.token.list {
color: #ed6a43;
}
.token.inserted {
background-color: #eaffea;
color: #55a532;
}
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background-color: #ffecec;
color: #bd2c00;
}
.token.bold {
font-weight: bold;
}
.token.italic {
font-style: italic;
}
/* JSON */
.language-json .token.property {
color: #183691;
}
.language-markup .token.tag .token.punctuation {
color: #333;
}
/* CSS */
code.language-css,
.language-css .token.function {
color: #0086b3;
}
/* YAML */
.language-yaml .token.atrule {
color: #63a35c;
}
code.language-yaml {
color: #183691;
}
/* Ruby */
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color: #333;
}
/* Markdown */
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color: #795da3;
}
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color: #795da3;
}
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color: #183691;
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color: #0086b3;
}
/* Bash */
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color: #0086b3;
}
/* highlight */
pre[data-line] {
position: relative;
padding: 1em 0 1em 3em;
}
pre[data-line] .line-highlight-wrapper {
position: absolute;
top: 0;
left: 0;
background-color: transparent;
display: block;
width: 100%;
}
pre[data-line] .line-highlight {
position: absolute;
left: 0;
right: 0;
padding: inherit 0;
margin-top: 1em;
background: hsla(24, 20%, 50%, .08);
background: linear-gradient(to right, hsla(24, 20%, 50%, .1) 70%, hsla(24, 20%, 50%, 0));
pointer-events: none;
line-height: inherit;
white-space: pre;
}
pre[data-line] .line-highlight:before,
pre[data-line] .line-highlight[data-end]:after {
content: attr(data-start);
position: absolute;
top: .4em;
left: .6em;
min-width: 1em;
padding: 0 .5em;
background-color: hsla(24, 20%, 50%, .4);
color: hsl(24, 20%, 95%);
font: bold 65%/1.5 sans-serif;
text-align: center;
vertical-align: .3em;
border-radius: 999px;
text-shadow: none;
box-shadow: 0 1px white;
}
pre[data-line] .line-highlight[data-end]:after {
content: attr(data-end);
top: auto;
bottom: .4em;
}
html body {
font-family: "Helvetica Neue", Helvetica, "Segoe UI", Arial, freesans, sans-serif;
font-size: 16px;
line-height: 1.6;
color: #333;
background-color: #fff;
overflow: initial;
box-sizing: border-box;
word-wrap: break-word
}
html body>:first-child {
margin-top: 0
}
html body h1,
html body h2,
html body h3,
html body h4,
html body h5,
html body h6 {
line-height: 1.2;
margin-top: 1em;
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}
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font-size: 1.5em;
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font-size: 1.25em;
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font-size: 1.1em;
font-weight: 600
}
html body h6 {
font-size: 1em;
font-weight: 600
}
html body h1,
html body h2,
html body h3,
html body h4,
html body h5 {
font-weight: 600
}
html body h5 {
font-size: 1em
}
html body h6 {
color: #5c5c5c
}
html body strong {
color: #000
}
html body del {
color: #5c5c5c
}
html body a:not([href]) {
color: inherit;
text-decoration: none
}
html body a {
color: #08c;
text-decoration: none
}
html body a:hover {
color: #00a3f5;
text-decoration: none
}
html body img {
max-width: 100%
}
html body>p {
margin-top: 0;
margin-bottom: 16px;
word-wrap: break-word
}
html body>ul,
html body>ol {
margin-bottom: 16px
}
html body ul,
html body ol {
padding-left: 2em
}
html body ul.no-list,
html body ol.no-list {
padding: 0;
list-style-type: none
}
html body ul ul,
html body ul ol,
html body ol ol,
html body ol ul {
margin-top: 0;
margin-bottom: 0
}
html body li {
margin-bottom: 0
}
html body li.task-list-item {
