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19<main class="docMainContainer_S4Cg docMainContainerEnhanced_j6X2"><div class="container padding-top--md padding-bottom--lg"><div class="row"><div class="col docItemCol_E8dH"><div class="docItemContainer_oCZa"><article><div class="tocCollapsible_bE1U theme-doc-toc-mobile tocMobile_UmiY"><button type="button" class="clean-btn tocCollapsibleButton_EMHn">СодеÑжание ÑÑой ÑÑÑаниÑÑ</button></div><div class="theme-doc-markdown markdown"><header><h1>ÐбознаÑÐµÐ½Ð¸Ñ Ð² ÑÑебнике</h1></header> 20<h2 class="anchor anchorTargetStickyNavbar_ahd2" id="ÑпеÑиалÑнаÑ-ÑеÑминологиÑ">СпеÑиалÑÐ½Ð°Ñ ÑеÑминологиÑ<a href="#ÑпеÑиалÑнаÑ-ÑеÑминологи�Ñ" class="hash-link" aria-label="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑÐ½Ð°Ñ ÑеÑминологиÑ" title="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑÐ½Ð°Ñ ÑеÑминологиÑ" translate="no">â</a></h2> 21<ul> 22<li class=""> 23<p><strong>ÐÑклик</strong> - ÑÐµÐ»ÐµÐ²Ð°Ñ Ð²ÐµÐ»Ð¸Ñина, коÑоÑÑÑ Ð¼Ñ Ð¿ÑедÑказÑваем.</p> 24</li> 25<li class=""> 26<p><strong>ÐÑизнак</strong> - извеÑÑное ÑвойÑÑво обÑекÑа, Ð´Ð»Ñ ÐºÐ¾ÑоÑого ÑÑÑоиÑÑÑ Ð¿Ñогноз.</p> 27</li> 28<li class=""> 29<p><strong>ÐекÑÐ¾Ñ Ð¿Ñизнаков</strong> - вÑе извеÑÑнÑе ÑвойÑÑва, запиÑаннÑе в виде векÑоÑа.</p> 30</li> 31<li class=""> 32<p><strong>ÐоделÑ</strong> - ÑÑнкÑиÑ, оÑобÑажаÑÑÐ°Ñ Ð²ÐµÐºÑÐ¾Ñ Ð¿Ñизнаков в пÑогнозное знаÑение оÑклика по некоÑоÑÐ¾Ð¼Ñ Ð¿ÑавилÑ.</p> 33</li> 34<li class=""> 35<p><strong>ÐаÑамеÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸</strong> - паÑамеÑÑÑ, Ð¾Ñ ÐºÐ¾ÑоÑÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¸ наÑÑÑаиваемÑе по обÑÑаÑÑей вÑбоÑке. ÐазÑваÑÑÑÑ Ñакже <strong>веÑами модели</strong>.</p> 36</li> 37<li class=""> 38<p><strong>ÐипеÑпаÑамеÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸</strong> - паÑамеÑÑÑ, Ð¾Ñ ÐºÐ¾ÑоÑÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¸ вÑбиÑаемÑе полÑзоваÑелем либо подбиÑаемÑе по оÑделÑной валидаÑионной вÑбоÑке.</p> 39</li> 40<li class=""> 41<p><strong>ÐлгоÑиÑм</strong> - Ñо же, ÑÑо и моделÑ, но Ñ Ð½Ð°ÑÑÑоеннÑми паÑамеÑÑами.</p> 42</li> 43<li class=""> 44<p><strong>СложноÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸</strong> в ÑÑебнике обознаÑÐ°ÐµÑ Ð²ÑÑазиÑелÑнÑÑ Ð³Ð¸Ð±ÐºÐ¾ÑÑÑ Ð¸Ð»Ð¸ ÑпоÑобноÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ подÑÑÑаиваÑÑÑÑ Ð¿Ð¾Ð´ обÑÑаÑÑие даннÑе. ÐÑли ÑаÑÑмаÑÑиваеÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ñ Ñ Ð½Ð¸Ð·ÐºÐ¾Ð¹ ÑложноÑÑÑÑ, Ñо ÑÐ°ÐºÐ°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð½Ð°Ð·ÑваеÑÑÑ <strong>пÑоÑÑой</strong>. Ðе пÑÑаÑÑ Ñ Ð²ÑÑиÑлиÑелÑной ÑложноÑÑÑÑ/пÑоÑÑоÑой, оÑноÑÑÑейÑÑ Ðº ÑиÑÐ»Ñ ÑлеменÑаÑнÑÑ Ð¾Ð¿ÐµÑаÑий, Ð½ÐµÐ¾Ð±Ñ Ð¾Ð´Ð¸Ð¼ÑÑ Ð´Ð»Ñ Ð²ÑÑиÑÐ»ÐµÐ½Ð¸Ñ ÑÑнкÑии.</p> 45</li> 46</ul> 47<h2 class="anchor anchorTargetStickyNavbar_ahd2" id="ÑкалÑÑÑ-векÑоÑÑ-и-маÑÑиÑÑ">СкалÑÑÑ, векÑоÑÑ Ð¸ маÑÑиÑÑ<a href="#ÑкалÑÑÑ-векÑоÑÑ-и-маÑÑиÑÑ" class="hash-link" aria-label="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СкалÑÑÑ, векÑоÑÑ Ð¸ маÑÑиÑÑ" title="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СкалÑÑÑ, векÑоÑÑ Ð¸ маÑÑиÑÑ" translate="no">â</a></h2> 48<ul> 49<li class=""> 50<p>ÐекÑоÑÑ Ð²Ñегда обознаÑаÑÑ Ð²ÐµÐºÑоÑÑ-ÑÑолбÑÑ (а не ÑÑÑоки), и обознаÑаÑÑÑÑ ÑÑÑоÑнÑми бÑквами, Ñакими как <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> или <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">x</mi></mrow><annotation encoding="application/x-tex">\mathbf{x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4444em"></span><span class="mord mathbf">x</span></span></span></span>. СкалÑÑнÑе знаÑÐµÐ½Ð¸Ñ (ÑиÑла) обознаÑаÑÑÑÑ ÑолÑко ÑÑÑоÑнÑми бÑквами, как <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>w</mi><mn>0</mn></msub></mrow><annotation encoding="application/x-tex">w_0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3011em"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">0</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span>.