# Finding Feature Representation Such That Two Samples Are Similar in Feature Space

Consider one specific useful function of our human brain: abstraction of object. Take the example of two pictures: if we are told the pictures are similar, we actually make conclusion about the aspects in which they are close to each other.

I'm considering whether machine can have the ability described. More accurately, is it possible to find and select a set of feature representations of two samples (e.g. image, sound) such that under those representations, the samples are similar with respect to a metric, say weighted euclidean norm?

• So you want Artificial Confirmation Bias? Jul 15 '12 at 16:35

I think you're looking for metric learning or Manifold learning. At a very high level, the idea behind both of these approaches is to learn the space (or transform) over which a set of (labeled) examples are close to one another.

• That is exactly "Global Metric Learning", which tries to keep examples in the same class close while separating examples in different classes. Jul 16 '12 at 21:09
• But can we learning a mapping, instead of a metric, to do this? Jul 16 '12 at 21:16
• I'm not sure I understand exactly what you're looking for. Could you explain what you mean by "learning a mapping instead of a metric" and why you would like to do this?
– Nick
Jul 16 '12 at 21:38
• Through Metric Learning, we learn a metric of the space measuring patterns such that those labeled similar are close and those labeled non-similar are distinguished. I'm wondering if we can learn a mapping from the original space to another space in which the same thing can be done. Jul 17 '12 at 12:47
• That's an interesting problem. I'm not aware of anything like that. Is there a specific problem you are trying to solve for which metric learning does not work?
– Nick
Jul 17 '12 at 18:40

Did you have a look at principal component analysis? It's basically the simplest of an array of dimension-reducing methods. It does the following:

Given a set of data points with with dimension, say, $n$, it transforms them into data points with dimension $k<n$, where $k$ is a parameter. The transformation is such that the first principal component has the highest variance in the data, the second one is orthogonal and has the 2nd-highest variance, and so on.

This intuitively gives you a vector which throws away all the information that is constant in the data, and filters out information that varies throughout your input. For instance, imagine you have 100 pictures of a hand from the same perspective. Then, after the PCA the first component might indicate the position of the thumb, the second one the space between index and middle finger, and so on.

• This is close, but no the same. Is it possible to select features automatically such that two samples labeled as similar is close under those feature representations? Jul 16 '12 at 2:28
• PCA does the opposite of (as I understand it) what the question is asking. PCA finds the dimensions that distinguish the data the most; it seems like the question wants dimensions that distinguish the data the least.
– Joe
Jul 16 '12 at 18:09
• @Joe, it we wants dimensions that distinguish the data the least, we can just take the orthogonal space of the result of PCA. But this learning problem is semi-supervised. We have some labels indicating which examples are similar. The algorithm should distinguish classes as much as possible, whereas reducing the diameter of each labeled class. Jul 16 '12 at 21:03
• @Strin can you clarify that in your question?
– Joe
Jul 17 '12 at 22:15