list-style: none
}
html body li>p {
margin-top: 0;
margin-bottom: 0
}
html body .task-list-item-checkbox {
margin: 0 .2em .25em -1.8em;
vertical-align: middle
}
html body .task-list-item-checkbox:hover {
cursor: pointer
}
html body blockquote {
margin: 16px 0;
font-size: inherit;
padding: 0 15px;
color: #5c5c5c;
border-left: 4px solid #d6d6d6
}
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margin-top: 0
}
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margin-bottom: 0
}
html body hr {
height: 4px;
margin: 32px 0;
background-color: #d6d6d6;
border: 0 none
}
html body table {
margin: 10px 0 15px 0;
border-collapse: collapse;
border-spacing: 0;
display: block;
width: 100%;
overflow: auto;
word-break: normal;
word-break: keep-all
}
html body table th {
font-weight: bold;
color: #000
}
html body table td,
html body table th {
border: 1px solid #d6d6d6;
padding: 6px 13px
}
html body dl {
padding: 0
}
html body dl dt {
padding: 0;
margin-top: 16px;
font-size: 1em;
font-style: italic;
font-weight: bold
}
html body dl dd {
padding: 0 16px;
margin-bottom: 16px
}
html body code {
font-family: Menlo, Monaco, Consolas, 'Courier New', monospace;
font-size: .85em !important;
color: #000;
background-color: #f0f0f0;
border-radius: 3px;
padding: .2em 0
}
html body code::before,
html body code::after {
letter-spacing: -0.2em;
content: "\00a0"
}
html body pre>code {
padding: 0;
margin: 0;
font-size: .85em !important;
word-break: normal;
white-space: pre;
background: transparent;
border: 0
}
html body .highlight {
margin-bottom: 16px
}
html body .highlight pre,
html body pre {
padding: 1em;
overflow: auto;
font-size: .85em !important;
line-height: 1.45;
border: #d6d6d6;
border-radius: 3px
}
html body .highlight pre {
margin-bottom: 0;
word-break: normal
}
html body pre code,
html body pre tt {
display: inline;
max-width: initial;
padding: 0;
margin: 0;
overflow: initial;
line-height: inherit;
word-wrap: normal;
background-color: transparent;
border: 0
}
html body pre code:before,
html body pre tt:before,
html body pre code:after,
html body pre tt:after {
content: normal
}
html body p,
html body blockquote,
html body ul,
html body ol,
html body dl,
html body pre {
margin-top: 0;
margin-bottom: 16px
}
html body kbd {
color: #000;
border: 1px solid #d6d6d6;
border-bottom: 2px solid #c7c7c7;
padding: 2px 4px;
background-color: #f0f0f0;
border-radius: 3px
}
@media print {
html body {
background-color: #fff
}
html body h1,
html body h2,
html body h3,
html body h4,
html body h5,
html body h6 {
color: #000;
page-break-after: avoid
}
html body blockquote {
color: #5c5c5c
}
html body pre {
page-break-inside: avoid
}
html body table {
display: table
}
html body img {
display: block;
max-width: 100%;
max-height: 100%
}
html body pre,
html body code {
word-wrap: break-word;
white-space: pre
}
}
.markdown-preview {
width: 100%;
height: 100%;
box-sizing: border-box
}
.markdown-preview .pagebreak,
.markdown-preview .newpage {
page-break-before: always
}
.markdown-preview pre.line-numbers {
position: relative;
padding-left: 3.8em;
counter-reset: linenumber
}
.markdown-preview pre.line-numbers>code {
position: relative
}
.markdown-preview pre.line-numbers .line-numbers-rows {
position: absolute;
pointer-events: none;
top: 1em;
font-size: 100%;
left: 0;
width: 3em;
letter-spacing: -1px;
border-right: 1px solid #999;
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none
}
.markdown-preview pre.line-numbers .line-numbers-rows>span {
pointer-events: none;
display: block;
counter-increment: linenumber
}
.markdown-preview pre.line-numbers .line-numbers-rows>span:before {
content: counter(linenumber);