</p> 51</li> 52<li class=""> 53<p>ÐаÑÑиÑÑ Ð¾Ð±Ð¾Ð·Ð½Ð°ÑаÑÑÑÑ Ð·Ð°Ð³Ð»Ð°Ð²Ð½Ñми бÑквами, Ñакими как <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">A</span></span></span></span>.</p> 54</li> 55<li class=""> 56<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi><mo>â½</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">A\succcurlyeq0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.82em;vertical-align:-0.1367em"></span><span class="mord mathnormal">A</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel amsrm">â½</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">0</span></span></span></span> - неоÑÑиÑаÑелÑно опÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð°Ñ Ð¼Ð°ÑÑиÑа <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal">A</span></span></span></span>.</p> 57</li> 58</ul> 59<h2 class="anchor anchorTargetStickyNavbar_ahd2" id="ÑпеÑиалÑнÑе-ÑимволÑ">СпеÑиалÑнÑе ÑимволÑ<a href="#ÑпеÑиалÑнÑе-ÑимволÑ" class="hash-l
59ink" aria-label="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑнÑе ÑимволÑ" title="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑнÑе ÑимволÑ" translate="no">â</a></h2> 60<ul> 61<li class=""> 62<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi mathvariant="double-struck">R</mi><mi>D</mi></msup></mrow><annotation encoding="application/x-tex">\mathbb{R}^D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8413em"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span></span></span></span></span></span></span></span></span></span></span> - <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span>-меÑнÑй векÑоÑ. РзапиÑи <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi><mo>â</mo><msup><mi mathvariant="double-struck">R</mi><mi>D</mi></msup></mrow><annotation encoding="application/x-tex">x\in\mathbb{R}^D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em"></span><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8413em"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span></span></span></span></span></span></span></span></span></span></span> ознаÑаеÑ, ÑÑо <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> пÑÐ¸Ð½Ð°Ð´Ð»ÐµÐ¶Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ñ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span>-меÑнÑÑ Ð²ÐµÐºÑоÑов, Ñ.е. ÑвлÑеÑÑÑ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span>-меÑнÑм векÑоÑом.</p> 63</li> 64<li class=""> 65<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">â</mi></mrow><annotation encoding="application/x-tex">\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">â</span></span></span></span> = Ð´Ð»Ñ Ð»Ñбого, напÑимеÑ, ÑÑловие, ÑÑо ÑинÑÑ Ð½Ð¸ÐºÐ¾Ð³Ð´Ð° не пÑевоÑÑ Ð¾Ð´Ð¸Ñ ÐµÐ´Ð¸Ð½Ð¸ÑÑ Ð·Ð°Ð¿Ð¸ÑÑваеÑÑÑ ÐºÐ°Ðº <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>sin</mi><mo>
65â¡</mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>â¤</mo><mn>1</mn><mtext>â â</mtext><mi mathvariant="normal">â</mi><mi>x</mi></mrow><annotation encoding="application/x-tex">\sin(x)\le 1 \;\forall x</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="mop">sin</span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â¤</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6944em"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord">â</span><span class="mord mathnormal">x</span></span></span></span>.</p> 66</li> 67<li class=""> 68<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span> - обÑее ÑиÑло пÑизнаков, назÑваемое Ñакже ÑазмеÑноÑÑÑÑ Ð¿Ñизнакового пÑоÑÑÑанÑÑва.</p> 69</li> 70<li class=""> 71<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">x</mi><mo>â</mo><msup><mi mathvariant="double-struck">R</mi><mi>D</mi></msup></mrow><annotation encoding="application/x-tex">\mathbf{x}\in \mathbb{R}^D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em"></span><span class="mord mathbf">x</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8413em"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span></span></span></span></span></span></span></span></span></span></span> - векÑÐ¾Ñ Ð¿Ñи�знаков, иногда обознаÑаемÑй как <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>x</mi></mrow><annotation encoding="application/x-tex">x</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">x</span></span></span></span> (пÑи опиÑании нейÑоÑеÑей ÑÑо Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ ÑензоÑом, опиÑÑваÑÑим обÑекÑ, напÑимеÑ, изобÑажение или его внÑÑÑеннее пÑедÑÑавление).