深度学习基础系列（三）之用 sklearn 实现 KNN算法

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#深度学习 #python #sklearn #KNN

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本文介绍了K近邻算法的基本原理及应用，包括算法的历史背景、输入形式、具体步骤与细节，探讨了算法的优点与局限性，并通过sklearn库实现了算法的具体操作。

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1. 综述

 1.1 Cover和Hart在1968年提出了最初的邻近算法
 1.2 分类(classification)算法
 1.3 输入基于实例的学习(instance-based learning), 懒惰学习(lazy learning)

2. 例子：

这里写图片描述

未知电影属于什么类型？

这里写图片描述

3. 算法详述

3.1 步骤：

1）为了判断未知实例的类别，以所有已知类别的实例作为参照

2）选择参数K

3）计算未知实例与所有已知实例的距离

4）选择最近K个已知实例

5）根据少数服从多数的投票法则(majority-voting)，让未知实例归类为K个最邻近样本中最多数的类别

3.2 细节:

  关于K
  关于距离的衡量方法:

  3.2.1 Euclidean Distance 定义

这里写图片描述

其他距离衡量：余弦值（cos）, 相关度（correlation）, 曼哈顿距离（Manhattan distance）

3.3 举例

这里写图片描述

4. 算法优缺点：

4.1 算法优点

      简单

      易于理解

      容易实现

      通过对K的选择可具备丢噪音数据的健壮性


 4.2 算法缺点

这里写图片描述

 需要大量空间储存所有已知实例

 算法复杂度高（需要比较所有已知实例与要分类的实例）

 当其样本分布不平衡时，比如其中一类样本过大（实例数量过多）占主导的时候，新的未知实例容易被归类为这个主导样本，因为这类样本实例的数量过大，但这个新的未知实例实际并木接近目标样本

5、用 sklearn 实现

In [61]: from sklearn import neighbors

In [62]: from sklearn import datasets

In [63]: knn = neighbors.KNeighborsClassifier()

In [64]: iris = datasets.load_iris()

