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8,9,10장 수식 번역

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Haesun Park
2018-04-25 23:13:00 +09:00
parent 3f68a2413f
commit 7956ac82e1
1 changed files with 25 additions and 28 deletions
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book_equations.ipynb
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@@ -634,12 +634,12 @@
},
"cell_type": "markdown",
"source": [
"# Chapter 8\n",
"# 8장\n",
"\n",
"**Equation 8-1: Principal components matrix**\n",
"**식 8-1: 주성분 행렬**\n",
"\n",
"$\n",
"\\mathbf{V}^T =\n",
"\\mathbf{V} =\n",
"\\begin{pmatrix}\n",
" \\mid & \\mid & & \\mid \\\\\n",
" \\mathbf{c_1} & \\mathbf{c_2} & \\cdots & \\mathbf{c_n} \\\\\n",
@@ -648,42 +648,39 @@
"$\n",
"\n",
"\n",
"**Equation 8-2: Projecting the training set down to _d_ dimensions**\n",
"**식 8-2: 훈련 세트를 _d_차원으로 투영하기**\n",
"\n",
"$\n",
"\\mathbf{X}_{d\\text{-proj}} = \\mathbf{X} \\cdot \\mathbf{W}_d\n",
"$\n",
"\n",
"\n",
"**Equation 8-3: PCA inverse transformation, back to the original number of dimensions**\n",
"**식 8-3: 원본의 차원 수로 되돌리는 PCA 역변환**\n",
"\n",
"$\n",
"\\mathbf{X}_{\\text{recovered}} = \\mathbf{X}_{d\\text{-proj}} \\cdot {\\mathbf{W}_d}^T\n",
"$\n",
"\n",
"\n",
"$ \\sum_{j=1}^{m}{w_{i,j}\\mathbf{x}^{(j)}} $\n",
"\n",
"\n",
"**Equation 8-4: LLE step 1: linearly modeling local relationships**\n",
"**식 8-4: LLE 단계 1: 선형적인 지역 관계 모델링**\n",
"\n",
"$\n",
"\\begin{split}\n",
"& \\hat{\\mathbf{W}} = \\underset{\\mathbf{W}}{\\operatorname{argmin}}{\\displaystyle \\sum\\limits_{i=1}^{m}} \\left\\|\\mathbf{x}^{(i)} - \\sum\\limits_{j=1}^{m}{w_{i,j}}\\mathbf{x}^{(j)}\\right\\|^2\\\\\n",
"& \\text{subject to }\n",
"& \\text{[조건] }\n",
"\\begin{cases}\n",
" w_{i,j}=0 & \\text{if }\\mathbf{x}^{(j)} \\text{ is not one of the }k\\text{ c.n. of }\\mathbf{x}^{(i)}\\\\\n",
" \\sum\\limits_{j=1}^{m}w_{i,j} = 1 & \\text{for }i=1, 2, \\dots, m\n",
" w_{i,j}=0 & \\mathbf{x}^{(j)} \\text{가 } \\mathbf{x}^{(i)} \\text{의 최근접 이웃 개 중 하나가 아닐때}\\\\\n",
" \\sum\\limits_{j=1}^{m}w_{i,j} = 1 & i=1, 2, \\dots, m \\text{ 일 때}\n",
"\\end{cases}\n",
"\\end{split}\n",
"$\n",
"\n",
"**In the text page 223:**\n",
"**290 페이지 본문 중에서**\n",
"\n",
"[...] then we want the squared distance between $\\mathbf{z}^{(i)}$ and $ \\sum_{j=1}^{m}{\\hat{w}_{i,j}\\mathbf{z}^{(j)}} $ to be as small as possible.\n",
"[...] $\\mathbf{z}^{(i)}$와 $ \\sum_{j=1}^{m}{\\hat{w}_{i,j}\\mathbf{z}^{(j)}} $ 사이의 거리가 최소화되어야 합니다.\n",
"\n",
"\n",
"**Equation 8-5: LLE step 2: reducing dimensionality while preserving relationships**\n",
"**식 8-5: LLE 단계 2: 관계를 보존하는 차원 축소**\n",
"\n",
"$\n",
"\\hat{\\mathbf{Z}} = \\underset{\\mathbf{Z}}{\\operatorname{argmin}}{\\displaystyle \\sum\\limits_{i=1}^{m}} \\left\\|\\mathbf{z}^{(i)} - \\sum\\limits_{j=1}^{m}{\\hat{w}_{i,j}}\\mathbf{z}^{(j)}\\right\\|^2\n",
@@ -697,9 +694,9 @@
},
"cell_type": "markdown",
"source": [
"# Chapter 9\n",
"# 9장\n",
"\n",
"**Equation 9-1: Rectified linear unit**\n",
"**식 9-1: ReLU 함수**\n",
"\n",
"$\n",
"h_{\\mathbf{w}, b}(\\mathbf{X}) = \\max(\\mathbf{X} \\cdot \\mathbf{w} + b, 0)\n",
@@ -713,37 +710,37 @@
},
"cell_type": "markdown",
"source": [
"# Chapter 10\n",
"# 10장\n",
"\n",
"**Equation 10-1: Common step functions used in Perceptrons**\n",
"**식 10-1: 퍼셉트론에서 일반적으로 사용하는 계단 함수**\n",
"\n",
"$\n",
"\\begin{split}\n",
"\\operatorname{heaviside}(z) =\n",
"\\begin{cases}\n",
"0 & \\text{if }z < 0\\\\\n",
"1 & \\text{if }z \\ge 0\n",
"0 & z < 0 \\text{ 일 때}\\\\\n",
"1 & z \\ge 0 \\text{ 일 때}\n",
"\\end{cases} & \\quad\\quad\n",
"\\operatorname{sgn}(z) =\n",
"\\begin{cases}\n",
"-1 & \\text{if }z < 0\\\\\n",
"0 & \\text{if }z = 0\\\\\n",
"+1 & \\text{if }z > 0\n",
"-1 & z < 0 \\text{ 일 때}\\\\\n",
"0 & z = 0 \\text{ 일 때}\\\\\n",
"+1 & z > 0 \\text{ 일 때}\n",
"\\end{cases}\n",
"\\end{split}\n",
"$\n",
"\n",
"\n",
"**Equation 10-2: Perceptron learning rule (weight update)**\n",
"**식 10-2: 퍼셉트론 학습 규칙(가중치 업데이트)**\n",
"\n",
"$\n",
"{w_{i,j}}^{(\\text{next step})} = w_{i,j} + \\eta (y_j - \\hat{y}_j) x_i\n",
"{w_{i,j}}^{(\\text{다음 스텝})}\\quad = w_{i,j} + \\eta (y_j - \\hat{y}_j) x_i\n",
"$\n",
"\n",
"\n",
"**In the text page 266:**\n",
"**342 페이지 본문 중에서**\n",
"\n",
"It will be initialized randomly, using a truncated normal (Gaussian) distribution with a standard deviation of $ 2 / \\sqrt{\\text{n}_\\text{inputs}} $.\n"
"이 행렬은 표준편차가 $ 2 / \\sqrt{\\text{n}_\\text{inputs} + \\text{n}_\\text{n_neurons}} $인 절단 정규(가우시안) 분포를 사용해 무작위로 초기화됩니다.\n"
]
},
{