Practical work KNN algorithm

EDUCATION IN ARTIFICIAL INTELLIGENCE

K NEAREST NEIGHBORS ALGORITHM

PREREQUISITES KNOWLEDGE PYTHON • • • • • • MATHEMATICS 𝑎(𝑥1 , 𝑦1 ) 𝑒𝑡 𝑏(𝑥2 , 𝑦2 ) 𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2

SOFTWARE

MATERIALS

INTRODUCTION

ACTIVITY STEPS

DISCOVERY OF THE K NEAREST NEIGHBORS IN THE SOFTWARE → →

→

→

→

TRAINING PHASE

• •

• •

Connect the robot

.

TEST PHASE •

PROGRAM THE K NEAREST NEIGHBORS ALGORITHM → →

→

→

→

def 𝑡𝑎𝑘𝑒_𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛(𝑠𝑒𝑛𝑠𝑜𝑟𝑠: 𝑙𝑖𝑠𝑡) → 𝑖𝑛𝑡

PROGRAMMING THE ALGORITHM DISTANCE CALCULATION

def 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑎: 𝑙𝑖𝑠𝑡, 𝑏: 𝑙𝑖𝑠𝑡) → 𝑓𝑙𝑜𝑎𝑡 𝑎 = [𝑥1 , 𝑦1 ] 𝑒𝑡 𝑏 = [𝑥2 , 𝑦2 ]

𝑑 = √(𝑥2 − 𝑥1 )2 + (𝑦2 − 𝑦1 )2

import math

y = math.sqrt(x)

y = x**2

# compute distance a = [0, 0] b = [1, 2] print("distance", distance(a, b))

COMPUTATION OF ALL DISTANCES

def 𝑎𝑙𝑙_𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒𝑠(𝑎: 𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡], 𝑡𝑟𝑎𝑖𝑛_𝑠𝑒𝑛𝑠𝑜𝑟𝑠: 𝑙𝑖𝑠𝑡[𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡]]) → 𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡] 𝑎 = [𝑥0 , 𝑦0 ]

𝑡𝑟𝑎𝑖𝑛_𝑠𝑒𝑛𝑠𝑜𝑟𝑠 = [[𝑥1 , 𝑦1 ], [𝑥2 , 𝑦2 ], … , [𝑥𝑛 , 𝑦𝑛 ]]

# compute all distances a = [0.4, 0.6] train_sensors = [[0, 0], [0, 1], [1, 0]] distance_list = all_distances(a, train_sensors) print('distances to data', distance_list)

FIND THE SMALLEST ELEMENT OF AN ARRAY

def 𝑓𝑖𝑛𝑑_𝑚𝑖𝑛𝑖𝑚𝑢𝑚(𝑑𝑙𝑖𝑠𝑡: 𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡]) → 𝑖𝑛𝑡

# minimum in a list idx_min = find_minimum(distance_list) print('index of minimum', idx_min)

NEAREST NEIGHBOR

def 𝑛𝑒𝑎𝑟𝑒𝑠𝑡_𝑛𝑒𝑖𝑔ℎ𝑏𝑜𝑟_𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛(𝑡𝑟𝑎𝑖𝑛_𝑠𝑒𝑛𝑠𝑜𝑟𝑠: 𝑙𝑖𝑠𝑡[𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡]], 𝑡𝑟𝑎𝑖𝑛_𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝑠: 𝑙𝑖𝑠𝑡[𝑖𝑛𝑡], 𝑎: 𝑙𝑖𝑠𝑡[𝑓𝑙𝑜𝑎𝑡]) → 𝑖𝑛𝑡

[𝑑1 , … , 𝑑𝑛 ]

𝑎 = [𝑥0 , 𝑦0 ] 𝑎𝑛𝑑 𝑡𝑟𝑎𝑖𝑛_𝑠𝑒𝑛𝑠𝑜𝑟𝑠 = [[𝑥1 , 𝑦1 ], [𝑥2 , 𝑦2 ], … , [𝑥𝑛 , 𝑦𝑛 ]] [𝑥𝑖 , 𝑦𝑖 ] 𝑑𝑖

𝑡𝑟𝑎𝑖𝑛_𝑑𝑒𝑐𝑖𝑠𝑖𝑜𝑛𝑠 =

# KNN a = [0.4, 0.6] train_sensors = [[0, 0], [0, 1], [1, 0]] train_decisions = [1, 2, 0] decision = nearest_neighbor_decision(train_sensors, train_decisions, a) print('KNN', decision)

USE OF YOUR ALGORITHM WITH THE ROBOT

train_sensors = train_decisions = None def learn(X_train, y_train): global train_sensors, train_decisions train_sensors, train_decisions = X_train, y_train loss = 0 return loss def take_decision(sensors): if train_sensors is None: return 0 return nearest_neigbor_decision(train_sensors, train_decisions, sensors)

TO GO FURTHER K NEAREST NEIGHBOURS

𝑘> 1, 𝑘 ∈ ℕ

INTRODUCTION TO NEURAL NETWORKS

CONCLUSION Notions learned : Supervised learning: By giving the robot a consistent dataset and an algorithm, it was able to generalise its decision making to situations it did not know before by approximating what was done before.

Nearest Neighbour Algorithm: By implementing classical algorithms such as calculating a distance or finding a minimum in a list, we discover that it is possible to program a machine learning program ourselves