k近邻

应用场景

• 产品推荐和推荐引擎

• 自然语言处理 (NLP) 算法的相关性排名

• 图像或视频的相似性搜索

过程

• 计算训练样本和测试样本中每个样本之间的距离

• 对距离进行排序

• 选择距离最小的k个样本: K小，噪音多，K大，边界模糊

• 根据k个样本的标签进行投票, 得到分类类别

距离

• 欧几里得距离

• 明可夫斯基距离

• 曼哈顿距离

• 余弦相似度

优化

• NDTree

• Approximate kNN 加速服务

  • Tree-based ANN

  • Locality-sensitive hashing (LSH)

  • Clustering based

• faiss

问答

Pros:

• Almost no assumption on f other than smoothness

• High capacity/complexity

• High accuracy given a large training set

• Supports online training (by simply memorizing)

• Readily extensible to multi-class and regression problems

Cons:

• Storage demanding

• Sensitive to outliers

• Sensitive to irrelevant data features (vs. decision trees)

• Needs to deal with missing data (e.g., special distances)

• Computationally expensive: O(ND) time for making each prediction

• Can speed up with index and/or approximation

code

# https://towardsdatascience.com/create-your-own-k-nearest-neighbors-algorithm-in-python-eb7093fc6339
import numpy as np

def eu_dist(x_train, x_test):
    distances = []
    for x_cur in x_train:
        distance = np.sqrt(np.sum((x_cur - x_test) ** 2))
        distances.append(distance)
    return distances

def KNN(x_train, y_train, x_test, k):
    # convert to numpy array
    x_train = np.array(x_train)
    y_train = np.array(y_train)
    x_test = np.array(x_test)

    # calculate the distance between x_train and x_test
    distances = eu_dist(x_train, x_test)
    # sort the distance and find the top-k in y_train
    dist_index = np.argsort(distances)[:k]
    topk_y = [y_train[index] for index in dist_index]

    # count the frequency in y_train
    dict = {}
    for y_cur in topk_y:
        y_cur = y_cur[0]
        dict[y_cur] = dict.get(y_cur, 0) + 1

    dict = list(dict.items())
    dict = sorted(dict, key=lambda x: x[1], reverse= True)

    # return the highest frequent value
    predict = dict[0][0]
    return predict

x_train = [[73.84, 241.89],
       [68.78, 162.31],
       [74.11, 212.74],
       [74.73, 220.04],
       [69.88, 206.34],
       [67.25, 152.21],
       [63.45, 156.39]
    ]

y_train = [
       [1],
       [1],
       [2],
       [1],
       [1],
       [2],
       [2],
       [1],
]

print(KNN(x_train, y_train, x_test, k))