[PYTHON] Cosine similarity matrix? You can get it right away with NumPy

Conclusion

def cos_sim_matrix(matrix):
    """
    item-given a feature matrix
Function to find the cosine similarity matrix between items
    """
    d = matrix @ matrix.T  # item-A matrix whose elements are the inner products of vectors

    #Each item to put in the denominator of cosine similarity-Square root of vector size
    norm = (matrix * matrix).sum(axis=1, keepdims=True) ** .5
    
    #Divide by the square root of the size of each item (somewhat smart!)
    return d / norm / norm.T

• Googling in English (such as "cosine similarity matrix numpy")
• Look closely at the original formula

Introduction

Do you guys like the cosine similarity matrix? I love: innocent :.

Especially when trying to perform collaborative filtering, I think we often try to make it.

Unfortunately, when I look it up in Japanese, I often see how to find the cosine similarity between two vectors, but I rarely see how to find the cosine similarity matrix that is a collection of them.

Or it may be obvious to someone with a little more numpy power, so I didn't specify it.

Therefore, I will leave it here as a memorandum for myself.

The mistakes I made by then

Please do not refer to this as it is a failure: cry :. It takes dozens of times longer than the above: poop :.

@numba.jit('f8(f8[:],f8[:])', nopython=True)
def _cos_sim(v1, v2):
    """
Returns the cosine similarity of two vectors
    """
    return np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))

@numba.jit('f8[:, :](f8[:,:])',nopython=True)
def item_similarities(item_user_matrix):
    """
Given an item user matrix
Function to find the similarity matrix between items
    """
    n = item_user_matrix.shape[0]  # n: item counts
    sims = np.identity(n)  #Similarity between the same items is 1

    for i in range(n):
        for j in range(i+1, n):
            sim = _cos_sim(item_user_matrix[i], item_user_matrix[j])
            sims[i][j] = sim
            sims[j][i] = sim
    return sims

Finally

I need more power ... !! (I need more power ... !!)