new small update
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@@ -165,7 +165,7 @@ $$
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{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\hat{x}_i^T\hat{x}_j,
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$$
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
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We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
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$$
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\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
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@@ -772,7 +772,7 @@ $$
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$$
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<p> <br>
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
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We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
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<p> <br>
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$$
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@@ -614,7 +614,7 @@ $$
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{\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,
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$$
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
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We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
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$$
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\lambda_i\left[y_i(\hat{w}^T\hat{x}_i+b) -(1-\xi_)\right]=0 \hspace{0.1cm}\forall i,
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@@ -619,7 +619,7 @@ $$
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{\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,
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$$
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and $ 0 \leq \lambda_i \leq C$.
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but now subject to the constraints \( \lambda_i\geq 0 \), \( \sum_i\lambda_iy_i=0 \) and \( 0\leq\lambda_i \leq C \).
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We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
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$$
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\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 @@
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"cell_type": "markdown",
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"metadata": {},
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"source": [
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"but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $ 0 \\leq \\lambda_i \\leq C$. \n",
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"but now subject to the constraints $\\lambda_i\\geq 0$, $\\sum_i\\lambda_iy_i=0$ and $0\\leq\\lambda_i \\leq C$. \n",
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"We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads"
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]
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},
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@@ -507,7 +507,7 @@ Inserting these constraints into the equation for ${\cal L}$ we obtain the same
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{\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,
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\]
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!et
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but now subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ and $ 0 \leq \lambda_i \leq C$.
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but now subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ and $0\leq\lambda_i \leq C$.
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We must in addition satisfy the Karush-Kuhn-Tucker condition which now reads
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!bt
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\[
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