2b:null 2c:["$","title",null,{"children":"Distance between the brownian bridges | Chuncheng | Observable"}] 31:[] 2f:{"id":"a8df5de56faa82c8","slug":"distance-between-the-brownian-bridges","title":"Distance between the brownian bridges","thumbnail":"1b0aa2fb91a3d6eb51230bcb39b8538f84255219d746c73451fbc52c6c41e0ba","access_level":"public","create_time":"$D2023-05-10T13:10:15.467Z","update_time":"$D2023-05-18T07:20:22.744Z","view_time":null,"first_public_time":"$D2023-05-10T13:10:15.467Z","fork":false,"stars":1,"starred":false,"owner":{"type":"team","id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":"starter_2024"},"version":283,"publish_version":null,"role":null,"authored":false,"authors":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null}],"members":[{"type":"individual","id":"16328058352682a8","login":"listenzcc","name":"Chuncheng","avatar_url":"https://avatars-next.observableusercontent.com/bb3c68e77a708a587ffc2d663bb83421f20d67991dbe6c1623c6e5d2fb73d15e","tier":null,"role":"editor"}],"comments":[],"custom_thumbnail":false,"trashed":false,"subscribed":null,"forks":0,"collection":{"id":"809c79db435f6961","slug":"brownian-bridge","title":"Brownian bridge","owner":{"id":"bcd65cef1cb4d2ed","login":"listenzcc","name":"Chuncheng"}},"type":"notebook","body":{"title":"Distance between the brownian bridges","cells":[{"id":0,"value":"# Distance between the brownian bridges","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":146,"value":"toc()","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":115,"value":"## Setup","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":108,"value":"viewof dataSetup = Inputs.form({\n length: Inputs.range([500, 1000], {\n label: \"Length (time points)\",\n value: 500,\n step: 1\n }),\n signals: Inputs.range([50, 100], {\n label: \"Signals (count)\",\n value: 50,\n step: 1\n })\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":131,"value":"### PCA distribute","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":186,"value":"viewof signalIdx = Inputs.range([0, data.n - 1], {\n label: \"Signal index\",\n step: 1,\n value: 0\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":209,"value":"viewof signal2Idx = Inputs.range([0, data.n - 1], {\n label: \"Signal-2 index\",\n step: 1,\n value: data.n - 1\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":99,"value":"Plot.plot({\n x: { grid: true, nice: true },\n y: { grid: true, nice: true },\n color: { legend: true, scheme: \"Cividis\" },\n marks: [\n Plot.dot(pcaTable, { x: \"f1\", y: \"f2\", fill: \"signal\" }),\n Plot.dot(pcaTable.slice(signalIdx, signalIdx + 1), {\n x: \"f1\",\n y: \"f2\",\n stroke: \"red\",\n r: 10,\n strokeWidth: 5\n }),\n Plot.dot(pcaTable.slice(signal2Idx, signal2Idx + 1), {\n x: \"f1\",\n y: \"f2\",\n stroke: \"green\",\n r: 10,\n strokeWidth: 5\n }),\n Plot.density(pcaTable, {\n x: \"f1\",\n y: \"f2\",\n stroke: \"steelblue\",\n strokeWidth: 0.3\n }),\n Plot.density(pcaTable, {\n x: \"f1\",\n y: \"f2\",\n stroke: \"steelblue\",\n thresholds: 4,\n opacity: 0.5\n }),\n Plot.frame()\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":201,"value":"Plot.plot({\n y: { grid: true },\n color: {\n legend: true\n },\n marks: [\n // Zero line\n Plot.ruleY([0], { stroke: \"gray\" }),\n Plot.line(\n data.filter((d) => d.signal === signalIdx),\n {\n x: (d) => d.time,\n y: \"brownianBridge\",\n stroke: \"red\"\n }\n ),\n Plot.line(\n data.filter((d) => d.signal === signal2Idx),\n {\n x: (d) => d.time,\n y: \"brownianBridge\",\n stroke: \"green\"\n }\n ),\n Plot.frame()\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":117,"value":"## Display\n### Distance histogram","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":64,"value":"Plot.plot({\n height: 200,\n x: { round: true },\n y: { grid: true },\n color: { legend: true },\n marks: [\n Plot.rectY(\n distanceTable,\n Plot.binX(\n { y: \"count\", fill: \"count\" },\n { x: \"v\", inset: 0, opacity: 0.8 }\n )\n ),\n Plot.ruleY([0])\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"Plot.plot({\n r: { range: [0, 14] },\n marginLeft: 50,\n marginRight: 25,\n marks: [Plot.dot(distanceTable, Plot.binX({ r: \"count\" }, { x: \"v\" }))]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":128,"value":"### Distance matrix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":41,"value":"Plot.plot({\n width: 600,\n height: 600,\n padding: 0,\n grid: true,\n x: { axis: \"top\", label: \"i\" },\n y: { label: \"j\" },\n color: { type: \"linear\", scheme: \"Blues\", legend: true },\n marks: [\n Plot.cell(distanceTable, {\n x: \"i\",\n y: \"j\",\n fill: \"v\",\n inset: 0.5\n })\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":134,"value":"### Time series","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":52,"value":"Plot.plot({\n width: width,\n y: { grid: true },\n color: {\n legend: true,\n scheme: \"Category10\"\n },\n marks: [\n // Zero line\n Plot.ruleY([0], { stroke: \"gray\" }),\n Plot.line(data, {\n x: (d) => d.time + d.signal * data.T,\n y: \"brownianAccumulate\",\n stroke: (d) => \"Seg\" + (\"000\" + d.signal).slice(-3),\n opacity: 0.3\n }),\n Plot.line(data, {\n x: (d) => d.time + d.signal * data.T,\n y: \"brownianBridge\",\n stroke: (d) => \"Seg\" + (\"000\" + d.signal).slice(-3)\n }),\n Plot.frame()\n ]\n})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":137,"value":"## Computation\n### PCA analysis","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":101,"value":"pcaTable = {\n const { data: feature1 } = predict,\n { n } = data;\n\n const table = [];\n for (let i = 0; i < n; ++i) {\n table.push({\n f1: feature1[i][0],\n f2: feature1[i][1],\n f3: feature1[i][2],\n signal: i\n });\n }\n\n return table;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":97,"value":"predict = pca.predict(distanceMatrix)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":94,"value":"pca = new PCA(distanceMatrix, { center: true, scale: true })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":92,"value":"PCA = (await require(\"https://bundle.run/ml-pca@4.0.2\")).PCA","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":139,"value":"### Distance analysis","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":34,"value":"distanceTable = {\n const mat = distanceMatrix,\n { T, n } = data,\n distanceTable = [];\n\n for (let i = 0; i < n; ++i) {\n for (let j = 0; j < n; ++j) {\n distanceTable.push({ i, j, v: mat[i][j] });\n }\n }\n\n return distanceTable;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"distanceMatrix = {\n const matrix = matrixBrownianBridge,\n { T, n } = data,\n distance = [];\n\n for (let i = 0; i < n; ++i) {\n const array = [...new Array(n).fill(0)];\n for (let j = i; j < n; ++j) {\n for (let t = 0; t < T; ++t) {\n array[j] += (matrix[t][i] - matrix[t][j]) ** 2;\n }\n }\n distance.push(array);\n }\n\n for (let i = 0; i < n; ++i) {\n for (let j = i; j < n; ++j) {\n distance[i][j] = Math.sqrt(distance[i][j]) / T;\n distance[j][i] = distance[i][j];\n }\n }\n\n return distance;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":141,"value":"### Raw data generation","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":15,"value":"matrixBrownianBridge = table2matrix(\"brownianBridge\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"table2matrix = (column = \"brownianBridge\") => {\n const { T, n } = data;\n\n const matrix = [];\n for (let t = 0; t < T; ++t) {\n matrix.push([...new Array(n).fill(0)]);\n }\n\n data.map((d) => {\n matrix[d.time][d.signal] = d[column];\n });\n\n return matrix;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"data = mkData(dataSetup.length, dataSetup.signals)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":249,"value":"rndEngine = d3.randomNormal()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":252,"value":"rndEngine1 = d3.randomBernoulli(0.5) //d3.randomUniform()","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":241,"value":"rnd = () => {\n // return rndEngine1() * 2 - 1;\n return rndEngine();\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":7,"value":"/**\n * Make data for T length and n signals.\n **/\nmkData = (T, n) => {\n const data = [];\n\n var x,\n xT = [],\n b,\n invT = 1.0 / T;\n\n for (let i = 0; i < n; ++i) {\n x = 0;\n\n for (let t = 0; t < T; ++t) {\n data.push({\n signal: i,\n time: t,\n brownian: x,\n brownianAccumulate: x + (i > 0 ? d3.sum(xT.slice(0, i)) : 0)\n });\n\n if (t === T - 1) {\n xT.push(x);\n } else {\n x += rnd();\n }\n }\n }\n\n data.map((d) => {\n b = d.brownian - (d.time + 1) * invT * xT[d.signal];\n Object.assign(d, { brownianBridge: b });\n });\n\n Object.assign(data, { T, n });\n\n return data;\n}","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"d3 = require(\"d3\")","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":143,"value":"import { toc } from \"@nebrius/indented-toc\"","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W31","stdlib":"1","titling":"auto"}} 30:"$2f:body"