In [65]: print(iris.data)
[[ 5.1  3.5  1.4  0.2]
 [ 4.9  3.   1.4  0.2]
 [ 4.7  3.2  1.3  0.2]
 [ 4.6  3.1  1.5  0.2]
 [ 5.   3.6  1.4  0.2]
 [ 5.4  3.9  1.7  0.4]
 [ 4.6  3.4  1.4  0.3]
 [ 5.   3.4  1.5  0.2]
 [ 4.4  2.9  1.4  0.2]
 [ 4.9  3.1  1.5  0.1]
 [ 5.4  3.7  1.5  0.2]
 [ 4.8  3.4  1.6  0.2]
 [ 4.8  3.   1.4  0.1]
 [ 4.3  3.   1.1  0.1]
 [ 5.8  4.   1.2  0.2]
 [ 5.7  4.4  1.5  0.4]
 [ 5.4  3.9  1.3  0.4]
 [ 5.1  3.5  1.4  0.3]
 [ 5.7  3.8  1.7  0.3]
 [ 5.1  3.8  1.5  0.3]
 [ 5.4  3.4  1.7  0.2]
 [ 5.1  3.7  1.5  0.4]
 [ 4.6  3.6  1.   0.2]
 [ 5.1  3.3  1.7  0.5]
 [ 4.8  3.4  1.9  0.2]
 [ 5.   3.   1.6  0.2]
 [ 5.   3.4  1.6  0.4]
 [ 5.2  3.5  1.5  0.2]
 [ 5.2  3.4  1.4  0.2]
 [ 4.7  3.2  1.6  0.2]
 [ 4.8  3.1  1.6  0.2]
 [ 5.4  3.4  1.5  0.4]
 [ 5.2  4.1  1.5  0.1]
 [ 5.5  4.2  1.4  0.2]
 [ 4.9  3.1  1.5  0.1]
 [ 5.   3.2  1.2  0.2]
 [ 5.5  3.5  1.3  0.2]
 [ 4.9  3.1  1.5  0.1]
 [ 4.4  3.   1.3  0.2]
 [ 5.1  3.4  1.5  0.2]
 [ 5.   3.5  1.3  0.3]
 [ 4.5  2.3  1.3  0.3]
 [ 4.4  3.2  1.3  0.2]
 [ 5.   3.5  1.6  0.6]
 [ 5.1  3.8  1.9  0.4]
 [ 4.8  3.   1.4  0.3]
 [ 5.1  3.8  1.6  0.2]
 [ 4.6  3.2  1.4  0.2]
 [ 5.3  3.7  1.5  0.2]
 [ 5.   3.3  1.4  0.2]
 [ 7.   3.2  4.7  1.4]
 [ 6.4  3.2  4.5  1.5]
 [ 6.9  3.1  4.9  1.5]
 [ 5.5  2.3  4.   1.3]
 [ 6.5  2.8  4.6  1.5]
 [ 5.7  2.8  4.5  1.3]
 [ 6.3  3.3  4.7  1.6]
 [ 4.9  2.4  3.3  1. ]
 [ 6.6  2.9  4.6  1.3]
 [ 5.2  2.7  3.9  1.4]
 [ 5.   2.   3.5  1. ]
 [ 5.9  3.   4.2  1.5]
 [ 6.   2.2  4.   1. ]
 [ 6.1  2.9  4.7  1.4]
 [ 5.6  2.9  3.6  1.3]
 [ 6.7  3.1  4.4  1.4]
 [ 5.6  3.   4.5  1.5]
 [ 5.8  2.7  4.1  1. ]
 [ 6.2  2.2  4.5  1.5]
 [ 5.6  2.5  3.9  1.1]
 [ 5.9  3.2  4.8  1.8]
 [ 6.1  2.8  4.   1.3]
 [ 6.3  2.5  4.9  1.5]
 [ 6.1  2.8  4.7  1.2]
 [ 6.4  2.9  4.3  1.3]
 [ 6.6  3.   4.4  1.4]
 [ 6.8  2.8  4.8  1.4]
 [ 6.7  3.   5.   1.7]
 [ 6.   2.9  4.5  1.5]
 [ 5.7  2.6  3.5  1. ]
 [ 5.5  2.4  3.8  1.1]
 [ 5.5  2.4  3.7  1. ]
 [ 5.8  2.7  3.9  1.2]
 [ 6.   2.7  5.1  1.6]
 [ 5.4  3.   4.5  1.5]
 [ 6.   3.4  4.5  1.6]
 [ 6.7  3.1  4.7  1.5]
 [ 6.3  2.3  4.4  1.3]
 [ 5.6  3.   4.1  1.3]
 [ 5.5  2.5  4.   1.3]
 [ 5.5  2.6  4.4  1.2]
 [ 6.1  3.   4.6  1.4]
 [ 5.8  2.6  4.   1.2]
 [ 5.   2.3  3.3  1. ]
 [ 5.6  2.7  4.2  1.3]
 [ 5.7  3.   4.2  1.2]
 [ 5.7  2.9  4.2  1.3]
 [ 6.2  2.9  4.3  1.3]
 [ 5.1  2.5  3.   1.1]
 [ 5.7  2.8  4.1  1.3]
 [ 6.3  3.3  6.   2.5]
 [ 5.8  2.7  5.1  1.9]
 [ 7.1  3.   5.9  2.1]
 [ 6.3  2.9  5.6  1.8]
 [ 6.5  3.   5.8  2.2]
 [ 7.6  3.   6.6  2.1]
 [ 4.9  2.5  4.5  1.7]
 [ 7.3  2.9  6.3  1.8]
 [ 6.7  2.5  5.8  1.8]
 [ 7.2  3.6  6.1  2.5]
 [ 6.5  3.2  5.1  2. ]
 [ 6.4  2.7  5.3  1.9]
 [ 6.8  3.   5.5  2.1]
 [ 5.7  2.5  5.   2. ]
 [ 5.8  2.8  5.1  2.4]
 [ 6.4  3.2  5.3  2.3]
 [ 6.5  3.   5.5  1.8]
 [ 7.7  3.8  6.7  2.2]
 [ 7.7  2.6  6.9  2.3]
 [ 6.   2.2  5.   1.5]
 [ 6.9  3.2  5.7  2.3]
 [ 5.6  2.8  4.9  2. ]
 [ 7.7  2.8  6.7  2. ]
 [ 6.3  2.7  4.9  1.8]
 [ 6.7  3.3  5.7  2.1]
 [ 7.2  3.2  6.   1.8]
 [ 6.2  2.8  4.8  1.8]
 [ 6.1  3.   4.9  1.8]
 [ 6.4  2.8  5.6  2.1]
 [ 7.2  3.   5.8  1.6]
 [ 7.4  2.8  6.1  1.9]
 [ 7.9  3.8  6.4  2. ]
 [ 6.4  2.8  5.6  2.2]
 [ 6.3  2.8  5.1  1.5]
 [ 6.1  2.6  5.6  1.4]
 [ 7.7  3.   6.1  2.3]
 [ 6.3  3.4  5.6  2.4]
 [ 6.4  3.1  5.5  1.8]
 [ 6.   3.   4.8  1.8]
 [ 6.9  3.1  5.4  2.1]
 [ 6.7  3.1  5.6  2.4]
 [ 6.9  3.1  5.1  2.3]
 [ 5.8  2.7  5.1  1.9]
 [ 6.8  3.2  5.9  2.3]
 [ 6.7  3.3  5.7  2.5]
 [ 6.7  3.   5.2  2.3]
 [ 6.3  2.5  5.   1.9]
 [ 6.5  3.   5.2  2. ]
 [ 6.2  3.4  5.4  2.3]
 [ 5.9  3.   5.1  1.8]]

