{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Wasserstein non-negative matrix factorisation\n",
    "\n",
    "*You are seeing the\n",
    "notebook output generated by\n",
    "[Literate.jl](https://github.com/fredrikekre/Literate.jl) from the\n",
    "[Julia source file](https://github.com/JuliaOptimalTransport/OptimalTransport.jl/blob/master/examples/nmf/script.jl).\n",
    "The rendered HTML can be viewed [in the docs](https://juliaoptimaltransport.github.io/OptimalTransport.jl/dev/examples/nmf/).*"
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "In this example, we implement Wasserstein non-negative matrix factorisation (W-NMF)\n",
    "following the paper [^RCP16] by Rolet et al.\n",
    "\n",
    "[^RCP16]: Rolet, Antoine, Marco Cuturi, and Gabriel Peyré. [\"Fast dictionary learning with a smoothed Wasserstein loss.\"](https://marcocuturi.net/Papers/rolet16fast.pdf) Artificial Intelligence and Statistics. PMLR, 2016.\n",
    "\n",
    "## Introduction\n",
    "\n",
    "Matrix decomposition is a classical problem in machine learning. Given a $m \\times n$ matrix $X$ representing $n$ repeated $m$-dimensional observations, one may seek matrices $D, \\Lambda$ of appropriate dimensions such that\n",
    "$$\n",
    "X \\approx D \\Lambda.\n",
    "$$\n",
    "For a target rank $k < \\min \\{ m, n \\}$, i.e. $D \\in \\mathbb{R}^{m \\times k}, \\Lambda \\in \\mathbb{R}^{k \\times n}$, this problem can be thought of as seeking a low-dimensional linear representation $D \\Lambda$ of the potentially high-dimensional dataset $X$.\n",
    "\n",
    "Lee and Seung [^LS99] observed that the data matrix $X$ is non-negative in many practical applications, and that naturally one may want the factor matrices $D, \\Lambda$ to be also non-negative.\n",
    "\n",
    "[^LS99]: Lee, Daniel D., and H. Sebastian Seung. \"Learning the parts of objects by non-negative matrix factorization.\" Nature 401.6755 (1999): 788-791.\n",
    "\n",
    "For a given $m \\times n$ matrix $X \\ge 0$, finding the factor matrices $D \\in \\mathbb{R}^{m \\times k}, \\Lambda \\in \\mathbb{R}^{k \\times n}$ such that $X \\approx D \\Lambda$ with $D \\ge 0, \\Lambda \\ge 0$ is known as the rank-$k$ non-negative matrix factorization (NMF) problem. Typically, such an approximate representation is sought by solving a minimisation problem\n",
    "$$\n",
    "\\min_{D \\in \\mathbb{R}^{m \\times k}, \\Lambda \\in \\mathbb{R}^{k \\times n}, D \\ge 0, \\Lambda \\ge 0} \\Phi(X, D \\Lambda),\n",
    "$$\n",
    "where $(X, Y) \\mapsto \\Psi(X, Y)$ is a loss function defined on matrices. Commonly used choices of $\\Phi$ include the squared Frobenius loss $\\Phi(X, Y) = \\| X - Y \\|_F^2$ and Kullback-Leibler divergence $\\Phi(X, Y) = \\sum_{ij} X_{ij} \\log(X_{ij}/Y_{ij})$.\n",
    "\n",
    "Both these loss functions (and many other common choices) decompose elementwise in their arguments, that is, they can be written as $\\Phi(X, Y) = \\sum_{ij} f(X_{ij}, Y_{ij})$ for some function $f$ acting on scalars.\n",
    "\n",
    "Rolet et al. note that pointwise loss functions cannot account for spatial correlations in datasets with underlying geometry, and propose to use entropy-regularised optimal transport as a loss function that is sensitive to the spatial arrangement of the data.\n",
    "They argue that for datasets such as images, optimal transport is a more natural choice of loss function, and that it achieves superior performance.\n",
    "\n",
    "In particular, suppose that the columns of $X$ encode image data, and that $C \\in \\mathbb{R}^{m \\times m}$ encodes the squared Euclidean distances on the imaging domain. The problem that Rolet et al. pose is\n",
