ML_Maschinelles_Lernen_Grundlagen/Exercise_1
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paul-loedige 2021-11-10 09:53:10 +01:00
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exercise.ipynb
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@ -25,7 +25,14 @@
"rewrite it in matrix form:\n", "rewrite it in matrix form:\n",
"\n", "\n",
"\\begin{align*}\n", "\\begin{align*}\n",
" g = \\alpha \\sum_i \\sum_j \\sum_k z_k x_{ij} q_i y_{jk}\n", " g &= \\alpha \\sum_i \\sum_j \\sum_k z_k x_{ij} q_i y_{jk}\\\\\n",
" &= \\alpha \\sum_i^I \\sum_j^J \\sum_k^K z_k x_{ij} q_i y_{jk}\\qquad (\\text{mit }I,J,K\\in \\mathbb{N})\\\\\n",
" &= Y\\cdot X \\cdot Q \\cdot Z \\cdot \\alpha\\\\\n",
" &= \\begin{bmatrix} y_{11} & \\cdots & y_{1J}\\\\ \\vdots & \\ddots & \\vdots\\\\ y_{K1} & \\cdots & y_{KJ}\\end{bmatrix} \\cdot\n",
" \\begin{bmatrix} x_{11} & \\cdots & x_{1I}\\\\ \\vdots & \\ddots & \\vdots\\\\ x_{J1} & \\cdots & x_{JI}\\end{bmatrix} \\cdot\n",
" \\begin{bmatrix} q_1 \\\\ \\vdots \\\\ q_I\\end{bmatrix} \\cdot\n",
" \\begin{bmatrix} z_1 & \\cdots & z_K\\end{bmatrix} \\cdot\n",
" \\alpha\n",
"\\end{align*}\n", "\\end{align*}\n",
"\n" "\n"
] ]
@ -1004,7 +1011,7 @@
"name": "python", "name": "python",
"nbconvert_exporter": "python", "nbconvert_exporter": "python",
"pygments_lexer": "ipython3", "pygments_lexer": "ipython3",
"version": "3.8.8" "version": "3.8.5"
} }
}, },
"nbformat": 4, "nbformat": 4,