</p> 72</li> 73<li class=""> 74<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi mathvariant="bold">x</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">\mathbf{x}_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5944em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathbf">x</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em"><span style="top:-2.55em;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 mathnormal mtight">i</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> - <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em"></span><span class="mord mathnormal">i</span></span></span></span>
74-й обÑÐµÐºÑ Ð²ÑбоÑки (<span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.02778em">D</span></span></span></span>-меÑнÑй векÑоÑ).</p> 75</li> 76<li class=""> 77<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msup><mi>x</mi><mi>j</mi></msup></mrow><annotation encoding="application/x-tex">x^j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8247em"></span><span class="mord"><span class="mord mathnormal">x</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8247em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight" style="margin-right:0.05724em">j</span></span></span></span></span></span></span></span></span></span></span> - <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>j</mi></mrow><annotation encoding="application/x-tex">j</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.854em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.05724em">j</span></span></span></span>-й пÑизнак векÑоÑа пÑизнаков <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">x</mi></mrow><annotation encoding="application/x-tex">\mathbf{x}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4444em"></span><span class="mord mathbf">x</span></span></span></span> (ÑкалÑÑ, Ñ.е. ÑиÑло).</p> 78</li> 79<li class=""> 80<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>y</mi></mrow><annotation encoding="application/x-tex">y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.1944em"></span><span class="mord mathnormal" style="margin-right:0.03588em">y</span></span></span></span> - иÑÑинное знаÑение оÑклика или Ñелевой пеÑеменной, коÑоÑÑÑ Ð¼Ñ Ð¿ÑедÑказÑваем (пÑи опиÑании нейÑоÑеÑей ÑÑо Ñакже Ð¼Ð¾Ð¶ÐµÑ Ð¾Ð±Ð¾Ð·Ð½Ð°ÑаÑÑ Ð²ÑÑ Ð¾Ð´ оÑделÑного блока).</p> 81</li> 82<li class=""> 83<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi>y</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{y}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8889em;vertical-align:-0.1944em"></span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord mathnormal" style="margin-right:0.03588em">y</span></span><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.1944em"><span class="mord">^</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em"><span></span></span></span></span></span></span></span></span> - пÑедÑказанное знаÑение оÑклика алгоÑиÑмом.</p> 84</li> 85<li class=""> 86<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="bold">w</mi></mrow><annotation encoding="application/x-tex">\mathbf{w}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4444em"></span><span class="mord mathbf" style="margin-right:0.01597em">w</span></span></span></span> - векÑÐ¾Ñ Ð²ÑÐµÑ Ð½Ð°ÑÑÑаиваемÑÑ Ð¿Ð°ÑамеÑÑов модели по обÑÑаÑÑей вÑбоÑке, наÐ