    "$$\n",
    "\\min_{D \\in \\mathbb{R}^{m \\times k}_{\\ge 0}, \\Lambda \\in \\mathbb{R}^{k \\times n}_{\\ge 0}} \\sum_{i = 1}^{n} \\operatorname{OT}_{\\varepsilon}(X_i, (D\\Lambda)_i) + \\rho_1 E(D) + \\rho_2 E(\\Lambda),\n",
    "$$\n",
    "where $\\operatorname{OT}_{\\varepsilon}(\\alpha, \\beta)$ is the entropy-regularised optimal transport loss between two probability distributions $\\alpha, \\beta$ for a cost $C$, and $E$ is an entropy barrier function (a smooth approximation to the non-negativity constraint),\n",
    "$$\n",
    "E(A) = \\sum_{ij} (A_{ij} \\log(A_{ij}) - 1).\n",
    "$$\n",
    "The parameters $\\rho_1, \\rho_2$ control how \"sharp\" the non-negativity constraints are. As $\\rho_1, \\rho_2 \\to 0$, the smoothed constraint approaches the hard non-negativity constraint. Finally, $\\varepsilon$ controls the regularisation level for the optimal transport loss.\n",
    "\n",
    "This example shows how this method can be implemented using functions from the `Dual` submodule of OptimalTransport.jl.\n",
    "\n",
    "## Set up prerequisites\n",
    "\n",
    "Load packages that will be required later."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "using OptimalTransport\n",
    "import OptimalTransport.Dual: Dual\n",
    "using MLDatasets: MLDatasets\n",
    "using StatsBase\n",
    "using Plots;\n",
    "default(; palette=:Set1_3)\n",
    "using LogExpFunctions\n",
    "using NNlib: NNlib\n",
    "using LinearAlgebra\n",
    "using Distances\n",
    "using Base.Iterators\n",
    "using NMF\n",
    "using Optim"
   ],
   "metadata": {},
   "execution_count": 1
  },
  {
   "cell_type": "markdown",
   "source": [
    "Define `simplex_norm!`, which normalises `x` to sum to `1` along `dims`."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "simplex_norm! (generic function with 1 method)"
     },
     "metadata": {},
     "execution_count": 2
    }
   ],
   "cell_type": "code",
   "source": [
    "function simplex_norm!(x; dims=1)\n",
    "    return x .= x ./ sum(x; dims=dims)\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 2
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Implementation\n",
    "\n",
    "We now implement Wasserstein-NMF. Rolet et al. split the original non-convex problem into a pair of convex problems, one for $D$ and one for $\\Lambda$.\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\min_{D \\in \\mathbb{R}^{m \\times k}} \\sum_{i = 1}^{n} \\operatorname{OT}_{\\varepsilon}(X_i, (D\\Lambda)_i) + \\rho_2 E(D), \\\\\n",
    "&\\min_{\\Lambda \\in \\mathbb{R}^{k \\times n}} \\sum_{i = 1}^{n} \\operatorname{OT}_{\\varepsilon}(X_i, (D\\Lambda)_i) + \\rho_1 E(\\Lambda).\n",
    "\\end{aligned}\n",
    "$$\n",
    "For each of these problems, the dual problem can be derived (see Section 3.3 of Rolet et al. for details on how this is done). These turn out to be\n",
    "$$\n",
    "\\begin{aligned}\n",
    "&\\min_{G \\in \\mathbb{R}^{m \\times n}} \\sum_{i = 1}^n \\operatorname{OT}_{\\varepsilon}^*(X_i, G_i) + \\rho_2 \\sum_{i = 1}^{n} E^*(-(G \\Lambda^\\top)_i / \\rho_2) \\\\\n",
    "&\\min_{G \\in \\mathbb{R}^{m \\times n}} \\sum_{i = 1}^n \\operatorname{OT}_{\\varepsilon}^*(X_i, G_i) + \\rho_1 \\sum_{i = 1}^{n} E^*(-(D^\\top G)_i / \\rho_1).\n",
    "\\end{aligned}\n",
    "$$\n",
    "The semi-dual of entropy-regularised optimal transport loss, $\\operatorname{OT}_{\\varepsilon}$, is implemented as `Dual.ot_entropic_semidual` and its gradient can be computed by `Dual.ot_entropic_semidual_grad`. $E^*$ turns out to be `logsumexp`, for which we implement a wrapper function:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function E_star(x; dims=1)\n",