color: #999;
display: block;
padding-right: .8em;
text-align: right
}
.markdown-preview .mathjax-exps .MathJax_Display {
text-align: center !important
}
.markdown-preview:not([for="preview"]) .code-chunk .btn-group {
display: none
}
.markdown-preview:not([for="preview"]) .code-chunk .status {
display: none
}
.markdown-preview:not([for="preview"]) .code-chunk .output-div {
margin-bottom: 16px
}
.scrollbar-style::-webkit-scrollbar {
width: 8px
}
.scrollbar-style::-webkit-scrollbar-track {
border-radius: 10px;
background-color: transparent
}
.scrollbar-style::-webkit-scrollbar-thumb {
border-radius: 5px;
background-color: rgba(150, 150, 150, 0.66);
border: 4px solid rgba(150, 150, 150, 0.66);
background-clip: content-box
}
html body[for="html-export"]:not([data-presentation-mode]) {
position: relative;
width: 100%;
height: 100%;
top: 0;
left: 0;
margin: 0;
padding: 0;
overflow: auto
}
html body[for="html-export"]:not([data-presentation-mode]) .markdown-preview {
position: relative;
top: 0
}
@media screen and (min-width:914px) {
html body[for="html-export"]:not([data-presentation-mode]) .markdown-preview {
padding: 2em calc(50% - 457px)
}
}
@media screen and (max-width:914px) {
html body[for="html-export"]:not([data-presentation-mode]) .markdown-preview {
padding: 2em
}
}
@media screen and (max-width:450px) {
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<h1 class="mume-header" id="knowledge-embedding-%E7%9F%A5%E8%AF%86%E5%B5%8C%E5%85%A5-%E7%AE%80%E4%BB%8B">Knowledge
Embedding 知识嵌入 简介</h1>
<h2 class="mume-header" id="%E4%BB%BB%E5%8A%A1">任务</h2>
<p><strong>模型：</strong>
将一个知识抽象为一个三元组 <span
class="katex"><span class="katex-mathml"><math>
<semantics>
<mrow>
<mo>(</mo>
<mi>H</mi>
<mi>e</mi>
<mi>a</mi>
<mi>d</mi>
<mo separator="true">,</mo>
<mi>R</mi>
<mi>e</mi>
<mi>l</mi>
<mi>a</mi>
<mi>t</mi>
<mi>i</mi>
<mi>o</mi>
<mi>n</mi>
<mo separator="true">,</mo>
<mi>T</mi>
<mi>a</mi>
<mi>i</mi>
<mi>l</mi>
<mo>)</mo>
</mrow>
<annotation encoding="application/x-tex">(Head, Relation, Tail)</annotation>
</semantics>
</math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"
style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span
class="mord mathdefault" style="margin-right:0.08125em;">H</span><span
class="mord mathdefault">e</span><span class="mord mathdefault">a</span><span
class="mord mathdefault">d</span><span class="mpunct">,</span><span class="mspace"
style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault"
style="margin-right:0.00773em;">R</span><span class="mord mathdefault">e</span><span
class="mord mathdefault" style="margin-right:0.01968em;">l</span><span
class="mord mathdefault">a</span><span class="mord mathdefault">t</span><span
class="mord mathdefault">i</span><span class="mord mathdefault">o</span><span
class="mord mathdefault">n</span><span class="mpunct">,</span><span class="mspace"
style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault"
style="margin-right:0.13889em;">T</span><span class="mord mathdefault">a</span><span
class="mord mathdefault">i</span><span class="mord mathdefault"
style="margin-right:0.01968em;">l</span><span class="mclose">)</span></span></span></span>
其中 Head 和 Tail
是实体，表示有具体所指的物体或概念，Relation
表示实体间的关系。</p>
<p>
知识图谱使结构化的语义知识库，用于以符号形式描述物理世界中的概念和相互关系，其基本组成单位是上述三元组和实体及其相关
属性-值
对，实体间通过关系相互连接，构成网状的知识结构。如表示
<code>北京是中国的首都</code>
可以抽象为
<code>（北京，首都，中国）</code>。可以将知识图谱视为一个图，其中的点表示实体，边表示实体间的关系。使用较多的数据集有
WordNet(Miller 1995), Freebase(Bollacker stal. 2008)等。</p>
<p>如果使用基本的词嵌入方法如
word2vec：相当于一个 one-hot
编码，将一个词转换成一个长度等于字典大小的向量。
</p>
<pre data-role="codeBlock" data-info="text" class="language-text"><code>字典：['I', 'am', 'a', 'student']
