{
 "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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       "  \n",
       "  \"/>\n",
       "</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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   "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": [],
   "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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