    "    return logsumexp(x; dims=dims)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 3
  },
  {
   "cell_type": "markdown",
   "source": [
    "The gradient of `logsumexp` is `softmax`, so we define also its gradient:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function E_star_grad(x; dims=1)\n",
    "    return NNlib.softmax(x; dims=1)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 4
  },
  {
   "cell_type": "markdown",
   "source": [
    "Thus, for each problem we may define the dual objective and its gradient. We note that `ot_entropic_semidual(_grad)` automatically broadcasts along columns of its input. There is therefore no need to make multiple calls to the function, thus allowing for more efficient evaluation."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function dual_obj_weights(X, K, ε, D, G, ρ1)\n",
    "    return sum(Dual.ot_entropic_semidual(X, G, ε, K)) + ρ1 * sum(E_star(-D' * G / ρ1))\n",
    "end\n",
    "function dual_obj_weights_grad!(∇, X, K, ε, D, G, ρ1)\n",
    "    return ∇ .= Dual.ot_entropic_semidual_grad(X, G, ε, K) - D * E_star_grad(-D' * G / ρ1)\n",
    "end\n",
    "function dual_obj_dict(X, K, ε, Λ, G, ρ2)\n",
    "    return sum(Dual.ot_entropic_semidual(X, G, ε, K)) + ρ2 * sum(E_star(-G * Λ' / ρ2))\n",
    "end\n",
    "function dual_obj_dict_grad!(∇, X, K, ε, Λ, G, ρ2)\n",
    "    return ∇ .= Dual.ot_entropic_semidual_grad(X, G, ε, K) - E_star_grad(-G * Λ' / ρ2) * Λ\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 5
  },
  {
   "cell_type": "markdown",
   "source": [
    "The only remaining part of Wasserstein-NMF to implement is the conversion at optimality from the dual variable $G$ to the primal variables $D, \\Lambda$. From the results of Theorems 3 and 4 in Rolet et al., we have for $\\Lambda$:\n",
    "$$\n",
    "\\Lambda_i = \\operatorname{softmax}((-D^\\top G)_i / \\rho_1),\n",
    "$$\n",
    "and we have for $D$:\n",
    "$$\n",
    "D_i = \\operatorname{softmax}((-G \\Lambda^\\top)_i / \\rho_2).\n",
    "$$"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function getprimal_weights(D, G, ρ1)\n",
    "    return NNlib.softmax(-D' * G / ρ1; dims=1)\n",
    "end\n",
    "function getprimal_dict(Λ, G, ρ2)\n",
    "    return NNlib.softmax(-G * Λ' / ρ2; dims=1)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 6
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can now implement functions `solve_weights` and `solve_dict` that solve the respective dual problems for the next iterates of `Λ` and `D`."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "function solve_weights(X, K, ε, D, ρ1; alg, options)\n",
    "    opt = optimize(\n",
    "        g -> dual_obj_weights(X, K, ε, D, g, ρ1),\n",
    "        (∇, g) -> dual_obj_weights_grad!(∇, X, K, ε, D, g, ρ1),\n",
    "        zero.(X),\n",
    "        alg,\n",
    "        options,\n",
    "    )\n",
    "    return getprimal_weights(D, Optim.minimizer(opt), ρ1)\n",
    "end\n",
    "function solve_dict(X, K, ε, Λ, ρ2; alg, options)\n",
    "    opt = optimize(\n",
    "        g -> dual_obj_dict(X, K, ε, Λ, g, ρ2),\n",
    "        (∇, g) -> dual_obj_dict_grad!(∇, X, K, ε, Λ, g, ρ2),\n",
    "        zero.(X),\n",
    "        alg,\n",
    "        options,\n",
    "    )\n",
    "    return getprimal_dict(Λ, Optim.minimizer(opt), ρ2)\n",
    "end;"
   ],
   "metadata": {},
   "execution_count": 7
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Example: noisy univariate Gaussians\n",
    "\n",