In [66]: print(iris.target)
[0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2
 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2
 2 2]

In [67]: knn.fit(iris.data, iris.target)
Out[67]: 
KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',
           metric_params=None, n_jobs=1, n_neighbors=5, p=2,
           weights='uniform')

In [68]: newLbale = [1, 2, 5, 7]
In [70]: knn.predict(newLbale)
/Users/xiaolian/anaconda/lib/python3.6/site-packages/sklearn/utils/validation.py:395: DeprecationWarning: Passing 1d arrays as data is deprecated in 0.17 and will raise ValueError in 0.19. Reshape your data either using X.reshape(-1, 1) if your data has a single feature or X.reshape(1, -1) if it contains a single sample.
  DeprecationWarning)
Out[70]: array([2])

In [71]: newLable = [2, 3, 8, 9]

In [72]: knn.predict(newLable)
/Users/xiaolian/anaconda/lib/python3.6/site-packages/sklearn/utils/validation.py:395: DeprecationWarning: Passing 1d arrays as data is deprecated in 0.17 and will raise ValueError in 0.19. Reshape your data either using X.reshape(-1, 1) if your data has a single feature or X.reshape(1, -1) if it contains a single sample.
  DeprecationWarning)
Out[72]: array([2])

In [73]: newLbale = [1, 1, 1, 1]

In [74]: knn.predict(newLable)
/Users/xiaolian/anaconda/lib/python3.6/site-packages/sklearn/utils/validation.py:395: DeprecationWarning: Passing 1d arrays as data is deprecated in 0.17 and will raise ValueError in 0.19. Reshape your data either using X.reshape(-1, 1) if your data has a single feature or X.reshape(1, -1) if it contains a single sample.
  DeprecationWarning)
Out[74]: array([2])

In [75]: knn.predict([0.1,0.2,0.3,0.4])
/Users/xiaolian/anaconda/lib/python3.6/site-packages/sklearn/utils/validation.py:395: DeprecationWarning: Passing 1d arrays as data is deprecated in 0.17 and will raise ValueError in 0.19. Reshape your data either using X.reshape(-1, 1) if your data has a single feature or X.reshape(1, -1) if it contains a single sample.
  DeprecationWarning)
Out[75]: array([0])