86·ÑваемÑÑ Ñакже веÑами модели (в конÑекÑÑе обÑабоÑки ÑекÑÑа <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>w</mi></mrow><annotation encoding="application/x-tex">w</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal" style="margin-right:0.02691em">w</span></span></span></span> Ð¼Ð¾Ð¶ÐµÑ Ð¾Ð±Ð¾Ð·Ð½Ð°ÑаÑÑ Ñлово).</p> 87</li> 88<li class=""> 89<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">w_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">��â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> - оÑделÑнÑй паÑамеÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ (в конÑекÑÑе обÑабоÑки ÑекÑÑа <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><msub><mi>w</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">w_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5806em;vertical-align:-0.15em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.02691em">w</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.3117em"><span style="top:-2.55em;margin-left:-0.0269em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">i</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span></span></span></span> Ð¼Ð¾Ð¶ÐµÑ Ð¾Ð±Ð¾Ð·Ð½Ð°ÑаÑÑ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>i</mi></mrow><annotation encoding="application/x-tex">i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6595em"></span><span class="mord mathnormal">i</span></span></span></span>-ое Ñлово).</p> 90</li> 91<li class=""> 92<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mover accent="true"><mi mathvariant="bold">w</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{\mathbf{w}}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7079em"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.7079em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord mathbf" style="margin-right:0.01597em">w</span></span><span style="top:-3.0134em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.1667em"><span class="mord">^</span></span></span></span></span></span></span></span></span></span> - оÑенка векÑоÑа паÑамеÑÑов.</p> 93</li> 94<li class=""> 95<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>N</mi></mrow><annotation encoding="application/x-tex">N</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.10903em">N</span></span></span></span> - ÑиÑло обÑекÑов в обÑÑаÑÑей вÑбоÑке.</p> 96</li> 97<li class=""> 98<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>X</mi><mo>
98â</mo><msup><mi mathvariant="double-struck">R</mi><mrow><mi>N</mi><mo>Ã</mo><mi>D</mi></mrow></msup></mrow><annotation encoding="application/x-tex">X\in\mathbb{R}^{N \times D}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em"></span><span class="mord mathnormal" style="margin-right:0.07847em">X</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8413em"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em">N</span><span class="mbin mtight">Ã</span><span class="mord mathnormal mtight" style="margin-right:0.02778em">D</span></span></span></span></span></span></span></span></span></span></span></span> - маÑÑиÑа "обÑекÑÑ-пÑизнаки", назÑÐ²Ð°ÐµÐ¼Ð°Ñ Ñакже маÑÑиÑей пÑизнаков (feature matrix), в коÑоÑой ÐºÐ°Ð¶Ð´Ð°Ñ ÑÑÑока - векÑÐ¾Ñ Ð¿Ñизнаков ÑооÑвеÑÑÑвÑÑÑего обÑекÑа вÑбоÑки наблÑдений. ÐнаÑÐµÐ½Ð¸Ñ Ð¿Ñизнака Ð´Ð»Ñ ÑазнÑÑ Ð¾Ð±ÑекÑов Ð¸Ð´ÐµÑ Ð² ÑооÑвеÑÑÑвÑÑÑем ÑÑолбÑе ÑÑой маÑÑиÑÑ (в конÑекÑÑе нейÑоÑеÑей ÑÑо Ñакже Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð²Ñ Ð¾Ð´Ð½Ð°Ñ Ð¸Ð½ÑоÑмаÑÐ¸Ñ Ð¾Ð± извеÑÑнÑÑ Ð¾Ð±ÑекÑÐ°Ñ Ð² лÑбом, не ÑолÑко векÑоÑном, виде).</p> 99</li> 100<li class=""> 101<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>Y</mi><mo>â</mo><msup><mi mathvariant="double-struck">R</mi><mi>N</mi></msup></mrow><annotation encoding="application/x-tex">Y\in\mathbb{R}^{N}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7224em;vertical-align:-0.0391em"></span><span class="mord mathnormal" style="margin-right:0.22222em">Y</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.8413em"></span><span class="mord"><span class="mord mathbb">R</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8413em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em">N</span></span></span></span></span></span></span></span></span></span></span></span> - векÑÐ¾Ñ Ð¾Ñкликов (желаемÑÑ Ð¾ÑвеÑов алгоÑиÑма), пÑедÑÑавлÑÑÑий Ñобой векÑÐ¾Ñ Ð²ÐµÑеÑÑвеннÑÑ Ð·Ð½Ð°Ñений Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñи ÑегÑеÑÑии и каÑегоÑиалÑнÑй векÑÐ¾Ñ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ñи клаÑÑиÑикаÑии (в конÑекÑÑе нейÑоÑеÑей ÑÑо Ñакже Ð¼Ð¾Ð¶ÐµÑ Ð±ÑÑÑ Ð¸Ð½ÑоÑмаÑÐ¸Ñ Ð¾Ð± ожидаемÑÑ Ð¾ÑÐºÐ»Ð¸ÐºÐ°Ñ Ð² лÑбом, не ÑолÑко веÑеÑÑвенном, виде).