util/algorithm.py

from numpy.linalg import norm
from math import sqrt, exp
from numba import jit


def l1(x):
    return norm(x, ord=1)


def l2(x):
    return norm(x)


def common(x1, x2):
    # find common ratings
    overlap = (x1 != 0) & (x2 != 0)
    new_x1 = x1[overlap]
    new_x2 = x2[overlap]
    return new_x1, new_x2


def cosine_sp(x1, x2):
    'x1,x2 are dicts,this version is for sparse representation'
    total = 0
    denom1 = 0
    denom2 = 0
    try:
        for k in x1:
            if k in x2:
                total += x1[k] * x2[k]
                denom1 += x1[k] ** 2
                denom2 += x2[k] ** 2
        return total / (sqrt(denom1) * sqrt(denom2))
    except ZeroDivisionError:
        return 0


def euclidean_sp(x1, x2):
    'x1,x2 are dicts,this version is for sparse representation'
    total = 0
    try:
        for k in x1:
            if k in x2:
                total += x1[k] ** 2 - x2[k] ** 2
        return 1 / total
    except ZeroDivisionError:
        return 0


def cosine(x1, x2):
    # find common ratings
    # new_x1, new_x2 = common(x1,x2)
    # compute the cosine similarity between two vectors
    total = x1.dot(x2)
    denom = sqrt(x1.dot(x1) * x2.dot(x2))
    try:
        return total / denom
    except ZeroDivisionError:
        return 0

    # return cosine_similarity(x1,x2)[0][0]


def pearson_sp(x1, x2):
    total = 0
    denom1 = 0
    denom2 = 0
    overlapped = False
    try:
        mean1 = sum(x1.values()) / len(x1)
        mean2 = sum(x2.values()) / len(x2)
        for k in x1:
            if k in x2:
                total += (x1[k] - mean1) * (x2[k] - mean2)
                denom1 += (x1[k] - mean1) ** 2
                denom2 += (x2[k] - mean2) ** 2
                overlapped = True
        return total / (sqrt(denom1) * sqrt(denom2))
    except ZeroDivisionError:
        if overlapped:
            return 1
        return 0


def euclidean(x1, x2):
    # find common ratings
    new_x1, new_x2 = common(x1, x2)
    # compute the euclidean between two vectors
    diff = new_x1 - new_x2
    denom = sqrt((diff.dot(diff)))
    try:
        return 1 / denom
    except ZeroDivisionError:
        return 0


def pearson(x1, x2):
    # find common ratings
    # new_x1, new_x2 = common(x1, x2)
    # compute the pearson similarity between two vectors
    # ind1 = new_x1 > 0
    # ind2 = new_x2 > 0
    try:
        mean_x1 = x1.sum() / len(x1)
        mean_x2 = x2.sum() / len(x2)
        new_x1 = x1 - mean_x1
        new_x2 = x2 - mean_x2
        total = new_x1.dot(new_x2)
        denom = sqrt((new_x1.dot(new_x1)) * (new_x2.dot(new_x2)))
        return total / denom
    except ZeroDivisionError:
        return 0


def similarity(x1, x2, sim):
    if sim == 'pcc':
        return pearson_sp(x1, x2)
    if sim == 'euclidean':
        return euclidean_sp(x1, x2)
    else:
        return cosine_sp(x1, x2)


def normalize(vec, maxVal, minVal):
    'get the normalized value using min-max normalization'
    if maxVal > minVal:
        return (vec - minVal) / (maxVal - minVal)
    elif maxVal == minVal:
        return vec / maxVal
    else:
        print('error... maximum value is less than minimum value.')
        raise ArithmeticError


def sigmoid(val):
    return 1 / (1 + exp(-val))


def denormalize(vec, max_val, min_val):
    return min_val + (vec - 0.01) * (max_val - min_val)


@jit(nopython=True)
def find_k_largest(K, candidates):
    n_candidates = []
    for iid, score in enumerate(candidates[:K]):
        n_candidates.append((iid, score))
    n_candidates.sort(key=lambda d: d[1], reverse=True)
    k_largest_scores = [item[1] for item in n_candidates]
    ids = [item[0] for item in n_candidates]
    # find the K biggest scores
    for iid, score in enumerate(candidates):
        ind = K
        l = 0
        r = K - 1
        if k_largest_scores[r] < score:
            while r >= l:
                mid = int((r - l) / 2) + l
                if k_largest_scores[mid] >= score:
                    l = mid + 1
                elif k_largest_scores[mid] < score:
                    r = mid - 1
                if r < l:
                    ind = r
                    break
        # move the items backwards
        if ind < K - 2:
            k_largest_scores[ind + 2:] = k_largest_scores[ind + 1:-1]
            ids[ind + 2:] = ids[ind + 1:-1]
        if ind < K - 1:
            k_largest_scores[ind + 1] = score
            ids[ind + 1] = iid
    return ids, k_largest_scores