2d:null 2e:["$","title",null,{"children":"짧은 머신러닝 안내서: Gaussian Mixture | Humble Data Miner | Observable"}] 33:T7f6,--- ## Clustering? * 데이터포인트들의 특성으로 유사한 데이터들의 군집(cluster)을 찾는 알고리즘 * 결과군집 대한 정보가 없는 비지도적 학습방법(unsupervised learning) ## Gaussian Mixture? * Gaussian: 데이터를 잘 묘사하는 정규분포(Gaussian distribution) 찾음 * Mixture: 데이터를 k개 정규분포의 복합체(Mixture)로 근사(Approx.) * 사용자 입력값 k → 결과로 k개의 정규분포를 출력

${await FileAttachment("image.png").image({style:"width:70%;"})}	${await FileAttachment("image@2.png").image({style:"width:100%;"})}
xy평면상에서 좌표(0,0)을 중심으로 x자체분산, x와 y간 공분산, y자체분산이 각각 1,3/5,2인 정규분포의 표현	이변량 정규분표의 3차원 확률밀도 표현
Wikipedia - Multivariate normal distribution

## 확률밀도(Probability density)와 기여분(Responsibility) * 군집을 확률분포(정규분포)로 표현하기 때문에 * 한 점(데이터포인트)이 여러 확률분포상에 중첩되어 존재(Soft clustering) * 확률밀도(n×k): 한점의 위치가 주어졌을때 지정된 분포상에 발생할 확률 * 군집가중치(k): 한점의 위치를 모른다 가정할때 각 분포(군집)에 속할 확률 * 가중확률밀도(n×k): 확률밀도×군집가중치,군집의 영향력을 반영한 확률밀도 * 기여분(n×k): 각점이 각군집(가중치를 반영해)에 속할 확률 * 한점에 대해서, (특정 군집 가중확률밀도)/(모든 군집 가중확률밀도의 합)34:Tfc6,{ resample; const ps = 300; // square plot size const margin = { left:10, right:10, top:10, bottom: 10 }; const svg = d3.create("svg").attr("viewBox", [0, 0, width, ps]); const rands = [d3.randomNormal(-1,Math.sqrt(2)/1.5), d3.randomNormal(1,Math.sqrt(2)/1.5)]; const num_elems = [10,10]; const K = num_elems.length; const data = num_elems.map((n,i)=>d3.range(n).map(_=>{return {x:rands[i](),y:rands[i]()}})).reduce((acc,arr)=>{acc=acc.concat(arr); return acc;},[]); const stats = gaussian_mixture(data,{k:2,maxit:100}); const ex = d3.extent(data,d=>d.x); const ey = d3.extent(data,d=>d.y); const x = d3.scaleLinear().domain(ex).range([margin.left, ps-margin.right]); const y = d3.scaleLinear().domain(ey).range([ps-margin.bottom, margin.top]); const stat = stats.history.slice(-1)[0]; const cls_idx = stat.resp.map((resp,i)=>[Math.abs(resp[0]-resp[1]),i]).toSorted((lhs,rhs)=>lhs[0]-rhs[0])[0][1]; const gdists = svg.append("g") stat.ellps.map((e,i)=>gdists.append("ellipse") .attr("cx",0).attr("cy",0) .attr("rx",x(e.r1*radius_multiplier)-x(0)).attr("ry",y(0)-y(e.r2*radius_multiplier)) .attr("transform",`translate(${x(stat.means[i][0])},${y(stat.means[i][1])}),rotate(${-e.deg})`) .attr("stroke","none").attr("fill",`url(#radgrad${i})`) ); function adj_stroke_width(sw) { return sw < 1e-2 ? 0 : sw*3; } const glines = svg.append("g"); d3.range(K).map(ki=> glines.append("line") .attr("x1",x(stat.means[ki][0])).attr("y1",y(stat.means[ki][1])) .attr("x2",x(data[cls_idx].x)).attr("y2",y(data[cls_idx].y)) .attr("stroke","grey").attr("stroke-width", adj_stroke_width(stat.resp[cls_idx][ki]*2)) ); d3.range(data.length) .map(ni=>d3.range(K) .map(ki=>glines.append("line") .attr("x1",x(stat.means[ki][0])).attr("y1",y(stat.means[ki][1])) .attr("x2",x(data[ni].x)).attr("y2",y(data[ni].y)) .attr("stroke","white").attr("stroke-width", adj_stroke_width(stat.resp[ni][ki])) )); const gpts = svg.append("g"); gpts.append("circle") .attr("r",6).attr("cx",x(data[cls_idx].x)).attr("cy",y(data[cls_idx].y)).attr("stroke-width",6).attr("stroke","grey").attr("fill","none"); svg.append("g").attr("stroke","white").attr("stroke-opacity",1).attr("stroke-width",3).attr("fill","none").selectAll("circle") .data(data) .join("circle") .attr("r",6).attr("cx",d=>x(d.x)).attr("cy",d=>y(d.y)); const notes = stat.means.map(mean=>{return{mean:[(mean[0]+data[cls_idx].x)/2,(mean[1]+data[cls_idx].y)/2]}}); notes.forEach((note,i)=>{ const upside = note.mean[1]>notes[i?0:1].mean[1]; notes[i].upside = upside; notes[i].txtcenter = [x(note.mean[0]), upside?margin.top+10:ps-margin.bottom-10]; notes[i].resp = stat.resp[cls_idx][i]; notes[i].prob = stat.probs[cls_idx][i]; notes[i].wprob = stat.wprobs[cls_idx][i]; notes[i].weight = notes[i].wprob/notes[i].prob; notes[i].allwprob = stat.wprobs[cls_idx]; }); console.log(notes); const gnotes = svg.append("g"); notes.map((note,i)=> gnotes.append("path").attr("fill","none").attr("stroke","grey") .attr("d",`M ${x(note.mean[0])} ${y(note.mean[1])} V ${note.txtcenter[1]}`) .attr("marker-end","url(#arrow)") ); const texts = notes.map((note,i)=> gnotes.append("text").attr("fill","black").attr("font-size",13) .attr("text-anchor","middle").attr("dominant-baseline",note.upside?"auto":"hanging") .attr("x",note.txtcenter[0]).attr("y",note.txtcenter[1]) .text(` 확률밀도=${note.prob.toFixed(3)}, 군집가중치=${(note.weight).toFixed(2)}, 가중확률밀도=${note.prob.toFixed(3)}*${note.weight.toFixed(2)}=${note.wprob.toFixed(3)} ⇒ 기여분=${note.wprob.toFixed(3)}/(${note.allwprob[0].toFixed(3)}+${note.allwprob[1].toFixed(3)})=${note.resp.toFixed(2)}(${(note.resp*100).toFixed(0)}%)`) ); yield svg.node(); texts.forEach(text=>{ const bbox = text.node().getBBox(); if(bbox.x<0) text.attr("dx",-bbox.x); }); return svg.node(); }35:T14e5,{ const height = 700; const slider_height = 60; const margin = { left: 40, right:40, top:0, bottom: 20+slider_height }; const svg = d3.create("svg").attr("viewBox", [0, 0, width, height]); const data = rawdata; const ex = [d3.min(data,d=>d.x)-1,d3.max(data,d=>d.x)+1]; const ey = [d3.min(data,d=>d.y)-1,d3.max(data,d=>d.y)+1]; const ph = height - margin.bottom; const pw = Math.ceil(ph*(ex[1]-ex[0])/(ey[1]-ey[0])); const x = d3.scaleLinear().domain(ex).range([margin.left, margin.left+pw]); const y = d3.scaleLinear().domain(ey).range([margin.top+ph, margin.top]); const gdists = svg.append("g"); const dists = d3.range(gm_params.k).map((d,i)=>gdists.append("ellipse") .attr("cx",0).attr("cy",0) .attr("stroke","none").attr("fill",`url(#radgrad${i})`) ); const glines = svg.append("g"); const lines = d3.range(data.length) .map(ni=>d3.range(gm_params.k) .map(ki=>glines.append("line") .attr("x2",x(data[ni].x)).attr("y2",y(data[ni].y)).attr("stroke","white") )); const gpts = svg.append("g"); const points = data.map((d,i)=>gpts.append("circle") .attr("stroke","white").attr("stroke-opacity",1).attr("stroke-width",2).attr("fill","none") .attr("r",3).attr("transform",`translate(${x(d.x)},${y(d.y)})`) ); const labels = svg.append("g") .attr("font-size",10).attr("text-anchor","start").attr("dominant-baseline","middle").selectAll("text") .data(data) .join("text") .attr("x", d=>x(d.x)).attr("y", d=>y(d.y)).attr("dx",6).attr("dy",1) .text(d=>`${d.rank}.${d.name}`); svg.append("path").attr("fill","white").attr("stroke","none").attr("d",`M 0 0 H ${margin.left} V ${height} H 0 V 0`); svg.append("path").attr("fill","white").attr("stroke","none").attr("d",`M 0 ${height-margin.bottom} H ${width} V ${height} H 0`); const history = gm_result.history; const its = d3.range(-1,history.length,1); const slider = d3_slider.sliderBottom().min(-1).max(its.length-2).step(1).value(-1) .tickValues(its) .tickFormat(i=>`${i<0?"초기값":i==its.length-3?"정지":i==its.length-2?"