    "We set up each observation as a mixture of 3 Gaussians with means sampled from `N(6, σ), N(0, σ), N(-6, σ)` respectively, and mixture weights sampled uniformly from `[0, 1]`. The resulting mixture model is normalised to sum to 1 on the discrete domain `coord`."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "f(x, μ, σ) = exp.(-(x .- μ) .^ 2)\n",
    "coord = range(-12, 12; length=100)\n",
    "N = 100\n",
    "σ = 1\n",
    "X = hcat(\n",
    "    [\n",
    "        rand() * f(coord, σ * randn() + 6, 1) +\n",
    "        rand() * f(coord, σ * randn(), 1) +\n",
    "        rand() * f(coord, σ * randn() - 6, 1) for _ in 1:N\n",
    "    ]...,\n",
    ")\n",
    "X = simplex_norm!(X);"
   ],
   "metadata": {},
   "execution_count": 8
  },
  {
   "cell_type": "markdown",
   "source": [
    "We visualise the  observations."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=100}",
      "image/png": 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       "</svg>\n"
      ]
     },
     "metadata": {},
     "execution_count": 9
    }
   ],
   "cell_type": "code",
   "source": [
    "plot(coord, X; alpha=0.1, color=:blue, title=\"Input data\", legend=nothing)"
   ],
   "metadata": {},
   "execution_count": 9
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can apply NMF with a squared Frobenius loss using the NMF.jl package. We seek `k = 3` components.  This performs poorly, since the pointwise nature of the loss function cannot handle the translational noise in the data."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=3}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "cell_type": "code",
   "source": [
    "k = 3\n",
    "result = nnmf(X, k; alg=:multmse)\n",
    "plot(coord, result.W; title=\"NMF with Frobenius loss\", palette=:Set1_3)"
   ],
   "metadata": {},
   "execution_count": 10
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can now set up a cost matrix corresponding to the domain `coord`."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "C = pairwise(SqEuclidean(), coord)\n",
    "C = C / mean(C);"
   ],
   "metadata": {},
   "execution_count": 11
  },
  {
   "cell_type": "markdown",
   "source": [
    "Specify parameters"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "ε = 0.025\n",
    "ρ1, ρ2 = (5e-2, 5e-2);"
   ],
   "metadata": {},
   "execution_count": 12
  },
  {
   "cell_type": "markdown",
   "source": [
    "Compute Gibbs kernel"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "K = exp.(-C / ε);"
   ],
   "metadata": {},
   "execution_count": 13
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we use a random initialisation, where columns of `D` and `Λ` are normalised to sum to 1."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "D = rand(size(X, 1), k) # dictionary\n",
    "simplex_norm!(D; dims=1) # norm columnwise\n",
    "Λ = rand(k, size(X, 2)) # weights\n",
    "simplex_norm!(Λ; dims=1); # norm rowwise"
   ],
   "metadata": {},
   "execution_count": 14
  },
  {
   "cell_type": "markdown",
   "source": [
    "We now run 10 iterations of Wasserstein-NMF."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ Info: Wasserstein-NMF: iteration 1\n",
      "[ Info: Wasserstein-NMF: iteration 2\n",
      "[ Info: Wasserstein-NMF: iteration 3\n",
      "[ Info: Wasserstein-NMF: iteration 4\n",
      "[ Info: Wasserstein-NMF: iteration 5\n",
      "[ Info: Wasserstein-NMF: iteration 6\n",
      "[ Info: Wasserstein-NMF: iteration 7\n",
      "[ Info: Wasserstein-NMF: iteration 8\n",
      "[ Info: Wasserstein-NMF: iteration 9\n",
      "[ Info: Wasserstein-NMF: iteration 10\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "n_iter = 10\n",
    "for iter in 1:n_iter\n",
    "    @info \"Wasserstein-NMF: iteration $iter\"\n",
    "    D .= solve_dict(\n",
    "        X,\n",
    "        K,\n",
