A series of handwriting algorithms for Python machine learning KNN classification

There are several evidences 2020-11-13 12:40:50
series handwriting algorithms python machine


In reality , Rich people's neighbors may also be rich , Poor people's neighbors may also be poor . If your neighbors are rich , that , You're probably rich too . Based on this , We have it. KNN Algorithm .KNN The full name is K-Nearest Neighbors, namely K The nearest neighbor . He passes through the nearest to the predicted point K Neighbors to predict the predicted point .

As shown in the figure below , The green circle is the predicted point . It's surrounded by red triangles and blue squares . If we take K by 3, that , Its three neighbors are two red triangles and a blue square . Because of its neighbors , Most of all, the red triangle , So we predict it's also the red triangle .

 Insert picture description here
( Figure 1 )

First , We load data . Here we have iris Data sets, for example .

import math
from collections import Counter
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.colors import ListedColormap
# Create color maps
cmap_light = ListedColormap(['orange', 'cyan', 'cornflowerblue'])
cmap_bold = ListedColormap(['darkorange', 'c', 'darkblue'])
from sklearn import neighbors, datasets
n_neighbors = 15
# import some data to play with
iris = datasets.load_iris()
# we only take the first two features. We could avoid this ugly
# slicing by using a two-dim dataset
X = iris.data[:, :2]
y = iris.target

next , Let's write a KNNClassifier class . here , The most important parameter, of course, is k, Or call it n_neighbors. next , Let's write a fit Method . This method is in addition to “ remember ” Out of data , Not doing anything . Because of this feature , Our name is KNN by lazy algorithm. In the prediction method predict_one in , We first calculate the distance between the predicted point and each point in the dataset , We got d i s t a n c e _ a r r a y distance\_array distance_array. We use it numpy Inside argsort function , Sort these distances from small to large , And get their coordinates . Before we take it k A coordinate , Get the corresponding label n e i g h b o u r _ l a b e l s neighbour\_labels neighbour_labels. We use it python Inside Counter Get the number of occurrences of each tag , And pick the most frequent tags m o s t _ f r e q u e n t most\_frequent most_frequent. thus , The prediction of a point is done . We map once predict_one, obtain predict Method .

class KNNClassifier():
X=None
y=None
n_neighbors=0
def __init__(self, n_neighbors=15):
self.n_neighbors=n_neighbors
def fit(self, X, y):
self.X=np.array(X)
self.y=np.array(y)
def predict_one(self, p):
distance_array=np.array(list(map(lambda o: math.dist(p, o), self.X)))
argsorted=np.argsort(distance_array)
neighbours = argsorted[:self.n_neighbors]
neighbour_labels = y[neighbours]
occurence_count = Counter(neighbour_labels)
most_frequent = occurence_count.most_common(1)[0][0]
return most_frequent
def predict(self, X):
y_hat = np.array(list(map(self.predict_one, X)))
return y_hat

Words are always pale , Let's make a picture .

knn = KNNClassifier()
knn.fit(X, y)
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
h = .02 # step size in the mesh
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = knn.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.figure()
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold,
edgecolor='k', s=20)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("My KNN (k = %i)"
% (n_neighbors))
plt.show()

 Insert picture description here
( Figure 2 )

Is our algorithm right ? Compare the Scikit-learn Well

# we create an instance of Neighbours Classifier and fit the data.
clf = neighbors.KNeighborsClassifier(n_neighbors)
clf.fit(X, y)
# Plot the decision boundary. For that, we will assign a color to each
# point in the mesh [x_min, x_max]x[y_min, y_max].
x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
h = .02 # step size in the mesh
xx, yy = np.meshgrid(np.arange(x_min, x_max, h),
np.arange(y_min, y_max, h))
Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
# Put the result into a color plot
Z = Z.reshape(xx.shape)
plt.pcolormesh(xx, yy, Z, cmap=cmap_light)
# Plot also the training points
plt.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold,
edgecolor='k', s=20)
plt.xlim(xx.min(), xx.max())
plt.ylim(yy.min(), yy.max())
plt.title("Scikit-learn KNN (k = %i)"
% (n_neighbors))
plt.show()

 Insert picture description here
( Figure 3 )

Visually, the two are almost the same .

other

K The choice of
From Figure 1, we can see , If we put k from 3 Change to 5, The result has changed . therefore ,k The choice of is very important .k It has to be big enough , Is of reference significance .k And it has to be small enough , Otherwise, it will degenerate to the average .

distance
The European distance we use here . You can also use Manhattan distance , Or write a distance function by yourself . Distance can also be used as weights , The closer you get , The greater the weight .

Data redundancy
Some data , With him or without him , It has no effect on the result , Or little impact . such as ,k=5, Yes 100 A collection of data , that , Only the edge points make sense . At this time , You can remove some points , bring knn The speed of prediction is greatly improved . At this time KNN It becomes CNN(Condensed nearest neighbors)

Unsupervised
Besides classification , Return to ,KNN It can also be used for anomaly detection . To the furthest neighbor k The distance to k-distance, Compare this value directly , The bigger it is, the more likely it is to be an outlier .

Source code

https://github.com/EricWebsmith/machine_learning_from_scrach

reference

https://scikit-learn.org/stable/auto_examples/neighbors/plot_classification.html

https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KNeighborsClassifier.html

https://en.wikipedia.org/wiki/K-nearest_neighbors_algorithm

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