class: center, middle, inverse, title-slide .title[ # Dimension Reduction</br>Laplacian Eigenmaps ] .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 - Laplace-Beltrami Operator -- + Heat Equation -- - Graph Approximation -- + Algorithm -- - Applications -- - Reference is Belkin, M., & Niyogi, P. (2001). "Laplacian eigenmaps and spectral techniques for embedding and clustering. ", *NeurIPS*, **14**. --- class: center, middle, inverse # Some Physics --- # Motivation - In manifold learning we find functions `\(f:\calM\rightarrow\bbR^d\)` -- - For simplicity consider `\(d=1\)` (for now). -- - As a useful analogy think of the output dimension as representing "heat". -- - "Hot" points on the manifold should be close to other "hot" points and "cold" points should be close to other "cold" points. --- # A simplification - Suppose the manifold is just `\([0,1]\)`. -- - The physical interpretation is an idealised 1-D rod. -- - The function `\(f\)` indicates which part of the rod is hotter --- # A plot <img src="09LapEig_files/figure-html/unnamed-chunk-1-1.png" height="450" style="display: block; margin: auto;" /> --- # Heat diffusion - For a "good" function, how are the following quantities relevant? -- - The value of the first derivative. - The value of the second derivative. -- - On average, first derivative should be small in magnitude. -- - The value of the second derivative is connected to the idea of 'neighbourhood average'. --- # Extension - Consider `\(m\)`-dimensional Euclidean space as a manifold? -- - In this case an infintesimal change in the function is given by -- `$$df=\frac{\partial f}{\partial x_1}dx_1+\frac{\partial f}{\partial x_2}dx_2+\dots+\frac{\partial f}{\partial x_m}dx_m$$` -- - Vector of first partial derivatives should be "small" i.e. have a small norm on average. --- # Second derivative - Also of interest is the Laplacian -- `$$\frac{\partial^2 f}{\partial x^2_1}+\frac{\partial^2 f}{\partial x^2_2}+\dots+\frac{\partial^2 f}{\partial x^2_m}$$` -- - A local average of the function around any point `\(x\)` can be approximated in a way that depends on the Laplacian. -- - The Laplacian indicates whether points in the neigbourhood of `\(x\)` are "hotter" or "colder" than `\(x\)`. --- # Manifolds - Instead of Euclidean space we have a manifold -- + Imagine heat on a curved piece of metal with hot and cold regions. -- - Must define analogues to -- + The gradient + The Laplacian -- - Need to abstract from a specific coordinate system. --- # Gradient The gradient of `\(f\)`, denoted `\(\nabla f\)` where `\(f:\calM\rightarrow\bbR\)` is a vector field such that -- `$$df=g_\bx(\nabla f,d\bv)$$` where `\(g_\bx(.,.)\)` is the Riemannian (an inner product on the tangent space at `\(x\)`) and `\(d\bv\)` is an infintessimal tangent vector. --- # Laplace Beltrami Operator - The Laplace Beltrami operator is defined as -- `$$\Delta f=\nabla \cdot \nabla f$$` -- - It is a linear operator (maps functions to functions). -- - It is the Laplacian generalised for manifolds. -- - The local average of points around `\(x\)` depends on the value of `\(\Delta f\)` at `\(x\)` --- # Criterion - Why is this relevant for manifold learning? -- - The term `\(\int\limits_\calM ||\nabla f||^2\)` measures the average wiggliness of `\(f\)` on the manifold. -- - If nearby points on the input space are mapped to nearby points nearby on the output space this will be small. -- - This is a good