결과":(i+1).toFixed(0)}`) .value(-1).width(ph).fill(d3.schemeCategory10[3]).on("onchange", () => update(slider.value())); const giteration = svg.append("g").attr("class","ransac-iteration").attr("transform",`translate(120,${height-margin.bottom/2})`); giteration.call(slider); giteration.selectAll(".slider text").attr("font-size", "12"); giteration.selectAll(".axis text").attr("fill","grey"); giteration.append("text") .attr("text-anchor","middle").attr("dominant-baseline","middle") .attr("x","-70").attr("y",0).attr("dy",4).text("반복회차"); giteration.append("text") .attr("text-anchor","middle").attr("dominant-baseline","middle") .attr("x","-70").attr("y",20).attr("dy",4).text("(#iteration)"); svg.append("g").attr("transform",`translate(0,${height-margin.bottom})`).call(d3.axisBottom(x)); svg.append("g").attr("transform",`translate(${margin.left},0)`).call(d3.axisLeft(y).tickFormat(d=>`${d.toLocaleString()}`)); update(-1); function update(it) { it = Math.round(it); const n = data.length; const dur = anim_step_ms; const rm = radius_multiplier; const line = d3.line().x(d=>d[0]).y(d=>d[1]); const prev_item = it>0? gm_result.history[it-1] : gm_result.init; const curr_item = it>=0? gm_result.history[it] : gm_result.init; function adj_stroke_width(sw) { return sw < 1e-2? 0 : sw*2; } if(it<0) { const means = curr_item.means; const ellps = curr_item.ellps; for(let ki=0; ki < dists.length; ki++) { dists[ki].interrupt() .attr("rx",Math.abs(x(ellps[ki].r1*rm)-x(0))).attr("ry",Math.abs(y(ellps[ki].r2*rm)-y(0))) .attr("transform",`translate(${x(means[ki][0])},${y(means[ki][1])}),rotate(${-ellps[ki].deg})`); } for(let ni=0; ni < lines.length; ni++) { const klines = lines[ni]; for(let ki=0; ki < klines.length; ki++) { const resp = prev_item.resp[ni][ki]; klines[ki].interrupt() .attr("x1",x(means[ki][0])).attr("y1",y(means[ki][1])).attr("stroke-width",adj_stroke_width(resp)); } } } else { const [prev_means, curr_means] = [prev_item.means, curr_item.means]; const [prev_ellps, curr_ellps] = [prev_item.ellps, curr_item.ellps]; for(let ki=0; ki < dists.length; ki++) { let dist = dists[ki].interrupt() .attr("rx",Math.abs(x(prev_ellps[ki].r1*rm)-x(0))).attr("ry",Math.abs(y(prev_ellps[ki].r2*rm)-y(0))) .attr("transform",`translate(${x(prev_means[ki][0])},${y(prev_means[ki][1])}),rotate(${-prev_ellps[ki].deg})`); dist.transition().duration(dur) .attr("rx",Math.abs(x(curr_ellps[ki].r1*rm)-x(0))).attr("ry",Math.abs(y(curr_ellps[ki].r2*rm)-y(0))) .attr("transform",`translate(${x(curr_means[ki][0])},${y(curr_means[ki][1])}),rotate(${-curr_ellps[ki].deg})`); } for(let ni=0; ni < lines.length; ni++) { const klines = lines[ni]; for(let ki=0; ki < klines.length; ki++) { const resp = prev_item.resp[ni][ki]; klines[ki].interrupt() .attr("x1",x(prev_means[ki][0])).attr("y1",y(prev_means[ki][1])).attr("stroke-width",adj_stroke_width(resp)); } } } } return svg.node(); }36:T452,function kmeans_clustering(X,C,maxit) { const N = X.length; const K = C.length; let L = d3.range(N).map(_=>-1); const hist_rmse = []; for(let it = 0; it < maxit; it++) { // relabel L = d3.range(N).map(_=>-1); for(let ni = 0; ni < N; ni++) { let min_dist = Infinity; for(let ci = 0; ci < K; ci++) { const dist = edist(X[ni],C[ci]); if(min_dist <= dist) continue; L[ni] = ci; min_dist = dist; } } // recenter C = C.map((_,i)=>[0,0]); let cnt = C.map(_=>0); for(let ni = 0; ni < N; ni++) { const c = L[ni]; C[c][0]+=X[ni][0]; C[c][1]+=X[ni][1]; cnt[c] += 1; } for(let c = 0; c < C.length; c++) { C[c][0] /= cnt[c]; C[c][1] /= cnt[c]; } // calc RMSE let rmse = 0; for(let i = 0; i < L.length; i++) { const c = L[i]; rmse += sqdiff(X[i],C[c]); } rmse = Math.sqrt(rmse/N); const stop = (hist_rmse.length > 0 && hist_rmse.slice(-1)[0] == rmse); if(stop) { break; } hist_rmse.push(rmse); } return L; }37:Td1f,function gaussian_mixture(data, params) { const N = data.length; const X = data.map(row=>[row.x,row.y]); const K = params.k; const reg_covar = 1e-6; function conv_covar_radiideg(covar) { const [[a,b],[_b,c]] = covar; const [term1,term2] = [(a+c)/2,Math.sqrt(((a-c)/2)**2 + b**2)]; const [lmbd1,lmbd2] = [term1+term2,term1-term2]; const rad = Math.abs(b) < Number.EPSILON ? (a>=c ? 0:Math.PI/2) : Math.atan2(lmbd1-a,b); return {r1:Math.max(Math.sqrt(lmbd1),1e-1),r2:lmbd2<0?1e-1:Math.max(Math.sqrt(lmbd2),1e-1),deg:rad*180/Math.PI}; } function est_gauss_params(X, resp) { const nk = d3.range(K).map(ki=>Math.max(resp.reduce((acc,row)=>{acc+=row[ki];return acc;},0),Number.EPSILON*100)); const means = d3.range(K).map( ki=>d3.range(N).reduce((acc,ni)=>{ const prb = resp[ni][ki]; acc[0]+=prb*X[ni][0]; acc[1]+=prb*X[ni][1]; return acc; },[0,0]).map(sum=>sum/nk[ki])); const covars = d3.range(K).map(ki=>{ const diff = d3.range(N).map(ni=>[X[ni][0]-means[ki][0],X[ni][1]-means[ki][1]]); const covar_cross = diff.reduce((acc,d,ni)=>{ acc+=resp[ni][ki]*d[0]*d[1]; return acc; },0)/nk[ki]; const covar_self = [ diff.reduce((acc,d,ni)=>{ acc+=resp[ni][ki]*d[0]*d[0]; return acc; },0)/nk[ki]+reg_covar, diff.reduce((acc,d,ni)=>{ acc+=resp[ni][ki]*d[1]*d[1]; return acc; },0)/nk[ki]+reg_covar ]; const covar = [[covar_self[0], covar_cross], [covar_cross, covar_self[1]]]; return covar; }); return [nk, means, covars]; } function est_gauss_prob(X,means,covars) { const dists = d3.range(K).map(ki=>new Gaussian({sigma:covars[ki],mu:means[ki]})); return X.map(x=>dists.map(dist=>dist.density(x))); } const stats = {}; /* initialize internal paramters*/ let resp = null; if(gm_init_method == "k-means") { const C_init = d3.shuffle(d3.range(N)).slice(0,K).map(ni=>X[ni]); const L_init = kmeans_clustering(X,C_init,300); resp = L_init.map(lbl=>d3.range(K).map(ki=>ki==lbl?1:0)); } else { const rand = d3.randomUniform(); resp = d3.range(N).map(_=>d3.range(K).map(_=>rand())); resp.forEach((row,i)=>{ const sum = d3.sum(row); row.forEach((_,i)=>{row[i]/=sum;}) }); } let [nk, means, covars] = est_gauss_params(X,resp); let weights = nk.map(cnt=>cnt/N); stats.init = {means:means, covars:covars, ellps: covars.map(covar=>conv_covar_radiideg(covar)), resp:resp}; let lb = Number.NEGATIVE_INFINITY; let converged = false; let it = 0; stats.history = []; for(; it < gm_params.maxit; it++) { const prev_lb = lb; // E-step const probs = est_gauss_prob(X, means, covars); const wgt_probs = probs.map(prob=>d3.range(K).map(ki=>weights[ki]*prob[ki])); const wgt_prob_sums = wgt_probs.map(prob=>d3.sum(prob)); resp = wgt_probs.map((wp,ni)=>d3.range(K).map(ki=>wp[ki]/wgt_prob_sums[ni])); // M-step [nk, means, covars] = est_gauss_params(X,resp); weights = nk.map(cnt=>cnt/N); stats.history.push({probs:probs, wprobs:wgt_probs, means:means, covars:covars, ellps: covars.map(covar=>conv_covar_radiideg(covar)), resp:resp}); lb = d3.mean(wgt_prob_sums.map(sum=>Math.log(sum))); if(Math.abs(lb-prev_lb)<1e-4) { stats.history.push(stats.history.slice(-1)[0]); break; } } return stats; }38:T518,{ const rg_values = [ [1, 0.0], [0.9, 0.022878745280337582], [0.8, 0.04845500650402822], [0.7, 0.07745097999287161], [0.6, 0.11092437480817825], [0.5, 0.15051499783199068], [0.4, 0.19897000433601886], [0.3, 0.2614393726401688], [0.2, 0.34948500216800954], [0.1, 0.5], [0.01, 1.0]]; const svg = d3.create("svg").attr("width",0).attr("height",0); 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Gaussian Mixture","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":28,"value":"$33","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":548,"value":"viewof resample = Inputs.button(\"기여분 계산 예제데이터 재생성\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":380,"value":"$34","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":76,"value":"---\n## 알고리즘 개요\n1. 초기 기여분 설정(K-means결과 또는 랜덤생성) → 군집(정규분포) 형태 계산\n2. 다음과정을 가중확률분포가 크게 변하지 않을때까지 반복\n 1. E-step: 군집(정규분포)의 평균,분산 → 각점의 군집에 대한 기여분 계산\n 2. M-step: 이전 E-step에서 계산한 기여분 → 군집(정규분포) 평균,분산 계산\n\n## 알고리즘 동작 예시\n* 데이터셋: 시총상위49종목(+1하위종목)의 일가격변동 t-SNE 결과\n* 파라메터: 군집(정규분포)의 수(k)\n* 반복회차를 변경하면 해당 반복내에서 일어나는 알고리즘 동작을 시작화\n * 속빈 흰색테두리 점 = 데이터포인트\n * 색상을 포함한 그라데이션 음영지역 = 정규분포의 확률밀도 표현\n * 흰색 실선 = 기여분(0에 가까울수록 희미하고 1에 가까울수록 뚜렷함)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":146,"value":"viewof rerun = Inputs.button(\"다시계산\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":340,"value":"viewof gm_init_method = Inputs.select([\"k-means\",\"random-uniform\"], {label: \"초기화 방법\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":79,"value":"viewof gm_params = {\n const dim = {w:340*2,h:65};\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, dim.w, dim.h])\n .attr(\"width\", dim.w)\n .attr(\"height\", dim.h);\n \n const samples = [1,2,3,4,5,6,7,8,9,10,15,20];\n const slider_samples = d3_slider.sliderBottom().min(d3.min(samples)).max(d3.max(samples))\n .tickValues(samples).tickFormat(v=>v.toFixed(0))\n .value(3).step(1).width(dim.w-40).fill(\"black\").on(\"onchange\", () => svg.dispatch(\"input\"));\n const gsamples = svg.append(\"g\").attr(\"class\",\"kmeans-param-k\").attr(\"transform\",`translate(20,30)`);\n gsamples.call(slider_samples);\n gsamples.append(\"text\")\n .attr(\"text-anchor\",\"middle\").attr(\"dominant-baseline\",\"hanging\")\n .attr(\"x\",\"140\").attr(\"y\",-30).attr(\"dy\",4).text(\"군집의 수(k)\");\n \n return Object.defineProperty(\n svg.node(), \n \"value\", \n {get: () => ({k:slider_samples.value(), maxit:100})}\n );\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":84,"value":"$35","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":613,"value":"## 알고리즘의 강점과 약점\n\n* 강점\n * 여러 군집이 중첩 가능\n * 다중적 특성을 가진 데이터 탐색\n * 군집의 형태가 연관관계를 포함\n * 군집내에 점들이 독립적 혹은 선형\n* 약점\n * 적절한 k값 지정이 어려움(K-means와 동일)\n * k값을 변경해 나온 결과중 선택\n * 가능한 결과값의 조합이 폭발적으로 증가\n * 초기값에 따라 상이한 결과들이 많이 발생\n * k값 하나에 대해서도 초기값을 다수 바꿔가며 결과를 선택해야함\n * 안정된 결과를 위해 필요로 하는 데이터포인트의 양이 기하급수적 증가\n * 데이터의 발생이 구형(Sphere)이라는 한정적 가정\n * 저차원 측정데이터(오류가 한정된 범위내 일어나는)에만 유리\n * 차원축소등 데이터의 변형을 가한경우 이상치 탐지가 어려움\n * 비수치형(non-numeric) 데이터에 적용이 어렵다\n * 계산비용이 비싼 연산을 많이 사용하고 반복이 길다\n \n## 그럼에도 불구하고 학계의 사랑을 받는 이유\n * 다양한 클러스터링 알고리즘들의 통합 일반이론\n\n | Gaussian Mixture의 특수한 형태로 볼때 | 여전히 다른점\n :-: | :-: | :-:\nK-means | ∞크기를 갖는 완전한 구형으로 정규분포를 한정 | 