class: center, middle, inverse, title-slide .title[ # Dimension Reduction</br>Isomap ] .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 - Geodesics -- + Approximation using NN graph -- - Isomap algorithm -- - Applications -- - Initially proposed in J. B. Tenenbaum, V. de Silva, J. C. Langford, (2000), "A Global Geometric Framework for Nonlinear Dimensionality Reduction", *Science* **290**, pp. 2319–2323. --- class: center, middle, inverse # Isomap --- # Idea - Recall MDS takes distances as inputs. -- - These are typically Euclidean -- - If non-Euclidean distances are used as inputs, then the output still represents these distances quite accurately. -- - ISOMAP uses geodesic distances along the manifold as inputs. --- # Toy example Consider the following data <img src="07Isomap_files/figure-html/unnamed-chunk-1-1.png" height="450" style="display: block; margin: auto;" /> --- # Manifold Lying on a manifold. <img src="07Isomap_files/figure-html/unnamed-chunk-2-1.png" height="450" style="display: block; margin: auto;" /> --- # Euclidean distance Blue points close in ambient space. <img src="07Isomap_files/figure-html/unnamed-chunk-3-1.png" height="450" style="display: block; margin: auto;" /> --- # Geodesic Distance But not on manifold. <img src="07Isomap_files/figure-html/unnamed-chunk-4-1.png" height="450" style="display: block; margin: auto;" /> --- # Input distances - Classical MDS would use the distance in blue as an input -- - The idea behind Isomap is to use the distance in green as an input. -- - However to compute the geodesic (green) distance we need to know the manifold. -- - Instead we approximate the geodesic distance --- # Geodesic Distance Geodesic can be approximated. <img src="07Isomap_files/figure-html/unnamed-chunk-5-1.png" height="450" style="display: block; margin: auto;" /> --- # Geodesic Distance Try zooming. <div id="htmlwidget-80771b55bc8811ae9dcd" style="width:100%;height:450px;" class="widgetframe html-widget"></div> <script type="application/json" data-for="htmlwidget-80771b55bc8811ae9dcd">{"x":{"url":"07Isomap_files/figure-html//widgets/widget_unnamed-chunk-6.html","options":{"xdomain":"*","allowfullscreen":false,"lazyload":false}},"evals":[],"jsHooks":[]}</script> --- class: center, middle, inverse # Algorithm --- # Step 1: Nearest Neighbours - Find the neighbourhood graph -- + Neighbourhood within a ball `\(\epsilon\)`-Isomap + Neearest neighbours `\(K\)`-Isomap -- - As edge weights use the Euclidean distance between points --- # Example <img src="07Isomap_files/figure-html/unnamed-chunk-7-1.png" height="450" style="display: block; margin: auto;" /> --- # Graph <img src="07Isomap_files/figure-html/unnamed-chunk-8-1.png" height="450" style="display: block; margin: auto;" /> --- # Step 2: Shortest Path - Find shortest path on graph, between every pair of points. -- - Algorithms to do this -- + Dijkstra's method + Floyd- Warshall algorithm + and more... -- - Let's look at a simple example for one pair --- # Path from 8 to 10 <img src="07Isomap_files/figure-html/unnamed-chunk-9-1.png" height="450" style="display: block; margin: auto;" /> --- # Shortest path <img src="07Isomap_files/figure-html/unnamed-chunk-10-1.png" height="450" style="display: block; margin: auto;" /> --- # On original plot <img src="07Isomap_files/figure-html/unnamed-chunk-11-1.png" height="450" style="display: block; margin: auto;" /> --- # On original plot <img src="07Isomap_files/figure-html/unnamed-chunk-12-1.png" height="450" style="display: block; margin: auto;" /> --- # Approximation - The approximate geodesic distance is given by the sum of the edge weights along the shortest path. -- - The quality of this approximation depends on + Size of `\(\epsilon\)` or `\(K\)` + The density of points `\(\alpha\)` + Curvature of manifold + Dimension of ambient space + Connectedness of graph --- # More precisely For arbitrarily small `\(\lambda_1\)`, `\(\lambda_2\)` and `\(\mu\)`, with probability `\(1-\mu\)` `$$\delta_\calM(\bx_i,\bx_j)(1-\lambda_1)\leq\hat{\delta}_\calM(\bx_i,\bx_j)\\\leq\delta_\calM(\bx_i,\bx_j)(1+\lambda_2)$$` if some conditions hold for `\(\epsilon\)` (or `\(K\)`) and the density `\(\alpha\)` of points on the manifold. --- # Step 3: MDS - Carry out classical MDS however... -- - Use the approximate geodesic distances as inputs -- - Notes on MDS for more details. --- class: center, middle, inverse # Application --- # S Curve ```r dat <- loadDataSet("3D S Curve") plot(dat,type='3varsrgl') ``` <div id="rgl56108" style="width:504px;height:504px;" class="rglWebGL html-widget"></div> <script type="application/json" 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A9PXs6Pyey/T7NSt++l2wtPoWEJD6yOPa85Lc1P1qh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mc/6vuU8oz8NBe0/QzR8PwT4tD9Rpoc/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\n9j+LYCi/I/dRPxoh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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> --- # MDS ```r mdsout <- embed(dat, "MDS") plot(mdsout, type = "2vars") ``` <img src="07Isomap_files/figure-html/unnamed-chunk-15-1.png" height="450" style="display: block; margin: auto;" /> --- # Isomap (K=20) ```r isoout <- embed(dat, "Isomap", knn = 20) plot(isoout, type = "2vars") ``` <img src="07Isomap_files/figure-html/unnamed-chunk-16-1.png" height="450" style="display: block; margin: auto;" /> --- # Isomap (K=4) ```r isoout <- embed(dat, "Isomap", knn = 4) plot(isoout, type = "2vars") ``` <img src="07Isomap_files/figure-html/unnamed-chunk-17-1.png" height="450" style="display: block; margin: auto;" /> --- # Isomap (K=500) ```r isoout <- embed(dat, "Isomap", knn = 500) plot(isoout, type = "2vars") ``` <img src="07Isomap_files/figure-html/unnamed-chunk-18-1.png" height="450" style="display: block; margin: auto;" /> --- # Pros and Cons - Advantages + Exploits geometry + Global in the sense that all pairwise geodesic distances are used. -- - Disadvantages + Floyd Warshall algorithm is `\(O(n^3)\)` + Eigendecomposition for MDS is `\(O(n^3)\)` + Not clear how to pick `\(K\)` or `\(\epsilon\)` --- class: center, middle, inverse #Questions?