Performing feature hashing

With feature hashing, the categories of a variable are converted into a series of binary vectors using a hashing function. How does this work? First, we determine, arbitrarily, the number of binary vectors to represent the category. For example, let's say we would like to use five vectors. Next, we need a hash function that will take a category and return a number between 0 and n-1, where n is the number of binary vectors. In our example, the hash function should return a value between 0 and 4. Let's say our hash function returns the value of 3 for the category blue. That means that our category blue will be represented by a 0 in the vectors 0, 1, 2, and 4 and 1 in the vector 3: [0,0,0,1,0]. Any hash function can be used as long as it returns a number between 0 and n-1.