How to distinguish Methods for Classification Is there a difference between methods for classification that are using the "raw-signal" as features and methods that are extracting features?
For example, there are methods which are based on calculating the correlation of signal a and b if the correlation is high enough, then it is a match.
On the other hand there are methods which are extracting features from signal a and b seperately (such as extrema, variance,..) and are classifying based on these features.
For me the latter ones are more abstract. Is this just an subjective feeling?
If they ARE distinguishable how to formalize (refer to) it?
 A: Yeah I would say you're on to something. This reminded me of the beginning of chapter 16 of Murphy's Machine Learning: a Probabilistic Perspective:

Although this [kernel methods (from the previous two chapters)] can work well, it relies on having a good kernel
  function to measure the similarity between data vectors. Often coming
  up with a good kernel function is quite difficult. For example, how do
  we define the similarity between two images? Pixel-wise comparison of
  intensities (which is what a Gaussian kernel corresponds to) does not
  work well. Although it is possible (and indeed common) to
  hand-engineer kernels for specific tasks (see e.g., the pyramid match
  kernel in Section 14.2.7), it would be more interesting if we could
  learn the kernel

Then they go on to say

An alternative approach is to dispense with kernels altogether, and
  try to learn useful features $\phi(x)$ directly from the input data.
  That is, we will create what we call an adaptive basis function model
  (ABM), which is a model of the form $$ f(x) = w_0 + \sum_{m=1}^M w_m
 \phi_m(x) $$ where $\phi_m(x)$  is the m’th basis function, which is
  learned from data. This framework covers all of the models we will
  discuss in this chapter.

Some of the methods that he includes in this adaptive basis function model category are classification trees, generalized additive models, boosting, feedforward neural networks, ensemble learning, and others. 
A: On first thought, I think this dilemma is beside the point and that the distinction is an artificial one. 
Firstly, the initial "raw" set of numbers could be defined as a feature of the emitting source, so I am not sure that the definition of what is a feature and what is not is too explicit. For example, wikipedia uses the generic definition of a machine learning feature as:

an individual measurable property or characteristic of a phenomenon being observed

Moreover, classification algorithms - and in general, learning algorithms - work on numbers, manipulating them to build a model that classifies the input. If these numbers are good at describing and delineating the structure of the problem (e.g. good at separating the classes), then all is well.
If not, we combine and manipulate these numbers (i.e. computing features out of them) in order to arrive at a different set of numbers that is better at explaining the structure and thus, does better as the input for the classification algorithm.
The latter, though, is always doing the same thing - working on a set numbers to perform classification. 
I do not know if some algorithms could work better on a class of features (eg always do better using low rather than using high level features), though - would be nice to know if some do.
