Does a linear classifier has spatial awareness? Say we are trying to classify images using a linear classifier, and in our training set we have say cars in the middle on a white background. If in our test set, we shift the cars to the right but keep it in the same white background, will it be correctly classified with high accuracy by a linear classifier??
In my opinion it shouldn't as say we created template of the car classifier and dot producted it with our test image, the score will be lower as compared to some other test example with car in the middle.
 A: In most object detection tasks, many variations of an original image are fed into a classifier after a series of different transformations (panning, zooming, rotating, ...). Hence, while the classifier itself is often not spatially aware, that should not pose too big a problem in practice. 
The final prediction is then typically the highest match. In your example, the output score (say, the probability that the image contains a car), would be the highest score that is produced by the classifier for any of the image's variations.
A: rudra
you are totally correct.  That's why you need a non linear classifier : effectively to implement multiple separate templates to approximate translation invariance (see convolutional NNs).
In addition you typically look at smaller features (the receptive field in CNN vocabulary) to deal with both translation rotation and occlusion effects.
linear classifiers such as SVMs are used with 'bag of words' with eg sift feature vectors ( again splitting the picture into eg quadrants and calculating the feature vectors in those quadrants)
