class: center, middle, inverse, title-slide .title[ # Dimension Reduction</br>Determining Dimension ] .author[ ### Anastasios Panagiotelis ] .institute[ ### University of Sydney ] --- <script type="text/x-mathjax-config"> MathJax.Hub.Config({ TeX: { Macros: { bA: "{\\mathbf{A}}", bC: "{\\mathbf{C}}", bv: "{\\mathbf{v}}", bw: "{\\mathbf{w}}", bx: "{\\mathbf{x}}", bX: "{\\mathbf{X}}", by: "{\\mathbf{y}}", bY: "{\\mathbf{Y}}", bw: "{\\mathbf{w}}", bW: "{\\mathbf{W}}", bK: "{\\mathbf{K}}", bz: "{\\mathbf{z}}", bU: "{\\mathbf{U}}", bS: "{\\mathbf{S}}", bff: "{\\mathbf{f}}", bD: "{\\mathbf{D}}", bL: "{\\mathbf{L}}", calL: "{\\mathcal{L}}", calM: "{\\mathcal{M}}", bbR: "{\\mathbb{R}}", bB: "{\\mathbf{B}}", bbb: "{\\mathbf{b}}", bLambda: "{\\boldsymbol{\\Lambda}}", bDelta: "{\\boldsymbol{\\Delta}}", bH: "{\\mathbf{H}}", bI: "{\\mathbf{I}}", biota: "{\\boldsymbol{\\iota}}", bN: "{\\mathbf{N}}", bQ: "{\\mathbf{Q}}" } } }); </script> #Outline - Spheres -- - Applications -- - Reference is Facco, E., d’Errico, M., Rodriguez, A., & Laio, A. (2017). Estimating the intrinsic dimension of datasets by a minimal neighborhood information. *Scientific reports*, **7(1)**, 1-8. --- class: center, middle, inverse # What is dimension --- # Lengths and volumes - Consider a 1-D 'ball'. -- - This is just a line. -- - What is the measure of a 1-D ball? -- + The measure is length and is `\(2r\)` where `\(r\)` is the radius. -- - What happens the the measure if we double radius of the 1-D ball? --- # In 2-D - Consider a 2-D 'ball'. -- - What is the measure of a 2-D ball? -- + The measure is area and is `\(\pi r^2\)` where `\(r\)` is the radius. -- - What happens the the measure if we double the radius of the 2-D ball? -- + Measure scaled up by `\(2^2=4\)`. --- # In 3-D - Consider a 3-D 'ball'. -- - What is the measure of a 3-D ball? -- + The measure is volume and is `\(\frac{4}{3}\pi r^3\)` where `\(r\)` is the radius. -- - What happens the the measure if we double the radius of the 3-D ball? -- + Measure scaled up by `\(2^3=8\)`. --- # Why does this matter? - Consider the nearest neighbour and second nearest neighbour of a point. -- - Consider a ball around the second nearest neighbor <img src="11Dimension_files/figure-html/unnamed-chunk-1-1.png" height="450" style="display: block; margin: auto;" /> --- # Why does this matter? - Consider the nearest neighbour and second nearest neighbour of a point. - Consider a ball around the second nearest neighbor <img src="11Dimension_files/figure-html/unnamed-chunk-2-1.png" height="450" style="display: block; margin: auto;" /> --- # Questions - In the previous example, the ratio of the distance to the second nearest neighbour to distance to the nearest neighbour is 2. -- - What is the probability that this ratio is greater than 2? -- - To answer calculate area of inner circle and divide by outer circle. -- - It is 0.25. -- - How would your answer change if it was a 3D ball? --- # Determine dimension - For each point find the ratio of the second nearest neighbour to the nearest neighbour (denoted `\(\mu\)`) - These follow a Pareto(1,d) distribution. The MLE is given by `$$\hat{d}=\frac{n-1}{\sum\limits_{i=1}^{n} log \mu_i}$$` --- # Code ```r data<-loadDataSet("Swiss Roll") dd<-as.matrix(dist(data@data)) dr<-apply(dd,2,sort) mu<-dr[3,]/dr[2,] dhat<-(length(mu)-1)/sum(log(mu)) dhat ``` ``` ## [1] 2.134324 ``` --- #Helix <div id="rgl75515" style="width:504px;height:504px;" class="rglWebGL html-widget"></div> <script type="application/json" 