new small update

This commit is contained in:
mhjensen
2018-11-05 14:23:11 +01:00
parent 44ca45170b
commit 401104c7ff
8 changed files with 6 additions and 6 deletions
+1 -1
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@@ -165,7 +165,7 @@ $$
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\hat{x}_i^T\hat{x}_j,
$$
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
$$
\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
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@@ -772,7 +772,7 @@ $$
$$
<p>&nbsp;<br>
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
<p>&nbsp;<br>
$$
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@@ -614,7 +614,7 @@ $$
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\hat{x}_i^T\hat{x}_j,
$$
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
$$
\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
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@@ -619,7 +619,7 @@ $$
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\hat{x}_i^T\hat{x}_j,
$$
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
$$
\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
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@@ -988,7 +988,7 @@
"cell_type": "markdown",
"metadata": {},
"source": [
"but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $ 0 \\leq \\lambda_i \\leq C$. \n",
"but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $0\\leq\\lambda_i \\leq C$. \n",
"We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads"
]
},
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@@ -507,7 +507,7 @@ Inserting these constraints into the equation for ${\cal L}$ we obtain the same
{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\hat{x}_i^T\hat{x}_j,
\]
!et
but now subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ and $ 0 \leq \lambda_i \leq C$.
but now subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ and $0\leq\lambda_i \leq C$.
We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
!bt
\[