Weighting features prior to SVM I'm building an object detector using HOG features and linear SVM. Some of the regions of the object are more "distinctive" so I would like to give more weight to the features extracted from those regions. (e.g. imagine we want to detect between mugs and glasses, then the most "distinctive" part is the mug's handle)
How could I do this? For sure there should be a more intelligent way than just replicating the features of those "distinctive" regions.
 A: I believe the term of art for you are seeking is "automatic relevance determination."
The conventional linear SVM has a kernel function that is the dot product of the two  feature vectors: $$K_1(x,x^\prime)=x^Tx^\prime.$$
One way to differentiate among features would be to estimate coefficients for each feature (i.e. element of $x$) separately, and add the results. The simplest case of this will use a diagonal, positive definite matrix $D$:
$$
K_2(x,x^\prime)=x^TDx.
$$
So now the result of $K_2$ is a weighted sum of the element-wise product of $x$ and $x^\prime$ various features.
Note that this isn't restricted just to the linear kernel. For example, the common radial basis function with Euclidean norm can be modified like so. For 
$$
K_3(x,x^\prime)=\exp\left( -(x-x^\prime)^TD(x-x^\prime)\right)
$$
since the product $(x-x^\prime)^TD(x-x^\prime)$ is a squared distance, with each axis weighted according to $D$.
Further generalization of this idea can be had by using non-diagonal (but still positive definite) $D$. Enforcing orthogonality of the data via some method such as PCA will obviate the need for non-diagonal $D$, but perhaps reduce interpret-ability of the outcome.
A: I think you are thinking about this the wrong way - you should let machine learning determine which parts of the object are discriminative and which are not. If you look at visualizations of models obtained with HOG+linear SVM, you see which cells get high importance according to the strength of the oriented edge.

This model, taken from Felzenszwalb's seminal DPM paper, shows that the cells with highest discriminative power are those near the head and shoudlers. Those around the head usually contain background, so the SVM learned to assign low weight.
If you have enough positive and negative training images (using your example, lots of mugs and non-mugs), your SVM should pick up that the handle is important, assuming the handle appears in consistent locations in the images.