criterion for a manifold learning. --- # Laplace Beltrami Operator - Why are second derivatives needed? -- - By Stokes' theorem `$$-\int\limits_\calM \Delta (f)f=\int\limits_\calM ||\nabla f||^2$$` -- - There is a bit of hand-waving here but the idea is to use a generalisation of integration by parts (and the product rule) on manifolds. --- class: inverse, middle, center #Discretisation --- # Solution - To solve this need to discretise the problem -- + Functions become vectors (function evaluated at each point of data) + Integrals become sums (over data points) + Operators become matrices -- - Laplacian Eigenmaps uses a discrete approximation for the Laplace Beltrami operator --- #Another Eigenvalue problem - Let `\(\bff\)` is a `\(n\)`-vector of the function evaluated at each input point `\(\bff=\left(f(\bx_1),\dots,f(\bx_n)\right)\)` -- - Let `\(\bD^{-1}\bL\)` is a `\(n\times n\)` matrix that approximates the Laplace Beltrami operator -- - Discrete approximation `$$-\int\limits_\calM \Delta (f)f\approx\bff'\bD^{-1}\bL\bff$$` -- - Minimised by solving `\(\bD^{-1}\bL\bff=\lambda\bff\)` --- # Roadmap - How to find `\(\bD\)` and `\(\bL\)`? -- - Exploit connection between Laplace Beltrami operator and heat equation. -- - Do lots of algebra. -- - Do a few approximations along the way. --- # The heat equation - Let `\(u(\bx_i,t)\)` be the heat at a point `\(\bx_i\in\calM\)` at time `\(t\)`. Also let `\(f\)` denote the initial heat distribution `\(f(\bx_i)=u(\bx_i,0)\)`. -- - Heat diffusion is described by the following differential equation -- `$$\Delta u = \frac{\partial}{\partial t}u$$` --- # Fundamental solution - An approximate solution is given by -- `$$u(\bx_i,t)\approx(4\pi t)^{-\frac{d}{2}}\int\limits_{\calM}e^{\frac{||\bx_i-\bz||^2}{4t}}f(\bz)d\bz$$` - Putting back into heat equation at `\(t=0\)` gives -- `$$\Delta f(\bx_i)\approx\frac{\partial}{\partial t}\left[(4\pi t)^{-\frac{d}{2}}\int\limits_{\calM}e^{\frac{||\bx_i-\bz||^2}{4t}}f(\bz)d\bz\right]_{t=0}$$` --- # Continuing - By the definition of a derivative -- `$$\Delta f(\bx_i)\approx\underset{t\rightarrow 0}{\lim}\frac{A(t)-A(0)}{t}$$` -- - Where `$$A(t)=(4\pi t)^{-\frac{d}{2}}\int\limits_{\calM}e^{\frac{||\bx_i-\bz||^2}{4t}}f(\bz)d\bz$$` -- - Note `\(A(0)=f(\bx_i)\)` --- # And more - Rearranging `$$-\Delta f(\bx_i)\approx\underset{t\rightarrow 0}{\lim}\frac{1}{t}\left[f(\bx_i)-A(t)\right]$$` where `$$A(t)=(4\pi t)^{-\frac{d}{2}}\int\limits_{\calM}e^{\frac{||\bx_i-\bz||^2}{4t}}f(\bz)d\bz$$` --- # Integral - Can use approximation `$$A(t)=\alpha\sum\limits_{\bx_j\in N(\bx_i)}w_{ij}f(\bx_j)$$` - where `\(w_{ij}=\begin{cases}e^{\frac{||\bx_i-\bx_j||^2}{4t}}\text{ if }\bx_i \text{ and }\bx_j\text{ neighbours}\\0\text{ otherwise}\end{cases}\)` -- - and `\(\alpha=k^{-1}(4\pi t)^{-\frac{d}{2}}\)` -- - Think of this like a Monte Carlo estimate. --- # Optimisation - Putting together `$$-\Delta f(\bx_i)\overset{\propto}{\sim}f(\bx_i)-\alpha\sum\limits_{\bx_j\in N(\bx_i)}w_{ij}f(\bx_j)$$` -- - Aim is to minimise above expression, so multiplying by a constant can be ignored. -- - How can this be written as matrices and vectors? --- # Matrices - The adjacency matrix `\(\bA\)` has element `\(w_{ij}\)` on row `\(i\)` and column `\(j\)`. -- - The degree matrix `\(\bD\)` is diagonal with `\(\sum_jw_{ij}\)` on row `\(i\)` and column `\(i\)`. -- - The graph Laplacian for a weighted graph is given by `\(\bL=\bD-\bA\)`. -- - The matrix to be