通过在字典中的位置对单词进行描述，如：
'I' ===> [1, 0, 0, 0]
'am' ===> [0, 1, 0, 0]
</code></pre>
<p>
显然这样的嵌入方式只能保证在有字典的情况下将词汇抽象成一个向量，但是主要缺点在于维数过高且忽视了词汇间的逻辑联系，不能满足大规模下的应用。所以有必要对
embedding 进行研究。</p>
<p>
现在为了提取出实体间的关系，知识嵌入主要分成了三个类别
张量分解(tensor
factorization)，基于翻译模型的求解(translation-based
approcah)和神经网络。本文主要的内容是有关第二类的，其中主要的方法是构建一个基于最大间隔的训练目标（参考SVM）。
</p>
<p>
在知识图谱中存在大量这样的三元组，结构也不尽相同，包括一对一，一对多，多对一和多对多。这样多样化的知识的形式为我们表示带来了很大困难。如何能描述，抽象这些实体从而快速推导出其中的关系成为了
Knowledge Embedding 的研究目标</p>
<h2 class="mume-header" id="%E8%AF%84%E4%BB%B7%E6%8C%87%E6%A0%87">评价指标</h2>
<p>对一个三元组 <span class="katex"><span class="katex-mathml"><math>
<semantics>
<mrow>
<mo>(</mo>
<mi>h</mi>
<mo separator="true">,</mo>
<mi>r</mi>
<mo separator="true">,</mo>
<mi>t</mi>
<mo>)</mo>
</mrow>
<annotation encoding="application/x-tex">(h, r, t)</annotation>
</semantics>
</math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"
style="height:1em;vertical-align:-0.25em;"></span><span class="mopen">(</span><span
class="mord mathdefault">h</span><span class="mpunct">,</span><span class="mspace"
style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault"
style="margin-right:0.02778em;">r</span><span class="mpunct">,</span><span class="mspace"
style="margin-right:0.16666666666666666em;"></span><span class="mord mathdefault">t</span><span
class="mclose">)</span></span></span></span>
任意用其他的实体替换头或者尾，并根据评价函数
<span class="katex"><span class="katex-mathml"><math>
<semantics>
<mrow>
<msub>
<mi>f</mi>
<mi>r</mi>
</msub>
</mrow>
<annotation encoding="application/x-tex">f_r</annotation>
</semantics>
</math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"
style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord"><span
class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="msupsub"><span
class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span
style="top:-2.5500000000000003em;margin-left:-0.10764em;margin-right:0.05em;"><span
class="pstrut" style="height:2.7em;"></span><span
class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight"
style="margin-right:0.02778em;">r</span></span></span></span><span
class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist"
style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>
计算每个新三元组的不相似程度，并对所有的得分进行降序排列。
</p>
<ol>
<li>
<p>mean rank<br>
对某个正确的三元组 (golden triplet)
进行上述的操作，并得到其在排序中的位置
<span class="katex"><span class="katex-mathml"><math>
<semantics>
<mrow>
<mi>i</mi>
<mi>n</mi>
<mi>d</mi>
<mi>e</mi>
<msub>
<mi>x</mi>
<mi>i</mi>
</msub>
</mrow>
<annotation encoding="application/x-tex">index_i</annotation>
</semantics>
</math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"
style="height:0.84444em;vertical-align:-0.15em;"></span><span class="mord mathdefault">i</span><span
class="mord mathdefault">n</span><span class="mord mathdefault">d</span><span
class="mord mathdefault">e</span><span class="mord"><span class="mord mathdefault">x</span><span
class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist"
style="height:0.31166399999999994em;"><span
style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut"
style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span
class="mord mathdefault mtight">i</span></span></span></span><span
class="vlist-s">​</span></span><span class="vlist-r"><span class="vlist"
style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span>。对所有的正确三元组进行上述操作得到的平均数即为所求。即<span
class="katex"><span class="katex-mathml"><math>
<semantics>
<mrow>
<mi>M</mi>
<mi>e</mi>
<mi>a</mi>
<mi>n</mi>
<mi>R</mi>
<mi>a</mi>
<mi>n</mi>
<mi>k</mi>
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mi>n</mi>
</mfrac>
<msubsup>
<mo>∑</mo>
<mrow>