some svm typos corrected

doc/src/SupportVMachines/svm.do.txt

@@ -342,7 +342,7 @@ possible margin $M$. Before we proceed, we need to remind ourselves
 about Lagrangian multipliers.
 
 !split
-===== A quick reminder on Lagrangian multipliers =====
+===== A quick Reminder on Lagrangian Multipliers =====
 
 Consider a function of three independent variables $f(x,y,z)$ . For the function $f$ to be an
 extreme we have
@@ -394,7 +394,7 @@ variables.
 Then $dz$ is no longer arbitrary.
 
 !split
-===== Adding the muliplier =====
+===== Adding the Multiplier =====
 
 However, we can add to
 !bt
@@ -441,7 +441,7 @@ If we have a set of constraints $\phi_k$ we have the equations
 !et
 
 !split
-===== Setting up the problem =====
+===== Setting up the Problem =====
 In order to solve the above problem, we define the following Lagrangian function to be minimized 
 !bt
 \[
@@ -634,11 +634,11 @@ y_i(\bm{w}^T\bm{x}_i+b) -(1-\xi_) \geq 0 \hspace{0.1cm}\forall i.
 !split
 ===== Kernels and non-linearity =====
 
-The cases we have studied till were all characterized by two classes
+The cases we have studied till now, were all characterized by two classes
 with a close to linear separability. The classifiers we have described
 so far find linear boundaries in our input feature space. It is
 possible to make our procedure more flexible by exploring the feature
-space using other basis expansions such higher-order polynomials,
+space using other basis expansions such as higher-order polynomials,
 wavelets, splines etc.
 
 If our feature space is not easy to separate, as shown in the figure
@@ -724,7 +724,7 @@ y_i(\bm{w}^T\bm{z}_i+b)= 1 \hspace{0.1cm}\forall i,
 \]
 !et
 from which we also find $b$.
-To compute $\bm{z}_i^T\bm{z}_j$ we define the kerne $K(\bm{x}_i,\bm{x}_j)$ as
+To compute $\bm{z}_i^T\bm{z}_j$ we define the kernel $K(\bm{x}_i,\bm{x}_j)$ as
 !bt
 \[
 K(\bm{x}_i,\bm{x}_j)=\bm{z}_i^T\bm{z}_j= \phi(\bm{x}_i)^T\phi(\bm{x}_j).
@@ -746,7 +746,7 @@ the dot product $(\bm{x}_i^T\bm{x}_j)^2$.
 This leads to the so-called
 kernel trick and the result leads to the same as if we went through
 the trouble of performing the transformation
-$(\phi(\bm{x}_i)^T\phi(\bm{x}_j)$ during the SVM calculations.
+$\phi(\bm{x}_i)^T\phi(\bm{x}_j)$ during the SVM calculations.
 
 
 !split