Merge branch 'master' of https://github.com/CompPhysics/MachineLearning

2020-11-26 12:00:21 +01:00
parent 83c5eaa705 f3be9b9268
commit 8a6accfca0
8 changed files with 12 additions and 12 deletions
@@ -178,7 +178,7 @@ kernel trick.
 Using our definition of the kernel, we can rewrite again the Lagrangian
 !bt
 \[
-{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\bm{x}_i^T\bm{z}_j,
+{\cal L}=\sum_i\lambda_i-\frac{1}{2}\sum_{ij}^n\lambda_i\lambda_jy_iy_j\bm{z}_i^T\bm{z}_j,
 \]
 !et
 subject to the constraints $\lambda_i\geq 0$, $\sum_i\lambda_iy_i=0$ in terms of a convex optimization problem
@@ -582,7 +582,7 @@ We have the general problem

 o With a given kernel we can thus define the matrix $\bm{P}$.
 o The matrix $\bm{P}$ has matrix elements $p_{ij}=y_iy_jK(\bm{x}_i,\bm{x}_j)$. Given a kernel $K$ and the targets $y_i$ this matrix is easy to set up.
-o The vector $\bm{q}$ is zero.
+o The vector $\bm{q}$ has all elements equal 1.
 o The constraint $\bm{y}^T\bm{\lambda}=0$ leads to $f=0$ and $\bm{A}=\bm{y}$.
 o To set up the matrix $\bm{G}$ we note that the inequalities $0\leq \lambda_i \leq C$ can be split up into $0\leq \lambda_i$ and $\lambda_i \leq C$. These two inequalities define then the matrix $\bm{G}$ and the vector $\bm{h}$.