multi-dimensional-scaling.ipynb

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  {
   "cell_type": "code",
   "execution_count": 142,
   "id": "dc1aada8-b7a5-4942-bc69-12e5f3600fd5",
   "metadata": {},
   "outputs": [],
   "source": [
    "using MultivariateStats\n",
    "using Plots\n",
    "using Optim"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "id": "676cbccc-c26c-4ccb-ae6a-e966062c0965",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "points = [0.04236404900185098 0.5706043052349906 0.7069500333195994 0.19326687415477062 0.594682915673788; 0.11491791460253942 0.8548723334643146 0.1690412629569895 0.5446601705314281 0.12525503327329712; 0.012358394364994196 0.27255852312724316 0.27685156879361006 0.2168123741061787 0.16803818104321333; 0.5613106490811601 0.21629937968499924 0.32767490503054786 0.9227032795281015 0.2812454715012348; 0.10800528956802324 0.8334687954849764 0.017621769457183634 0.36658251952327137 0.5765688237478639; 5.0 4.0 3.0 7.0 14.0; 5.0 6.0 5.0 4.0 3.0]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "7×5 Matrix{Float64}:\n",
       " 0.042364   0.570604  0.70695    0.193267   0.594683\n",
       " 0.114918   0.854872  0.169041   0.54466    0.125255\n",
       " 0.0123584  0.272559  0.276852   0.216812   0.168038\n",
       " 0.561311   0.216299  0.327675   0.922703   0.281245\n",
       " 0.108005   0.833469  0.0176218  0.366583   0.576569\n",
       " 5.0        4.0       3.0        7.0       14.0\n",
       " 5.0        6.0       5.0        4.0        3.0"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "points = rand(7, 5);\n",
    "points[6,:] .= [5.0, 4.0, 3.0, 7.0, 14.0];\n",
    "points[7,:] .= [5.0, 6.0, 5.0, 4.0, 3.0];\n",
    "@show points"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 144,
   "id": "602f5b76-5e37-4451-9253-a097ee2ebe9e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Classical MDS(indim = 7, outdim = 2)"
      ]
     },
     "execution_count": 144,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M = fit(MDS, points, maxoutdim=2, distances=false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 145,
   "id": "c8accb25-b30c-4bdb-80d2-fd7981fe91c1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2×7 Matrix{Float64}:\n",
       " -0.367397  2.00167   0.407144    0.110948  -1.94256   -79.2747    18.5223\n",
       "  0.274914  0.552255  0.0815158  -0.482635   0.758415    0.282563   1.23577"
      ]
     },
     "execution_count": 145,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2d = predict(M) * transpose(points)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 146,
   "id": "143fa171-d158-484f-a650-13b708375f90",
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   "outputs": [
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       "</svg>\n"
      ]
     },
     "execution_count": 146,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(d2d[1,:], d2d[2,:], legend = false)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 147,
   "id": "930a30fc-ad85-47c1-949e-6f01e31ca501",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "cost (generic function with 1 method)"
      ]
     },
     "execution_count": 147,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function dist(x, y)\n",
    "    x .- y |> x -> x .* x |> sum |> sqrt\n",
    "end\n",
    "\n",
    "function cost(x)\n",
    "    myx = reshape(x, 7, 2)\n",
    "    s = 0.0\n",
    "    for i in 1:6\n",
    "        for j in (i+1):7\n",
    "            s += (dist(myx[i,:], myx[j, :]) - dist(points[i,:], points[j,:]))^2.0\n",
    "        end\n",
    "    end\n",
    "    return s\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "id": "e7ae8820-5165-4805-b96c-5429163dfd5e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       " * Status: success\n",
       "\n",
       " * Candidate solution\n",
       "    Final objective value:     7.482287e-01\n",
       "\n",
       " * Found with\n",
       "    Algorithm:     Gradient Descent\n",
       "\n",
       " * Convergence measures\n",
       "    |x - x'|               = 1.34e-09 ≰ 0.0e+00\n",
       "    |x - x'|/|x'|          = 1.20e-10 ≰ 0.0e+00\n",
       "    |f(x) - f(x')|         = 1.89e-15 ≰ 0.0e+00\n",
       "    |f(x) - f(x')|/|f(x')| = 2.52e-15 ≰ 0.0e+00\n",
       "    |g(x)|                 = 8.71e-09 ≤ 1.0e-08\n",
       "\n",
       " * Work counters\n",
       "    Seconds run:   0  (vs limit Inf)\n",
       "    Iterations:    136\n",
       "    f(x) calls:    339\n",
       "    ∇f(x) calls:   339\n"
      ]
     },
     "execution_count": 148,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "initial = rand(7, 2)\n",
    "optresult = optimize(cost, initial, GradientDescent())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 149,
   "id": "4e0cdbb1-c48e-4c69-91ac-ca2c598ee9cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7×2 Matrix{Float64}:\n",
       "   3.60247  -0.024171\n",
       "   4.07177  -0.420142\n",
       "   4.34064   0.0440607\n",
       "   3.79577   0.622604\n",
       "   3.76334  -0.506984\n",
       " -11.1053    6.75789\n",
       "  -5.23702  -3.38922"
      ]
     },
     "execution_count": 149,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "d2d = reshape(optresult.minimizer, 7, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 150,
   "id": "0f39b6ff-9999-4d0f-8737-303e0eabfd69",
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 150,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scatter(d2d[:,1], d2d[:,2], legend = false)"
   ]
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   "execution_count": null,
   "id": "7a6d8715-4b2e-4113-9bea-6830b855c1a1",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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