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6yPkv/b7/eEo1Bn3psP0sZ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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n\nvoid main(void) {\n \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG)\n vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n \n#ifndef FIXED_QUADS\n gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n \n#ifdef IS_POINTS\n gl_PointSize = POINTSIZE;\n#endif\n \n vCol = aCol;\n \n#ifdef NEEDS_VNORMAL\n vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n /* normz should be calculated *after* projection */\n normz = (invPrMatrix*vNormal).z;\n#else\n vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n \n#ifdef NEEDS_VNORMAL\n vNormal = vec4(normalize(vNormal.xyz/vNormal.w), 1);\n#endif\n \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n vTexcoord = aTexcoord;\n#endif\n \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n pos = pos/pos.w;\n gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n vec4 pos = mvMatrix * vec4(aPos, 1.);\n pos = pos/pos.w + vec4(aOfs, 0.);\n gl_Position = prMatrix*pos;\n#endif\n \n#ifdef FAT_LINES\n /* This code was inspired by Matt Deslauriers' code in \n https://mattdesl.svbtle.com/drawing-lines-is-hard */\n vec2 aspectVec = vec2(uAspect, 1.0);\n mat4 projViewModel = prMatrix * mvMatrix;\n vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n currentProjected = currentProjected/currentProjected.w;\n vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n vec2 currentScreen = currentProjected.xy * aspectVec;\n vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n float len = uLwd;\n vec2 dir = vec2(1.0, 0.0);\n vPoint = aPoint;\n vLength = length(nextScreen - currentScreen)/2.0;\n vLength = vLength/(vLength 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ZUEC86YdBy0EWQEqB5L2oUD1BXnMDP5Y5ckB9KYNBuckMQKahUr9xN7RB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\nAP/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FP/nwAA/wAAVv8AAO//AAA//wAA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\nO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2 1\n// File 1 is the vertex shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\n\nattribute vec3 aPos;\nattribute vec4 aCol;\nuniform mat4 mvMatrix;\nuniform mat4 prMatrix;\nvarying vec4 vCol;\nvarying vec4 vPosition;\n\n#ifdef NEEDS_VNORMAL\nattribute vec3 aNorm;\nuniform mat4 normMatrix;\nvarying vec4 vNormal;\n#endif\n\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nattribute vec2 aTexcoord;\nvarying vec2 vTexcoord;\n#endif\n\n#ifdef FIXED_SIZE\nuniform vec3 textScale;\n#endif\n\n#ifdef FIXED_QUADS\nattribute vec3 aOfs;\n#endif\n\n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\nvarying float normz;\nuniform mat4 invPrMatrix;\n#else\nattribute vec3 aPos1;\nattribute vec3 aPos2;\nvarying float normz;\n#endif\n#endif // IS_TWOSIDED\n\n#ifdef FAT_LINES\nattribute vec3 aNext;\nattribute vec2 aPoint;\nvarying vec2 vPoint;\nvarying float vLength;\nuniform float uAspect;\nuniform float uLwd;\n#endif\n\n\nvoid main(void) {\n \n#ifndef IS_BRUSH\n#if defined(NCLIPPLANES) || !defined(FIXED_QUADS) || defined(HAS_FOG)\n vPosition = mvMatrix * vec4(aPos, 1.);\n#endif\n \n#ifndef FIXED_QUADS\n gl_Position = prMatrix * vPosition;\n#endif\n#endif // !IS_BRUSH\n \n#ifdef IS_POINTS\n gl_PointSize = POINTSIZE;\n#endif\n \n vCol = aCol;\n \n#ifdef NEEDS_VNORMAL\n vNormal = normMatrix * vec4(-aNorm, dot(aNorm, aPos));\n#endif\n \n#ifdef IS_TWOSIDED\n#ifdef HAS_NORMALS\n /* normz should be calculated *after* projection */\n normz = (invPrMatrix*vNormal).z;\n#else\n vec4 pos1 = prMatrix*(mvMatrix*vec4(aPos1, 1.));\n pos1 = pos1/pos1.w - gl_Position/gl_Position.w;\n vec4 pos2 = prMatrix*(mvMatrix*vec4(aPos2, 1.));\n pos2 = pos2/pos2.w - gl_Position/gl_Position.w;\n normz = pos1.x*pos2.y - pos1.y*pos2.x;\n#endif\n#endif // IS_TWOSIDED\n \n#ifdef NEEDS_VNORMAL\n vNormal = vec4(normalize(vNormal.xyz/vNormal.w), 1);\n#endif\n \n#if defined(HAS_TEXTURE) || defined(IS_TEXT)\n vTexcoord = aTexcoord;\n#endif\n \n#if defined(FIXED_SIZE) && !defined(ROTATING)\n vec4 pos = prMatrix * mvMatrix * vec4(aPos, 1.);\n pos = pos/pos.w;\n gl_Position = pos + vec4(aOfs*textScale, 0.);\n#endif\n \n#if defined(IS_SPRITES) && !defined(FIXED_SIZE)\n vec4 pos = mvMatrix * vec4(aPos, 1.);\n pos = pos/pos.w + vec4(aOfs, 0.);\n gl_Position = prMatrix*pos;\n#endif\n \n#ifdef FAT_LINES\n /* This code was inspired by Matt Deslauriers' code in \n https://mattdesl.svbtle.com/drawing-lines-is-hard */\n vec2 aspectVec = vec2(uAspect, 1.0);\n mat4 projViewModel = prMatrix * mvMatrix;\n vec4 currentProjected = projViewModel * vec4(aPos, 1.0);\n currentProjected = currentProjected/currentProjected.w;\n vec4 nextProjected = projViewModel * vec4(aNext, 1.0);\n vec2 currentScreen = currentProjected.xy * aspectVec;\n vec2 nextScreen = (nextProjected.xy / nextProjected.w) * aspectVec;\n float len = uLwd;\n vec2 dir = vec2(1.0, 0.0);\n vPoint = aPoint;\n vLength = length(nextScreen - currentScreen)/2.0;\n vLength = vLength/(vLength + len);\n if (vLength > 0.0) {\n dir = normalize(nextScreen - currentScreen);\n }\n vec2 normal = vec2(-dir.y, dir.x);\n dir.x /= uAspect;\n normal.x /= uAspect;\n vec4 offset = vec4(len*(normal*aPoint.x*aPoint.y - dir), 0.0, 0.0);\n gl_Position = currentProjected + offset;\n#endif\n \n#ifdef IS_BRUSH\n gl_Position = vec4(aPos, 1.);\n#endif\n}","fragmentShader":"#line 2 2\n// File 2 is the fragment shader\n#ifdef GL_ES\n#ifdef GL_FRAGMENT_PRECISION_HIGH\nprecision highp float;\n#else\nprecision mediump float;\n#endif\n#endif\nvarying vec4 vCol; // carries alpha\nvarying vec4 vPosition;\n#if defined(HAS_TEXTURE) || defined (IS_TEXT)\nvarying vec2 vTexcoord;\nuniform sampler2D uSampler;\n#endif\n\n#ifdef HAS_FOG\nuniform int uFogMode;\nuniform vec3 uFogColor;\nuniform vec4 uFogParms;\n#endif\n\n#if defined(IS_LIT) && !defined(FIXED_QUADS)\nvarying vec4 vNormal;\n#endif\n\n#if NCLIPPLANES > 0\nuniform vec4 vClipplane[NCLIPPLANES];\n#endif\n\n#if NLIGHTS > 0\nuniform mat4 mvMatrix;\n#endif\n\n#ifdef IS_LIT\nuniform vec3 emission;\nuniform float shininess;\n#if NLIGHTS > 0\nuniform vec3 ambient[NLIGHTS];\nuniform vec3 specular[NLIGHTS]; // light*material\nuniform vec3 diffuse[NLIGHTS];\nuniform vec3 lightDir[NLIGHTS];\nuniform bool viewpoint[NLIGHTS];\nuniform bool finite[NLIGHTS];\n#endif\n#endif // IS_LIT\n\n#ifdef IS_TWOSIDED\nuniform bool front;\nvarying float normz;\n#endif\n\n#ifdef FAT_LINES\nvarying vec2 vPoint;\nvarying float vLength;\n#endif\n\nvoid main(void) {\n vec4 fragColor;\n#ifdef FAT_LINES\n vec2 point = vPoint;\n bool neg = point.y < 0.0;\n point.y = neg ? (point.y + vLength)/(1.0 - vLength) :\n -(point.y - vLength)/(1.0 - vLength);\n#if defined(IS_TRANSPARENT) && defined(IS_LINESTRIP)\n if (neg && length(point) <= 1.0) discard;\n#endif\n point.y = min(point.y, 0.0);\n if (length(point) > 1.0) discard;\n#endif // FAT_LINES\n \n#ifdef ROUND_POINTS\n vec2 coord = gl_PointCoord - vec2(0.5);\n if (length(coord) > 0.5) discard;\n#endif\n \n#if NCLIPPLANES > 0\n for (int i = 0; i < NCLIPPLANES; i++)\n if (dot(vPosition, vClipplane[i]) < 0.0) discard;\n#endif\n \n#ifdef FIXED_QUADS\n vec3 n = vec3(0., 0., 