considered is `\(\bD^{-1}\bL\)`. -- Why? --- # Row `\(i\)` - Consider row `\(i\)` of `\(\bD^{-1}\bL\bff\)` -- `$$\begin{bmatrix}\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\\vdots&w_{ij_1}&\dots&\sum_jw_{ij}&\dots&w_{ij_2}&\vdots\\\vdots&\vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\\end{bmatrix}\begin{bmatrix}\vdots\\f(\bx_{j_1})\\\vdots\\f(\bx_i)\\\vdots\\\vdots\\f(\bx_{j_2})\end{bmatrix}$$` --- # In full - Row `\(i\)` evalutes to `$$\left[\sum_k w_{ik}\right]f(\bx_i)-\sum_j w_{ij}f(\bx_j)$$` -- - Premultiplying by `\(\bD^{-1}\)` is the same as dividing through by `\((\sum_k w_{ij})\)` yielding -- `$$f(\bx_i)-\frac{1}{\sum_k w_{ik}}\sum_j w_{ij}f(\bx_j)$$` --- # One last trick - From earlier -- `$$-\Delta f(\bx_i)\overset{\propto}{\sim}f(\bx_i)-\alpha\sum_j w_{ij}f(\bx_j)$$` -- - Need to show `\(\alpha=\frac{1}{\sum_k w_{ik}}\)` -- - Consider `\(f\)` is a constant function `\(f(\bx)=c\)` for all `\(\bx\)` --- # Constant Function - If `\(f\)` is a constant function, Laplace Beltrami operator should be zero. -- Why? -- - Therefore -- `$$-\Delta f(\bx_i)=c-\alpha\sum_j w_{ij}c=0$$` -- - Solving gives `\(\alpha=\frac{1}{\sum_j w_{ij}}\)` --- # The End - Putting everything together `\(\bD^{-1}\bL\bff\approx f(\bx_i)-\alpha\sum_j w_{ij}f(\bx_j)\overset{\propto}{\sim} -\Delta f(\bx_i)\)` - Minimising `\(-\int_\calM\Delta (f) f\)` is approximately the same as minimising `\(\bff'\bD^{-1}\bL\bff\)`. --- # The algorithm - Step 1: Find nearest neighbours graph. -- - Step 2: Find weighted Adjacency, Degree and Graph Laplacian matrices. -- - Step 3: Solve the generalised eigenvalue problem `\(\bL\bff=\lambda\bD\bff\)`. -- - Step 4: Discard eigenvector corresponding to the smallest eigenvalue (this will be a constant function). -- - Step 5: Keep eigenvectors corresponding to next `\(d\)` smallest eigenvectors as output. --- # Simplification - Limiting case as `\(t\rightarrow\infty\)` `$$w_{ij}=\begin{cases}1\text{ if }\bx_i \text{ and }\bx_j\text{ neighbours}\\0\text{ otherwise}\end{cases}$$` - Lose interpretation in terms of Laplace Beltrami operator -- - Still minimise (subject to `\(f(\bx_i)^2\sum_j w_{ij}=1\)`) `$$\sum_i\sum_j (f(\bx_i)-f(\bx_j))^2w_{ij}$$` --- class: middle, inverse, center #Implementation --- # Swiss Roll ```r datsr <- loadDataSet("Swiss Roll") plot(datsr,type='3varsrgl') ``` <div id="rgl28778" style="width:504px;height:504px;" class="rglWebGL html-widget"></div> <script type="application/json" 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uQK+l1kCbhd1ACO0nQSMQqEEC377Aw6SSQGlE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\nVkFTEztBF6egQb+Js0ApW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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> --- # Laplacian Eigenmaps (k=50) ```r leoutsr <- embed(datsr, "LaplacianEigenmaps") plot(leoutsr, type = "2vars") ``` <img src="09LapEig_files/figure-html/unnamed-chunk-4-1.png" height="450" style="display: block; margin: auto;" /> --- # Laplacian Eigenmaps (k=30) ```r leoutsr2 <- embed(datsr, "LaplacianEigenmaps",knn=30) plot(leoutsr2, type = "2vars") ``` <img src="09LapEig_files/figure-html/unnamed-chunk-5-1.png" height="450" style="display: block; margin: auto;" /> --- # Pros and Cons - Advantages + Fast due to exploitation of sparse eigenvalue algorithms + Elegant theoretical foundation -- - Disadvantages + Only captures local geometry + There are up to two tuning parameters to select.