</p> 102</li> 103<li class=""> 104<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>C</mi></mrow><annotation encoding="application/x-tex">C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6833em"></span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span> - ÑиÑло клаÑÑов в клаÑÑиÑикаÑии.</p> 105</li> 106<li class=""> 107<p>ÐлаÑÑÑ Ð¾Ð±Ð¾Ð·Ð½Ð°ÑаÑÑÑÑ ÑиÑÑами <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi>C</mi></mrow><annotation encoding="application/x-tex">1,2,...C</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8778em;vertical-align:-0.1944em"></span><span class="mord">1</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">2</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">...</span><span class="mord mathnormal" style="margin-right:0.07153em">C</span></span></span></span> в многоклаÑÑовой клаÑÑиÑикаÑии и -1,+1 в бинаÑной клаÑÑиÑикаÑии (на два клаÑÑа).<
107/p> 108</li> 109<li class=""> 110<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="script">L</mi><mo stretchy="false">(</mo><mover accent="true"><mi>y</mi><mo>^</mo></mover><mo separator="true">,</mo><mi>y</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">\mathcal{L}(\hat{y},y)</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="mord mathcal">L</span><span class="mopen">(</span><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord mathnormal" style="margin-right:0.03588em">y</span></span><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.1944em"><span class="mord">^</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em"><span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathnormal" style="margin-right:0.03588em">y</span><span class="mclose">)</span></span></span></span> - ÑÑнкÑÐ¸Ñ Ð¿Ð¾ÑеÑÑ Ð½Ð° одном обÑекÑе.</p> 111</li> 112<li class=""> 113<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>L</mi><mo stretchy="false">(</mo><mi mathvariant="bold">w</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mn>1</mn><mi>N</mi></mfrac><msubsup><mo>â</mo><mrow><mi>n</mi><mo>=</mo><mn>1</mn></mrow><mi>N</mi></msubsup><mi mathvariant="script">L</mi><mo stretchy="false">(</mo><msub><mover accent="true"><mi>y</mi><mo>^</mo></mover><mi>n</mi></msub><mo separator="true">,</mo><msub><mi>y</mi><mi>n</mi></msub><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">L(\mathbf{w})=\frac{1}{N}\sum_{n=1}^{N}\mathcal{L}(\hat{y}_n,y_{n})</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="mord mathnormal">L</span><span class="mopen">(</span><span class="mord mathbf" style="margin-right:0.01597em">w</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1.3262em;vertical-align:-0.345em"></span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8451em"><span style="top:-2.655em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em">N</span></span></span></span><span style="top:-3.23em"><span class="pstrut" style="height:3em"></span><span class="frac-line" style="border-bottom-width:0.04em"></span></span><span style="top:-3.394em"><span class="pstrut" style="height:3em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mtight">1</span></span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.345em"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:0em">â</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.9812em"><span style="top:-2.4003em;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 mtight"><span class="mord mathnormal mtight">n</span><span class="mrel mtight">=</span><span class="mord mtight">1</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight" style="margin-right:0.10903em">N</span></span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.2997em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord mathcal">L</span><span class="mopen">(</span><span class="mord"><span