Overview
A similarity measure is a function which takes two inputs and returns a number that indicates how similar the two inputs are. A similarity measure is often just an function that functions like a kernel, but doesnt necessary fit the strict definition of a kernel.
Similarity Measures
The following are commonly used similarity measures.
Cosine Similarity
{% cos(\vec{i}, \vec{j}) = \frac{\vec{i} \cdot \vec{j} }{||\vec{i}|| \times ||\vec{j}||} %}
Correlation
{% sim(\vec{i}, \vec{j}) = \frac{\sum(f_{i,p} - \bar{f_i}) (f_{j,p} - \bar{f_j}) }{\sqrt{\sum(f_{i,p} - \bar{f_i})^2} \sqrt{\sum(f_{j,p} - \bar{f_j})^2} } %}
Latent Factors
Latent Factor Models are common in statistical analysis, and can also be used to construct similarity measures.