Meaning of latent features? I'm trying to understand matrix factorization models for recommender systems and I always read 'latent features', but what does that mean? I know what a feature means for a training dataset but I'm not able to understand the idea of latent features. Every paper on the topic I can find is just too shallow.
Edit:
if you at least can point me to some papers that explain the idea.
 A: In the context of Factorization Method latent features are usually meant to characterize items along each dimension. Let me explain by example.
Suppose we have a matrix of item-users interactions $R$. The model assumption in Matrix Factorization methods is that each cell $R_{ui}$ of this matrix is generated by, for example, $p_u^T q_i$ — a dot product between latent vector $p_u$, describing user $u$ and a latent vector $q_i$, describing item $i$. Intuitively, this product measures how similar these vectors are. During training you want to find "good" vectors, such that the approximation error is minimized.
One may think that these latent features are meaningful, that is, there's a feature in user's vector $p_u$ like "likes items with property X" and corresponding feature in item's vector $q_i$ like "has property X". Unfortunately, unless it's somehow enforced, it's hard to find interpretable latent features. So, you can think of latent features that way, but not use these features to reason about the data.
A: Latent means not directly observable. The common use of the term in PCA and Factor Analysis is to reduce dimension of a large number of directly observable features into a smaller set of indirectly observable features.
A: Here your data is ratings given by various users to various movies. As others have pointed out, latent means not directly observable.  
For a movie, its latent features determine the amount of action, romance, story-line, a famous actor, etc. Similarly, for another dataset consisting of handwritten digits, the latent variables may be angle of edges, skew, etc.
A: I would say that factors are more representative than principal components to get a perception of 'latency'/hiddenness of a variable. Latency is one of the reasons why behavioral scientists measure perceptual constructs like feeling, sadness in terms of multiple items/measures and derive a number for such hidden variables which cannot be directly measured.