    "        ε,\n",
    "        Λ,\n",
    "        ρ2;\n",
    "        alg=LBFGS(),\n",
    "        options=Optim.Options(;\n",
    "            iterations=250, g_tol=1e-4, show_trace=false, show_every=10\n",
    "        ),\n",
    "    )\n",
    "    Λ .= solve_weights(\n",
    "        X,\n",
    "        K,\n",
    "        ε,\n",
    "        D,\n",
    "        ρ1;\n",
    "        alg=LBFGS(),\n",
    "        options=Optim.Options(;\n",
    "            iterations=250, g_tol=1e-4, show_trace=false, show_every=10\n",
    "        ),\n",
    "    )\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 15
  },
  {
   "cell_type": "markdown",
   "source": [
    "We observe that Wasserstein-NMF learns atoms (columns of $D$) corresponding to the three Gaussians used to generate the input data."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=3}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 16
    }
   ],
   "cell_type": "code",
   "source": [
    "plot(coord, D; title=\"NMF with Wasserstein loss\", palette=:Set1_3)"
   ],
   "metadata": {},
   "execution_count": 16
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Example: image data (MNIST)\n",
    "Here we will download MNIST dataset using MLDatasets.jl and downscale each image to 14x14 to allow for faster runtime (since we are running on CPU)."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "┌ Warning: MNIST.traindata() is deprecated, use `MNIST(split=:train)[:]` instead.\n",
      "└ @ MLDatasets ~/.julia/packages/MLDatasets/0MkOE/src/datasets/vision/mnist.jl:187\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "sizex, sizey = 28, 28\n",
    "factor = 2 # downscale factor\n",
    "Σ = hcat([sum(I(sizex)[:, i:(i + factor - 1)]; dims=2) for i in 1:factor:sizex]...)\n",
    "sizex, sizey = sizex ÷ factor, sizey ÷ factor\n",
    "N = 256\n",
    "x, y = MLDatasets.MNIST.traindata(Float64, sample(1:60_000, N; replace=false))\n",
    "x = permutedims(x, (2, 1, 3))\n",
    "x = cat([Σ' * x[:, :, i] * Σ for i in 1:N]...; dims=3)\n",
    "X = simplex_norm!(reshape(x, (sizex * sizey, :)));"
   ],
   "metadata": {},
   "execution_count": 17
  },
  {
   "cell_type": "markdown",
   "source": [
    "The columns of `X` now correspond to images \"flattened\" as vectors. We can preview a few images."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=25}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "cell_type": "code",
   "source": [
    "M = 25\n",
    "plot(\n",
    "    [\n",
    "        heatmap(\n",
    "            reshape(X[:, i], sizex, sizey);\n",
    "            legend=:none,\n",
    "            axis=nothing,\n",
    "            showaxis=false,\n",
    "            aspect_ratio=:equal,\n",
    "            c=:Blues,\n",
    "            yflip=true,\n",
    "        ) for i in 1:M\n",
    "    ]...;\n",
    "    layout=(5, M ÷ 5),\n",
    "    plot_title=\"Input images\",\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 18
  },
  {
   "cell_type": "markdown",
   "source": [
    "Now we can set up `coord`, cost matrix `C`, and specify parameters."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "coord = reshape(collect(product(1:sizex, 1:sizey)), :)\n",
    "C = pairwise(SqEuclidean(), coord)\n",
    "C = C / mean(C);\n",
    "ε = 0.0025\n",
    "ρ1, ρ2 = (5e-3, 5e-3);"
   ],
   "metadata": {},
   "execution_count": 19
  },
  {
   "cell_type": "markdown",
   "source": [
    "We compute the Gibbs kernel from `C`:"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "K = exp.(-C / ε);"
   ],
   "metadata": {},
   "execution_count": 20
  },
  {
   "cell_type": "markdown",
   "source": [
    "Let us aim to learn `k = 25` atoms."