class="mord accent"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.6944em"><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="mord mathnormal" style="margin-right:0.03588em">y</span></span><span style="top:-3em"><span class="pstrut" style="height:3em"></span><span class="accent-body" style="left:-0.1944em"><span class="mord">^</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.1944em"><span></span></span></span></span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathnormal mtight">n</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord"><span class="mord mathnormal" style="margin-right:0.03588em">y</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.1514em"><span style="top:-2.55em;margin-left:-0.0359em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathnormal mtight">n</span></span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.15em"><span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span> - ÑÑедние поÑеÑи на обÑÑаÑÑей вÑбоÑке (<em>ÑмпиÑиÑеÑкий ÑиÑк</em>).</p> 114</li> 115</ul> 116<h2 class="anchor anchorTargetStickyNavbar_ahd2" id="ÑпеÑиалÑнÑе-ÑÑнкÑии">СпеÑиалÑнÑе ÑÑнкÑии<a href="#ÑпеÑиалÑнÑе-ÑÑнкÑии" class="hash-l
116ink" aria-label="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑнÑе ÑÑнкÑии" title="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на СпеÑиалÑнÑе ÑÑнкÑии" translate="no">â</a></h2> 117<ul> 118<li class=""> 119<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="normal">#</mi><mo stretchy="false">[</mo><mo>â </mo><mo stretchy="false">]</mo></mrow><annotation encoding="application/x-tex">\#[\cdot]</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="mord">#</span><span class="mopen">[</span><span class="mord">â </span><span class="mclose">]</span></span></span></span> - ÑиÑло ÑлеменÑов, напÑимеÑ,</p> 120<ul> 121<li class=""> 122<p>#[обÑекÑов] = ÑиÑло обÑекÑов,</p> 123</li> 124<li class=""> 125<p>#[пÑизнаков] = ÑиÑло пÑизнаков</p> 126</li> 127</ul> 128</li> 129<li class=""> 130<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mo stretchy="false">[</mo><mi>z</mi><msub><mo stretchy="false">]</mo><mo lspace="0em" rspace="0em">+</mo></msub><mo>=</mo><mi>max</mi><mo>â¡</mo><mo stretchy="false">{</mo><mi>z</mi><mo separator="true">,</mo><mn>0</mn><mo stretchy="false">}</mo></mrow><annotation encoding="application/x-tex">[z]_{+}=\max\{z,0\}</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 mathnormal" style="margin-right:0.04398em">z</span><span class="mclose"><span class="mclose">]</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.2583em"><span style="top:-2.55em;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 mtight"><span class="mord mtight">+</span></span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:0.2083em"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em"></span><span class="mop">max</span><span class="mopen">{</span><span class="mord mathnormal" style="margin-right:0.04398em">z</span><span class="mpunct">,</span><span class="mspace" style="margin-right:0.1667em"></span><span class="mord">0</span><span class="mclose">}</span></span></span></span> - опеÑаÑÐ¾Ñ Ð¿Ð¾Ð»Ð¾Ð¶Ð¸ÑелÑной ÑÑезки (оÑÑавление неоÑÑиÑаÑелÑного знаÑÐµÐ½Ð¸Ñ Ð¸ занÑление оÑÑиÑаÑелÑного)</p> 131</li> 132<li class=""> 133<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi mathvariant="double-struck">I</mi><mo stretchy="false">[</mo><mtext>ÑÑловие</mtext><mo stretchy="false">]</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>1</mn><mo separator="true">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext>еÑли ÑÑловие вÑполнено</mtext></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>0</mn><mo separator="true">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mtext>еÑли ÑÑловие не вÑполнено</mtext></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\mathbb{I}[\text{ÑÑловие}]=\begin{cases} 1341, & \text{еÑли ÑÑловие вÑполнено}\\ 1350, & \text{еÑли ÑÑловие не вÑполнено} 136\end{cases}</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="mord mathbb">I</span><span class="mopen">[</span><span class="mord text"><span class="mord cyrillic_fallback">ÑÑловие</span></span><span class="mclose">]</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:3em;vertical-align:-1.25em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">
