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KNN random circles

Fixel Algorithms

KNN random circles#

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Revision History#

Version

Date

User

Content / Changes

1.0.000

09/03/2024

Royi Avital

First version

Open In Colab

# Import Packages

# General Tools
import numpy as np
import scipy as sp
import pandas as pd

# Machine Learning
from sklearn.datasets import make_circles
from sklearn.neighbors import KNeighborsClassifier

# Image Processing

# Machine Learning

# Miscellaneous
import math
import os
from platform import python_version
import random
import timeit

# Typing
from typing import Callable, Dict, List, Optional, Set, Tuple, Union

# Visualization
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns

# Jupyter
from IPython import get_ipython
from IPython.display import Image, display
from ipywidgets import Dropdown, FloatSlider, interact, IntSlider, Layout

Notations#

  • (?) Question to answer interactively.

  • (!) Simple task to add code for the notebook.

  • (@) Optional / Extra self practice.

  • (#) Note / Useful resource / Food for thought.

Code Notations:

someVar    = 2; #<! Notation for a variable
vVector    = np.random.rand(4) #<! Notation for 1D array
mMatrix    = np.random.rand(4, 3) #<! Notation for 2D array
tTensor    = np.random.rand(4, 3, 2, 3) #<! Notation for nD array (Tensor)
tuTuple    = (1, 2, 3) #<! Notation for a tuple
lList      = [1, 2, 3] #<! Notation for a list
dDict      = {1: 3, 2: 2, 3: 1} #<! Notation for a dictionary
oObj       = MyClass() #<! Notation for an object
dfData     = pd.DataFrame() #<! Notation for a data frame
dsData     = pd.Series() #<! Notation for a series
hObj       = plt.Axes() #<! Notation for an object / handler / function handler

Code Exercise#

  • Single line fill

vallToFill = ???

  • Multi Line to Fill (At least one)

# You need to start writing
????

  • Section to Fill

#===========================Fill This===========================#
# 1. Explanation about what to do.
# !! Remarks to follow / take under consideration.
mX = ???

???
#===============================================================#

# Configuration
# %matplotlib inline

seedNum = 512
np.random.seed(seedNum)
random.seed(seedNum)

# Matplotlib default color palette
lMatPltLibclr = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd', '#8c564b', '#e377c2', '#7f7f7f', '#bcbd22', '#17becf']
# sns.set_theme() #>! Apply SeaBorn theme

runInGoogleColab = 'google.colab' in str(get_ipython())

# Constants

FIG_SIZE_DEF    = (8, 8)
ELM_SIZE_DEF    = 50
CLASS_COLOR     = ('b', 'r')
EDGE_COLOR      = 'k'
MARKER_SIZE_DEF = 10
LINE_WIDTH_DEF  = 2

# Courses Packages
import sys
sys.path.append('../')
sys.path.append('../../')
sys.path.append('../../../')
from utils.DataVisualization import Plot2DLinearClassifier, PlotBinaryClassData

# General Auxiliary Functions

# Parameters

# Data Generation
numCircles0 = 250
numCircles1 = 250
numSwaps    = 50 #<! Number of samples to swap between inner circle and outer circle
noiseLevel  = 0.03


# Data Visualization
elmSize     = ELM_SIZE_DEF
classColor0 = CLASS_COLOR[0]
classColor1 = CLASS_COLOR[1]

numGridPts = 250

Generate / Load Data#

# Generate Data
numCircles = numCircles0 + numCircles1
mX, vY     = make_circles((numCircles0, numCircles1), shuffle = False, noise = noiseLevel, random_state = seedNum)

print(f'The features data shape: {mX.shape}')
print(f'The labels data shape: {vY.shape}')

The features data shape: (500, 2)
The labels data shape: (500,)

# Swap Data Samples
# Swapping some samples between the classes.
# The first numCircles0 are for class 0.
vSwapIdx = np.random.choice(numCircles0, numSwaps, replace = False)
vY[vSwapIdx] = 1
vSwapIdx = numCircles0 + np.random.choice(numCircles1, numSwaps, replace = False)
vY[vSwapIdx] = 0

Plot the Data#

# Display the Data

hA = PlotBinaryClassData(mX, vY)
hA.set_xlabel('x1')
hA.set_ylabel('x2')

Text(0, 0.5, 'x2')
../../../../_images/d257d4447e429ae73f478ce8079031b00cf2894460c98140ac976b0cfe957f84.png

Train a K-NN Classifier#

The K-NN classifier, given a new sample \(\boldsymbol{x}_{i}\) basically do as following:

  1. Find the K nearest samples (By the chosen distance function) to the given point.

  2. Build an histogram of the classes of the K points.

  3. Set the class of \(\boldsymbol{x}_{i}\) to be the \(\arg \max\) of the histogram.

(?) In case there is non unique \(\arg \max\) in (3), what should be done?
(?) Can you think on alternative decision rules for step (3)? - sum of distances???

# Grid of the data support
v0       = np.linspace(mX[:, 0].min() - 0.1, mX[:, 0].max() + 0.1, numGridPts)
v1       = np.linspace(mX[:, 1].min() - 0.1, mX[:, 1].max() + 0.1, numGridPts)
XX0, XX1 = np.meshgrid(v0, v1)
XX       = np.c_[XX0.ravel(), XX1.ravel()]

def PlotKnn( K ):
    # Train the a K-NN classifier
    oKnnClassifier = KNeighborsClassifier(n_neighbors = K, p = 2).fit(mX, vY) #<! Training on the data
    
    # Plot classification
    Z = oKnnClassifier.predict(XX) #<! Prediction on the grid (The support)
    Z = Z.reshape(XX0.shape)

    hF, hA = plt.subplots(figsize = (8, 8))
    hA = PlotBinaryClassData(mX, vY, hA = hA, axisTitle = f'K-NN Classifier - $K = {K}$')
    hA.contourf(XX0, XX1, Z, colors = [classColor0, classColor1], alpha = 0.3, levels = [-0.5, 0.5, 1.5])

# Display the Geometry of the Classifier

kSlider = IntSlider(min = 1, max = 21, step = 2, value = 1, layout = Layout(width = '30%'))
interact(PlotKnn, K = kSlider)

plt.show()
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