최근접이 아닌 점들을 배제 불가\nMean shift | bandwidth크기를 갖는 완전한 구형으로 정규분포를 한정 | 군집할당의 방법이 상이\n \n * 전체적으로 갖춰져있는 수학적 이론기반 ⇒ 논문은 실활용보다 이론수학이 우선","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":643,"value":"---\n\n## 참고자료\n* 다변량 정규분포 위키: [Wikipedia - Multivariate normal distribution](https://en.wikipedia.org/wiki/Multivariate_normal_distribution)\n* 정규분포 복합체 위키: [Wikipedia - Mixture#Gaussian_mixture_model](https://en.wikipedia.org/wiki/Mixture_model#Gaussian_mixture_model)\n* sklearn GaussianMixture python 모듈: [sklearn.mixture.GaussianMixture](https://scikit-learn.org/stable/modules/generated/sklearn.mixture.GaussianMixture.html)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":662,"value":"---\n## 부연설명 동영상\n\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":5,"value":"---\n## Appendix","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"","database":"$undefined"},{"id":93,"value":"rawdata = await FileAttachment(\"krx_cap50_tsne_2d.csv\").csv({typed: \"auto\"})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"rawdata","database":"$undefined"},{"id":112,"value":"gm_result = {\n rerun;\n return gaussian_mixture(rawdata, gm_params); \n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":86,"value":"viewof anim_step_ms = Inputs.range([500,2000], {step:500,value:1000,label:\"anim 최소단위(ms)\"});","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"point_symbol = d3.symbol(d3.symbolCircle)","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":88,"value":"symbols = {\n const symbols = [\n d3.symbol(d3.symbolCross),\n d3.symbol(d3.symbolTriangle),\n d3.symbol(d3.symbolDiamond),\n d3.symbol(d3.symbolSquare),\n d3.symbol(d3.symbolStar),\n ];\n const colors = d3.schemeCategory10;\n return d3.merge(symbols.map(sym=>colors.map(color=>({s:sym,c:color}))));\n};","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":3,"value":"html``","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"d3_slider = require(\"d3-simple-slider\")","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":17,"value":"Gaussian = require('https://bundle.run/multivariate-gaussian@3.3.1')","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"sample_gaussian = new Gaussian({mu:[0,0],sigma:[[1,0.5],[0.5,1]]})","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":73,"value":"sample_gaussian.density([1, 0])","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":220,"value":"colors20 = {\n const original = ['#1f77b4', '#aec7e8', '#ff7f0e', '#ffbb78', '#2ca02c', '#98df8a', '#d62728', '#ff9896', '#9467bd', '#c5b0d5', '#8c564b', '#c49c94', '#e377c2', '#f7b6d2', '#7f7f7f', '#c7c7c7', '#bcbd22', '#dbdb8d', '#17becf', '#9edae5'];\n return original.filter((_,i)=>i%2==0).concat(original.filter((_,i)=>i%2==1));\n}","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":157,"value":"{\n const svg = d3.create(\"svg\")\n .attr(\"viewBox\", [0, 0, 200, 200])\n .attr(\"width\", 200)\n .attr(\"height\", 200);\n const radius = 80;\n const circle = svg.append(\"circle\").attr(\"cx\",0).attr(\"cy\",0).attr(\"r\",radius);\n circle.style(\"fill\",\"url(#radgrad0)\")\n circle.attr(\"transform\",`translate(${radius},${radius})`);\n const ellipse = svg.append(\"ellipse\").attr(\"cx\",0).attr(\"cy\",0).attr(\"rx\",radius*2).attr(\"ry\",radius/2).attr(\"fill\",\"url(#radgrad2)\"); 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