136{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord">1</span><span class="mpunct">,</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord">0</span><span class="mpunct">,</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord cyrillic_fallback">еÑли</span><span class="mord"> </span><span class="mord cyrillic_fallback">ÑÑловие</span><span class="mord"> </span><span class="mord cyrillic_fallback">вÑполнено</span></span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord text"><span class="mord cyrillic_fallback">еÑли</span><span class="mord"> </span><span class="mord cyrillic_fallback">ÑÑловие</span><span class="mord"> </span><span class="mord cyrillic_fallback">не</span><span class="mord"> </span><span class="mord cyrillic_fallback">вÑполнено</span></span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p> 137</li> 138<li class=""> 139<p><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mtext>sign</mtext><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.36em" columnalign="left left" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mn>1</mn><mo separator="true">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo>â¥</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mo>â</mo><mn>1</mn><mo separator="true">,</mo></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo><</mo><mn>0</mn></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">\text{sign}(x)=\begin{cases} 1401, & x\ge0\\ 141-1, & x<0 142\end{cases}</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="mord text"><span class="mord">sign</span></span><span class="mopen">(</span><span class="mord mathnormal">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:3em;vertical-align:-1.25em"></span><span class="minner"><span class="mopen delimcenter" style="top:0em"><span class="delimsizing size4">{</span></span><span class="mord"><span class="mtable"><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord">1</span><span class="mpunct">,</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord">â</span><span class="mord">1</span><span class="mpunct">,</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span><span class="arraycolsep" style="width:1em"></span><span class="col-align-l"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.69em"><span style="top:-3.69em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">â¥</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord">0</span></span></span><span style="top:-2.25em"><span class="pstrut" style="height:3.008em"></span><span class="mord"><span class="mord mathnormal">x</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel"><</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mord">0</span></span></span></span><span class="vlist-s">â</span></span><span class="vlist-r"><span class="vlist" style="height:1.19em"><span></span></span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p> 143</li> 144</ul> 145<h2 class="anchor anchorTargetStickyNavbar_ahd2" id="опиÑание-алгоÑиÑмов">ÐпиÑание алгоÑиÑмов<a href="#опиÑание-алгоÑиÑмов" class="hash-l
145ink" aria-label="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на ÐпиÑание алгоÑиÑмов" title="ÐÑÑÐ¼Ð°Ñ ÑÑÑлка на ÐпиÑание алгоÑиÑмов" translate="no">â</a></h2> 146<ul> 147<li class=""> 148<p>:= ознаÑÐ°ÐµÑ "пÑиÑвоиÑÑ Ð·Ð½Ð°Ñение". ÐапÑимеÑ, пÑиÑвоение пеÑеменной <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi></mrow><annotation encoding="application/x-tex">t</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em"></span><span class="mord mathnormal">t</span></span></span></span> знаÑени�Ñ Ð½Ð¾Ð»Ñ Ð·Ð°Ð¿Ð¸ÑÑваеÑÑÑ Ð² виде <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>t</mi><mo>:</mo><mo>=</mo><mn>0</mn></mrow><annotation encoding="application/x-tex">t:=0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6151em"></span><span class="mord mathnormal">t</span><span class="mspace" style="margin-right:0.2778em"></span><span class="mrel">:=</span><span class="mspace" style="margin-right:0.2778em"></span></span><span class="base"><span class="strut" style="height:0.6444em"></span><span class="mord">0</span></span></span></span>.