Kristian Schultz преди 4 години
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  1. 1147 0
      documentation/NNSearch_idea.svg

+ 1147 - 0
documentation/NNSearch_idea.svg

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+             id="text291518"><tspan
+               sodipodi:role="line"
+               id="tspan291516"
+               style="stroke-width:0.264583px"
+               x="18.342405"
+               y="159.10248">Sort { π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan460111">0</tspan>, π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan460109">1</tspan>, ... π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan460107">n</tspan> } = { 0, 1,2, ..., n } so that Δ(i, π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan460113">j</tspan> ) ≤  Δ(i, π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan460115">j+1</tspan>) for all j in {0, 1, ... , n-1}</tspan></text>
+          <text
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+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="18.104017"
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+             id="text305581"><tspan
+               sodipodi:role="line"
+               id="tspan305579"
+               style="stroke-width:0.264583px"
+               x="18.104017"
+               y="163.87959">N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan411745">i</tspan> ← ∅</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+               sodipodi:role="line"
+               id="tspan305579-8"
+               style="stroke-width:0.264583px"
+               x="28.944956"
+               y="195.11205">N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan428417">i</tspan> ← (N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan428415">i</tspan> / {a}) ∪ {π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan469603">k</tspan>}</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+             id="text305581-9-4"><tspan
+               sodipodi:role="line"
+               id="tspan305579-8-4"
+               style="stroke-width:0.264583px"
+               x="25.098562"
+               y="177.36166">N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan414177">i</tspan> ← N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan414179">i</tspan> ∪ {π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan463559">k</tspan>}</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="22.054419"
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+             id="text314906"><tspan
+               sodipodi:role="line"
+               id="tspan314902"
+               style="letter-spacing:-0.0258171px;stroke-width:0.264583px"
+               x="22.054419"
+               y="181.84773">else:</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
+               x="22.054419"
+               y="188.46231"
+               id="tspan314904" /></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="25.25202"
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+               sodipodi:role="line"
+               id="tspan315490"
+               style="stroke-width:0.264583px"
+               x="25.25202"
+               y="185.85492">a ← a in N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan416893">i</tspan> with Δ(i, a) ≥ Δ(i, b) for all b in N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan416895">i</tspan></tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="25.25202"
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+             id="text322619"><tspan
+               sodipodi:role="line"
+               id="tspan322617"
+               style="stroke-width:0.264583px"
+               x="25.25202"
+               y="190.35423"
+               dy="0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1">if ‖x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan421609">a</tspan> - x‖ &gt; ‖x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan424307"
+   dy="0 1">πk</tspan> - x‖:</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="28.944956"
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+             id="text326428"><tspan
+               sodipodi:role="line"
+               id="tspan326426"
+               style="stroke-width:0.264583px"
+               x="28.944956"
+               y="204.12785">break loop for k; next x</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="25.25202"
+             y="199.61136"
+             id="text326434"><tspan
+               sodipodi:role="line"
+               id="tspan326432"
+               style="stroke-width:0.264583px"
+               x="25.25202"
+               y="199.61136">if ‖x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan430379">a</tspan> - x‖ &lt; Δ(π<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan473861">k</tspan> , i):</tspan></text>
+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+             id="path331964" />
+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             d="m 22.601484,182.80787 v 24.98717 h 3.534653"
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+             sodipodi:nodetypes="ccc" />
+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+             sodipodi:nodetypes="ccc" />
+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             d="m 25.366253,200.21987 v 5.31599 h 3.534653"
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+             sodipodi:nodetypes="ccc" />
+          <path
+             style="fill:none;fill-rule:evenodd;stroke:#000000;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+             sodipodi:nodetypes="ccc" />
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+               sodipodi:role="line"
+               id="tspan334681"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="217.08237">return (N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan335599">0</tspan>, N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan335597">1</tspan>, N<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan335595">2</tspan>, ..., N<tspan
+   style="font-size:65%;baseline-shift:sub"
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+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
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+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
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+               sodipodi:role="line"
+               id="tspan337908"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="126.62011">x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan342466">s</tspan> ← x in data so that d(x, x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan342468">0</tspan>) ≥ d(y, x<tspan
+   style="font-size:65%;baseline-shift:sub"
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+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
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+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="14.083701"
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+             id="text342562"><tspan
+               sodipodi:role="line"
+               id="tspan342558"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="131.22527">x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan345168">e</tspan> ← x in data so that d(x, x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan342554">s</tspan>) ≥ d(y, x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan342556">s</tspan>) for all y in data</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
+               x="14.083701"
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+               id="tspan342560" /></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="14.083701"
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+             id="text349910"><tspan
+               sodipodi:role="line"
+               id="tspan349906"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="135.81717">v ← (x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan350672">e</tspan> - x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan350670">s</tspan>) / d(x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan350668">e</tspan> - x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan350666">s</tspan>)</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="142.69556"
+               id="tspan349908" /></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="14.083701"
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+             id="text354793"><tspan
+               sodipodi:role="line"
+               id="tspan354789"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="140.32047">H ← ( ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan354781">0 </tspan>- x‖, ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368131">1</tspan> - x‖, ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368133">2</tspan> - x‖, ..., ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368135">n</tspan> - x‖ )</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
+               x="14.083701"
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+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="14.083701"
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+               sodipodi:role="line"
+               id="tspan368305"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="144.91502">K ← ( ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368297">0 </tspan>- x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan370869">0</tspan>‖, ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368299">1</tspan> - x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan370867">1</tspan>‖, ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368301">2</tspan> - x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan370865">2</tspan>‖, ..., ‖x'<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan368303">n</tspan> - x<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan370863">n</tspan>‖ )</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="151.79341"
+               id="tspan368307" /></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:2.64583px;line-height:6.61458px;font-family:sans-serif;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
+             x="14.083701"
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+             id="text371257"><tspan
+               sodipodi:role="line"
+               id="tspan371253"
+               style="stroke-width:0.264583px"
+               x="14.083701"
+               y="149.80223">Δ(i, j) = sqrt( (K<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan372735">i</tspan> - K<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan372733">j</tspan>)<tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan372727">2</tspan> + (H<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan372725">i</tspan> - H<tspan
+   style="font-size:65%;baseline-shift:sub"
+   id="tspan372723">j</tspan>)<tspan
+   style="font-size:65%;baseline-shift:super"
+   id="tspan372721">2</tspan> )</tspan><tspan
+               sodipodi:role="line"
+               style="stroke-width:0.264583px"
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