K最邻近算法和局部敏感哈希LSH

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1. 计算已知类别数据集中的点与当前点之间的距离2. 按照距离递增次序排序3. 选取与当前点距离最小的k个点4. 确定前k个点所在类别的出现频率5.返回前k个点出现频率最高的类别作为当前点的预测分类

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def extract_feature() :    text = ""    post_set = []; class_set = []; feature = []    jieba.analyse.set_stop_words("stop_word.txt")    for index in range(len(dict_list)) :        with open("./lily/" + dict_list[index] + ".txt", "r") as my_file :            #读入每个板块所有的帖子                        for post in my_file :                 post_set.append(list(jieba.cut(post, cut_all = False))) #将post字符串存入list                class_set.append(index)                text += post            feature.extend(jieba.analyse.extract_tags(text, 100))    return feature, post_set, class_set

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def createQuery(post_set, feature) :    query_set = []    vec_size = len(feature)    for post in post_set :        vector = [0] * vec_size        for word in post :            if word in feature :                vector[feature.index(word)] += 1        query_set.append(vector)    return query_setdef makeVector(post, feature, size) :    vector = [0] * size    for word in post :        if word in feature :            vector[feature.index(word)] += 1    return vector

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def knnClassify(vecX, query_set, class_set, k) :    query_set = array(query_set)    query_set_size = query_set.shape[0]    mid_mat = tile(vecX, (query_set_size, 1)) - query_set    sqrt_two = mid_mat ** 2    sqrt_distances = sqrt_two.sum(axis = 1)    distances = sqrt_distances ** 0.5    sorted_dist = distances.argsort()    class_count = {}    for i in range(k) :        label = class_set[sorted_dist[i]]        class_count[label] = class_count.get(label, 0) + 1    sort_class_count = sorted(class_count.iteritems(), key = operator.itemgetter(1), reverse = True)    return sort_class_count[0][0]

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hash function需要满足以下两个条件：1）如果d(x,y) ≤ d1， 则h(x) = h(y)的概率至少为p1；2）如果d(x,y) ≥ d2， 则h(x) = h(y)的概率至多为p2；其中d(x,y)表示x和y之间的距离，d1 < d2， h(x)和h(y)分别表示对x和y进行hash变换。满足以上两个条件的hash functions称为(d1,d2,p1,p2)-sensitive。而通过一个或多个(d1,d2,p1,p2)-sensitive的hash function对原始数据集合进行hashing生成一个或多个hash table的过程称为Locality-sensitive Hashing。

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//Cosine distance的计算#计算向量的模def magnitudeProd(vec1, vec2) :    total1 = 0    total2 = 0    for i in xrange(dimension) :        val1 = vec1[i]        val2 = vec2[i]        total1 += val1**2        total2 += val2**2    return (total1 * total2)**0.5#计算两个向量之间的夹角, 看是否在一个角度范围内def cosineDistance(vec1, vec2) :    mag_prod = magnitudeProd(vec1, vec2)    if mag_prod == 0 :        return 0    return dotProduct(vec1, vec2) / magnitudeProd(vec1, vec2)#计算两个向量的内积def dotProduct(vec1, vec2) :    total = 0    for i in xrange(len(vec1)) :        total += vec1[i] * vec2[i]    return total

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def localitySensitiveHash(vec, planes) :    dot_prod_list = [dotProduct(vec, plane) for plane in planes]    return (sum([2 ** i if dot_prod_list[i] > 0 else 0 for i in xrange(0, len(dot_prod_list))]) % 8)hash_table = [(localitySensitiveHash(row, planes), class_set[class_index]) for class_index, row in enumerate(train_set)]hash_dict = defaultdict(list)for (hash_value, class_index) in hash_table :    hash_dict[hash_value].append(class_index)