1.);\n#elif defined(IS_LIT)\n vec3 n = normalize(vNormal.xyz);\n#endif\n \n#ifdef IS_TWOSIDED\n if ((normz <= 0.) != front) discard;\n#endif\n \n#ifdef IS_LIT\n vec3 eye = normalize(-vPosition.xyz/vPosition.w);\n vec3 lightdir;\n vec4 colDiff;\n vec3 halfVec;\n vec4 lighteffect = vec4(emission, 0.);\n vec3 col;\n float nDotL;\n#ifdef FIXED_QUADS\n n = -faceforward(n, n, eye);\n#endif\n \n#if NLIGHTS > 0\n for (int i=0;i<NLIGHTS;i++) {\n colDiff = vec4(vCol.rgb * diffuse[i], vCol.a);\n lightdir = lightDir[i];\n if (!viewpoint[i])\n lightdir = (mvMatrix * vec4(lightdir, 1.)).xyz;\n if (!finite[i]) {\n halfVec = normalize(lightdir + eye);\n } else {\n lightdir = normalize(lightdir - vPosition.xyz/vPosition.w);\n halfVec = normalize(lightdir + eye);\n }\n col = ambient[i];\n nDotL = dot(n, lightdir);\n col = col + max(nDotL, 0.) * colDiff.rgb;\n col = col + pow(max(dot(halfVec, n), 0.), shininess) * specular[i];\n lighteffect = lighteffect + vec4(col, colDiff.a);\n }\n#endif\n \n#else // not IS_LIT\n vec4 colDiff = vCol;\n vec4 lighteffect = colDiff;\n#endif\n \n#ifdef IS_TEXT\n vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n \n#ifdef HAS_TEXTURE\n#ifdef TEXTURE_rgb\n vec4 textureColor = lighteffect*vec4(texture2D(uSampler, vTexcoord).rgb, 1.);\n#endif\n \n#ifdef TEXTURE_rgba\n vec4 textureColor = lighteffect*texture2D(uSampler, vTexcoord);\n#endif\n \n#ifdef TEXTURE_alpha\n vec4 textureColor = texture2D(uSampler, vTexcoord);\n float luminance = dot(vec3(1.,1.,1.), textureColor.rgb)/3.;\n textureColor = vec4(lighteffect.rgb, lighteffect.a*luminance);\n#endif\n \n#ifdef TEXTURE_luminance\n vec4 textureColor = vec4(lighteffect.rgb*dot(texture2D(uSampler, vTexcoord).rgb, vec3(1.,1.,1.))/3., lighteffect.a);\n#endif\n \n#ifdef TEXTURE_luminance_alpha\n vec4 textureColor = texture2D(uSampler, vTexcoord);\n float luminance = dot(vec3(1.,1.,1.),textureColor.rgb)/3.;\n textureColor = vec4(lighteffect.rgb*luminance, lighteffect.a*textureColor.a);\n#endif\n \n fragColor = textureColor;\n\n#elif defined(IS_TEXT)\n if (textureColor.a < 0.1)\n discard;\n else\n fragColor = textureColor;\n#else\n fragColor = lighteffect;\n#endif // HAS_TEXTURE\n \n#ifdef HAS_FOG\n // uFogParms elements: x = near, y = far, z = fogscale, w = (1-sin(FOV/2))/(1+sin(FOV/2))\n // In Exp and Exp2: use density = density/far\n // fogF will be the proportion of fog\n // Initialize it to the linear value\n float fogF;\n if (uFogMode > 0) {\n fogF = (uFogParms.y - vPosition.z/vPosition.w)/(uFogParms.y - uFogParms.x);\n if (uFogMode > 1)\n fogF = mix(uFogParms.w, 1.0, fogF);\n fogF = fogF*uFogParms.z;\n if (uFogMode == 2)\n fogF = 1.0 - exp(-fogF);\n // Docs are wrong: use (density*c)^2, not density*c^2\n // https://gitlab.freedesktop.org/mesa/mesa/-/blob/master/src/mesa/swrast/s_fog.c#L58\n else if (uFogMode == 3)\n fogF = 1.0 - exp(-fogF*fogF);\n fogF = clamp(fogF, 0.0, 1.0);\n gl_FragColor = vec4(mix(fragColor.rgb, uFogColor, fogF), fragColor.a);\n } else gl_FragColor = fragColor;\n#else\n gl_FragColor = fragColor;\n#endif // HAS_FOG\n \n}","players":[],"webGLoptions":{"preserveDrawingBuffer":true}},"evals":[],"jsHooks":[]}</script> --- # Code ```r dd<-as.matrix(dist(data@data)) dr<-apply(dd,2,sort) mu<-dr[3,]/dr[2,] dhat<-(length(mu)-1)/sum(log(mu)) dhat ``` ``` ## [1] 3.012847 ``` --- # Conclusions - The intrinsic dimension can be estimated using nothing more than nearest neighbour information. -- - Can be generalised to include more than 2 NN -- - Good idea to trim large values of the ratio of NN. -- - Method is not robust if too much noise is added.