从勾股定理到余弦相似度-程序员的数学基础

# -*- coding: utf-8 -*-import numpy as npimport numpy.linalg as linalg  def cos_similarity(v1, v2):    num = float(np.dot(v1.T, v2))  # 若为行向量则 A.T * B    denom = linalg.norm(v1) * linalg.norm(v2)    if denom > 0:        cos = num / denom  # 余弦值        sim = 0.5 + 0.5 * cos  # 归一化        return sim    return 0  if __name__ == '__main__':     u_tag_list = [        ["女", "26", "是", "白领"],        ["女", "35", "是", "白领"],        ["女", "30", "是", "白领"],        ["女", "22", "是", "白领"],        ["女", "20", "是", "白领"]    ]    new_user = ["女", "20", "是", "白领"]     u_tag_vector = np.array([        [1, 26, 1, 1],        [1, 35, 1, 1],        [1, 30, 1, 1],        [1, 22, 1, 1],        [1, 20, 1, 1]    ])     c1 = u_tag_vector[0]    c1 += u_tag_vector[1]    c1 += u_tag_vector[2]    c1 += u_tag_vector[3]    c1 += u_tag_vector[4]    c1 = c1/5         new_user_v1 = np.array([1, 36, 1, 1])    new_user_v2 = np.array([-1, 20, 0, 1])    print("vector-u1: ", list(map(lambda x: '%.2f' % x, new_user_v1.tolist()[0:10])))    print("vector-u2: ", list(map(lambda x: '%.2f' % x, new_user_v2.tolist()[0:10])))    print("vector-c1: ", list(map(lambda x: '%.2f' % x, c1.tolist()[0:10])))    print("sim<u1,c1>: ", cos_similarity(c1, new_user_v1))    print("sim<u2,c1>: ", cos_similarity(c1, new_user_v2))

# -*- coding: utf-8 -*-import numpy as npimport numpy.linalg as linalgimport cv2  def cos_similarity(v1, v2):    num = float(np.dot(v1.T, v2))  # 若为行向量则 A.T * B    denom = linalg.norm(v1) * linalg.norm(v2)    if denom > 0:        cos = num / denom  # 余弦值        sim = 0.5 + 0.5 * cos  # 归一化        return sim    return 0  def build_image_vector(im):    """     :param im:    :return:    """    im_vector = []     im2 = cv2.resize(im, (500, 300))    w = im2.shape[1]    h = im2.shape[0]    h_step = 30    w_step = 50     for i in range(0, w, w_step):        for j in range(0, h, h_step):            each = im2[j:j+h_step, i:i+w_step]            b, g, r = each[:, :, 0], each[:, :, 1], each[:, :, 2]            im_vector.append(np.mean(b))            im_vector.append(np.mean(g))            im_vector.append(np.mean(r))    return np.array(im_vector)  def show(imm):    imm2 = cv2.resize(imm, (510, 300))    print(imm2.shape)    imm3 = imm2[0:50, 0:30]    cv2.imshow("aa", imm3)     cv2.waitKey()    cv2.destroyAllWindows()    imm4 = imm2[51:100, 0:30]    cv2.imshow("bb", imm4)    cv2.waitKey()    cv2.destroyAllWindows()    imm2.fill(0)  def build_image_collection_vector(p_name):    path = "D:\\python-workspace\\cos-similarity\\images\\"     c1_vector = np.zeros(300)    for pic in p_name:        imm = cv2.imread(path + pic)        each_v = build_image_vector(imm)        a=list(map(lambda x:'%.2f' % x, each_v.tolist()[0:10]))        print("p1: ", a)        c1_vector += each_v    return c1_vector/len(p_name)  if __name__ == '__main__':     v1 = build_image_collection_vector(["food1.jpg", "food2.jpg", "food3.jpg"])    v2 = build_image_collection_vector(["pet1.jpg", "pet2.jpg", "pet3.jpg"])     im = cv2.imread("D:\\python-workspace\\cos-similarity\\images\\pet4.jpg")    v3 = build_image_vector(im)    print("v1,v3:", cos_similarity(v1,v3))    print("v2,v3:", cos_similarity(v2,v3))    a = list(map(lambda x: '%.2f' % x, v3.tolist()[0:10]))    print("p1: ", a)    im2 = cv2.imread("D:\\python-workspace\\cos-similarity\\images\\food4.jpg")    v4 = build_image_vector(im2)     print("v1,v4:", cos_similarity(v1, v4))    print("v2,v4:", cos_similarity(v2, v4))

# -*- coding: utf-8 -*-import numpy as npimport numpy.linalg as linalgimport jieba  def cos_similarity(v1, v2):    num = float(np.dot(v1.T, v2))  # 若为行向量则 A.T * B    denom = linalg.norm(v1) * linalg.norm(v2)    if denom > 0:        cos = num / denom  # 余弦值        sim = 0.5 + 0.5 * cos  # 归一化        return sim    return 0  def build_doc_tf_vector(doc_list):    num = 0    doc_seg_list = []    word_dic = {}    for d in doc_list:        seg_list = jieba.cut(d, cut_all=False)        seg_filterd = filter(lambda x: len(x)>1, seg_list)         w_list = []        for w in seg_filterd:            w_list.append(w)            if w not in word_dic:                word_dic[w] = num                num+=1         doc_seg_list.append(w_list)     print(word_dic)     doc_vec = []     for d in doc_seg_list:        vi = [0] * len(word_dic)        for w in d:           vi[word_dic[w]] += 1        doc_vec.append(np.array(vi))        print(vi[0:40])    return doc_vec, word_dic  def build_query_tf_vector(query, word_dic):    seg_list = jieba.cut(query, cut_all=False)    vi = [0] * len(word_dic)    for w in seg_list:        if w in word_dic:            vi[word_dic[w]] += 1    return vi  if __name__ == '__main__':    doc_list = [        """         受全球疫情影响，3月苹果宣布关闭除大中华区之外数百家全球门店，其庞大的供应链体系也受到冲击，         尽管目前富士康等代工厂已经开足马力恢复生产，但相比之前产能依然受限。中国是iPhone生产的大本营，         为了转移风险，iPhone零部件能否实现印度制造？实现印度生产的最大难点就是，相对中国，印度制造业仍然欠发达        """,        """        苹果是一种低热量的水果，每100克产生大约60千卡左右的热量。苹果中营养成分可溶性大，容易被人体吸收，故有“活水”之称。        它有利于溶解硫元素，使皮肤润滑柔嫩。        """,        """        在生活当中，香蕉是一种很常见的水果，一年四季都能吃得着，因其肉质香甜软糯，且营养价值高，所以深受老百姓的喜爱。        那么香蕉有什么具体的功效，你了解吗？        """    ]     query = "苹果是我喜欢的水果"     doc_vector, word_dic = build_doc_tf_vector(doc_list)     query_vector = build_query_tf_vector(query, word_dic)     print(query_vector[0:35])     for i, doc in enumerate(doc_vector):        si = cos_similarity(doc, query_vector)        print("doc", i, ":", si)