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "k = 25;"
   ],
   "metadata": {},
   "execution_count": 21
  },
  {
   "cell_type": "markdown",
   "source": [
    "Initialise again randomly"
   ],
   "metadata": {}
  },
  {
   "outputs": [],
   "cell_type": "code",
   "source": [
    "D = rand(size(X, 1), k) # dictionary\n",
    "simplex_norm!(D; dims=1) # norm columnwise\n",
    "Λ = rand(k, size(X, 2)) # weights\n",
    "simplex_norm!(Λ; dims=1); # norm rowwise"
   ],
   "metadata": {},
   "execution_count": 22
  },
  {
   "cell_type": "markdown",
   "source": [
    "We now run 15 iterations of Wasserstein-NMF."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ Info: Wasserstein-NMF: iteration 1\n",
      "[ Info: Wasserstein-NMF: iteration 2\n",
      "[ Info: Wasserstein-NMF: iteration 3\n",
      "[ Info: Wasserstein-NMF: iteration 4\n",
      "[ Info: Wasserstein-NMF: iteration 5\n",
      "[ Info: Wasserstein-NMF: iteration 6\n",
      "[ Info: Wasserstein-NMF: iteration 7\n",
      "[ Info: Wasserstein-NMF: iteration 8\n",
      "[ Info: Wasserstein-NMF: iteration 9\n",
      "[ Info: Wasserstein-NMF: iteration 10\n",
      "[ Info: Wasserstein-NMF: iteration 11\n",
      "[ Info: Wasserstein-NMF: iteration 12\n",
      "[ Info: Wasserstein-NMF: iteration 13\n",
      "[ Info: Wasserstein-NMF: iteration 14\n",
      "[ Info: Wasserstein-NMF: iteration 15\n"
     ]
    }
   ],
   "cell_type": "code",
   "source": [
    "n_iter = 15\n",
    "for iter in 1:n_iter\n",
    "    @info \"Wasserstein-NMF: iteration $iter\"\n",
    "    D .= solve_dict(\n",
    "        X,\n",
    "        K,\n",
    "        ε,\n",
    "        Λ,\n",
    "        ρ2;\n",
    "        alg=LBFGS(),\n",
    "        options=Optim.Options(;\n",
    "            iterations=250, g_tol=1e-4, show_trace=false, show_every=10\n",
    "        ),\n",
    "    )\n",
    "    Λ .= solve_weights(\n",
    "        X,\n",
    "        K,\n",
    "        ε,\n",
    "        D,\n",
    "        ρ1;\n",
    "        alg=LBFGS(),\n",
    "        options=Optim.Options(;\n",
    "            iterations=250, g_tol=1e-4, show_trace=false, show_every=10\n",
    "        ),\n",
    "    )\n",
    "end"
   ],
   "metadata": {},
   "execution_count": 23
  },
  {
   "cell_type": "markdown",
   "source": [
    "We can inspect the atoms learned (columns of `D`):"
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=25}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 24
    }
   ],
   "cell_type": "code",
   "source": [
    "plot(\n",
    "    [\n",
    "        heatmap(\n",
    "            reshape(D[:, i], sizex, sizey);\n",
    "            legend=:none,\n",
    "            axis=nothing,\n",
    "            showaxis=false,\n",
    "            aspect_ratio=:equal,\n",
    "            c=:Blues,\n",
    "            yflip=true,\n",
    "        ) for i in 1:k\n",
    "    ]...;\n",
    "    layout=(5, k ÷ 5),\n",
    "    plot_title=\"Learned atoms\",\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 24
  },
  {
   "cell_type": "markdown",
   "source": [
    "Finally, we can look at the images constructed by the low-rank approximation `DΛ` and compare to the original images that we previewed earlier."
   ],
   "metadata": {}
  },
  {
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "Plot{Plots.GRBackend() n=25}",
      "image/png": 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      ]
     },
     "metadata": {},
     "execution_count": 25
    }
   ],
   "cell_type": "code",
   "source": [
    "X_hat = D * Λ\n",
    "plot(\n",
    "    [\n",
    "        heatmap(\n",
    "            reshape(X_hat[:, i], sizex, sizey);\n",
    "            legend=:none,\n",
    "            axis=nothing,\n",
    "            showaxis=false,\n",
    "            aspect_ratio=:equal,\n",
    "            c=:Blues,\n",
    "            yflip=true,\n",
    "        ) for i in 1:M\n",
    "    ]...;\n",
    "    layout=(5, M ÷ 5),\n",
    "    plot_title=\"Low rank approximation\",\n",
    ")"
   ],
   "metadata": {},
   "execution_count": 25
  },
  {
   "cell_type": "markdown",
   "source": [
    "---\n",
    "\n",
    "*This notebook was generated using [Literate.jl](https://github.com/fredrikekre/Literate.jl).*"
   ],
   "metadata": {}
  }
 ],
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