</p> 149</li> 150<li class=""> 151<p><em>ÐÑимпÑоÑиÑеÑÐºÐ°Ñ ÑложноÑÑÑ Ð°Ð»Ð³Ð¾ÑиÑмов</em> обознаÑаеÑÑÑ ÐºÐ°Ðº <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mo>â </mo><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(\cdot)</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="mord mathnormal" style="margin-right:0.02778em">O</span><span class="mopen">(</span><span class="mord">â </span><span class="mclose">)</span></span></span></span>. ÐапÑимеÑ, ÑложноÑÑÑ ÑвелиÑÐµÐ½Ð¸Ñ Ð²ÑÐµÑ ÑлеменÑов <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi></mrow><annotation encoding="application/x-tex">n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">n</span></span></span></span>-меÑного векÑоÑа на единиÑÑ Ñавна <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><mi>n</mi><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n)</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="mord mathnormal" style="margin-right:0.02778em">O</span><span class="mopen">(</span><span class="mord mathnormal">n</span><span class="mclose">)</span></span></span></span>, а аÑимпÑоÑиÑеÑÐºÐ°Ñ ÑложноÑÑÑ ÑвелиÑÐµÐ½Ð¸Ñ Ð½Ð° единиÑÑ Ð²ÑÐµÑ ÑлеменÑов маÑÑиÑÑ <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>n</mi><mo>Ã</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">n \times n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.6667em;vertical-align:-0.0833em"></span><span class="mord mathnormal">n</span><span class="mspace" style="margin-right:0.2222em"></span><span class="mbin">Ã</span><span class="mspace" style="margin-right:0.2222em"></span></span><span class="base"><span class="strut" style="height:0.4306em"></span><span class="mord mathnormal">n</span></span></span></span> - <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mi>O</mi><mo stretchy="false">(</mo><msup><mi>n</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow><annotation encoding="application/x-tex">O(n^2)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0641em;vertical-align:-0.25em"></span><span class="mord mathnormal" style="margin-right:0.02778em">O</span><span class="mopen">(</span><span class="mord"><span class="mord mathnormal">n</span><span class="msupsub"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8141em"><span style="top:-3.063em;margin-right:0.05em"><span class="pstrut" style="height:2.7em"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span></span></span></span></span></span><span class="mclose">)</span></span></span></span>.</p> 152</li> 153</ul></div></article><nav class="docusaurus-mt-lg pagination-nav" aria-label="СÑÑаниÑа докÑменÑа"></nav></div></div><div class="col col--3"><div class="tableOfContents_FsCt thin-scrollbar theme-doc-toc-desktop"><ul class="table-of-contents table-of-contents__left-border"><li><a href="#ÑпеÑиалÑнаÑ-ÑеÑминологиÑ" class="table-of-contents__link toc-highlight">СпеÑиалÑÐ½Ð°Ñ ÑеÑминологиÑ</a></li><li><a href="#ÑкалÑÑÑ-векÑоÑÑ-и-маÑÑиÑÑ" class="table-of-contents__link toc-highlight">СкалÑÑÑ, векÑоÑÑ Ð¸ маÑÑиÑÑ</a></li><li><a href="#ÑпеÑиалÑнÑе-ÑимволÑ" class="table-of-contents__link toc-highlight">СпеÑиалÑнÑе ÑимволÑ</a></li><li><a href="#ÑпеÑиалÑнÑе-ÑÑнкÑии" class="table-of-contents__link toc-highlight">СпеÑиалÑнÑе ÑÑнкÑии</a></li><li><a href="#опиÑание-алгоÑиÑмов" class="table-of-contents__link toc-highlight">ÐпиÑание алгоÑиÑмов</a></li></ul></div></div></div></div></main></div></div></div><footer class="theme-layout-footer footer footer--dark"><div class="container container-fluid"><div class="footer__bottom text--center">
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