Perceptron

Perceptron¶

In [1]:

import numpy as np
import pandas as pd

import numpy as np import pandas as pd

1. Data preparation¶

In [2]:

def prepare_data(csv):
    # Getting data ready
    data = pd.read_csv(csv)

    # Data normalisation
    data['Age'] = data['Age'] / 100

    # z-score normalisation
    data['Income'] = (data['Income'] - data['Income'].mean()) / data['Income'].std()
    data['Previous Purchases'] = (data['Previous Purchases'] - data['Previous Purchases'].mean()) / data['Previous Purchases'].std()

    return data

def prepare_data(csv): # Getting data ready data = pd.read_csv(csv) # Data normalisation data['Age'] = data['Age'] / 100 # z-score normalisation data['Income'] = (data['Income'] - data['Income'].mean()) / data['Income'].std() data['Previous Purchases'] = (data['Previous Purchases'] - data['Previous Purchases'].mean()) / data['Previous Purchases'].std() return data

2. Setting up the perceptron¶

In [3]:

def prepare_matrices(data):
    # Prepare input matrix and prediction matrix
    X = []
    Y = []
    for idx, rows in data.iterrows():
        x, y = rows.iloc[:-1].to_numpy(), rows.iloc[-1]
        X.append(x)
        Y.append(y)

    X = np.array(X)
    Y = np.array(Y)

    return X, Y

def prepare_matrices(data): # Prepare input matrix and prediction matrix X = [] Y = [] for idx, rows in data.iterrows(): x, y = rows.iloc[:-1].to_numpy(), rows.iloc[-1] X.append(x) Y.append(y) X = np.array(X) Y = np.array(Y) return X, Y

In [4]:

def get_weights_bias(input_size):
    # Init weights
    W = np.random.rand(input_size)

    # init weights
    b = np.random.rand(1)

    return W, b

def get_weights_bias(input_size): # Init weights W = np.random.rand(input_size) # init weights b = np.random.rand(1) return W, b

In [7]:

data = prepare_data('../data/purchase_prediction.csv')
X, Y = prepare_matrices(data)
W, b = get_weights_bias(X.shape[1])

data = prepare_data('../data/purchase_prediction.csv') X, Y = prepare_matrices(data) W, b = get_weights_bias(X.shape[1])

3. Training¶

In [8]:

# Sigmoid activation
def sigmoid(H):
    return 1 / (1 + np.exp(-H))

# BCE 
def cross_entropy(y, y_pred):
    y_pred = np.clip(y_pred, 1e-9, 1 - 1e-9)
    return -np.sum(y*np.log(y_pred) + (1-y)*np.log(1-y_pred)) / len(y)

# BCE grad
def cross_entropy_grad(y, y_pred):
    return -np.mean((y/y_pred) + ((1-y)/(1-y_pred)))

# Sigmoid activation def sigmoid(H): return 1 / (1 + np.exp(-H)) # BCE def cross_entropy(y, y_pred): y_pred = np.clip(y_pred, 1e-9, 1 - 1e-9) return -np.sum(y*np.log(y_pred) + (1-y)*np.log(1-y_pred)) / len(y) # BCE grad def cross_entropy_grad(y, y_pred): return -np.mean((y/y_pred) + ((1-y)/(1-y_pred)))

In [9]:

epochs = 100000
lr = 0.01
print_after = 10000

for epoch in range(1, epochs+1):
    ###
    # feed forward
    # sum
    H = np.matmul(X, W) + b

    # activation
    A = sigmoid(H)

    # calc binary cross entropy loss
    loss = cross_entropy(Y, A)

    ###
    # backpropagate
    dz = A - Y
    dw = (1/len(Y)) * np.matmul(X.T, dz)
    db = (1/len(Y)) * np.sum(dz)

    # update weights
    W = W - lr*dw
    b = b - lr*db

    if epoch % print_after == 0:
        print(f"Epoch: {epoch}/{epochs}| Loss: {loss}")

epochs = 100000 lr = 0.01 print_after = 10000 for epoch in range(1, epochs+1): ### # feed forward # sum H = np.matmul(X, W) + b # activation A = sigmoid(H) # calc binary cross entropy loss loss = cross_entropy(Y, A) ### # backpropagate dz = A - Y dw = (1/len(Y)) * np.matmul(X.T, dz) db = (1/len(Y)) * np.sum(dz) # update weights W = W - lr*dw b = b - lr*db if epoch % print_after == 0: print(f"Epoch: {epoch}/{epochs}| Loss: {loss}")

Epoch: 10000/100000| Loss: 0.14486881031094775
Epoch: 20000/100000| Loss: 0.12188557399732414
Epoch: 30000/100000| Loss: 0.10799112930053398
Epoch: 40000/100000| Loss: 0.09740161380919043
Epoch: 50000/100000| Loss: 0.08875526442831948
Epoch: 60000/100000| Loss: 0.08147343673857062
Epoch: 70000/100000| Loss: 0.0752295171311487
Epoch: 80000/100000| Loss: 0.06980930346019368
Epoch: 90000/100000| Loss: 0.06505985371220571
Epoch: 100000/100000| Loss: 0.060866222059249894

Testing¶

In [11]:

x_1 = np.array([0.32, 0.671181, 0.493606])
x_2 = np.array([0.48, -0.979264, -0.211545])
def predict(input_x):
    H = np.matmul(input_x, W)
    A = sigmoid(H)
    print(A)
    if A > 0.5:
        print(1)
    else:
        print(0)

predict(x_1) # 1
predict(x_2) # 0

x_1 = np.array([0.32, 0.671181, 0.493606]) x_2 = np.array([0.48, -0.979264, -0.211545]) def predict(input_x): H = np.matmul(input_x, W) A = sigmoid(H) print(A) if A > 0.5: print(1) else: print(0) predict(x_1) # 1 predict(x_2) # 0

0.9968600634790575
1
0.0006271349965844889
0

In [12]:

data

data

Out[12]:

	Age	Income	Previous Purchases	Purchased
0	0.25	-0.429116	-0.916696	0
1	0.32	0.671181	0.493606	1
2	0.48	-0.979264	-0.211545	0
3	0.18	-1.254339	-0.916696	0
4	0.65	1.771478	1.198756	1
5	0.42	0.396107	-0.916696	0
6	0.28	-0.539146	-0.211545	1
7	0.55	1.221330	1.903907	1
8	0.35	0.011003	0.493606	1
9	0.22	-0.869235	-0.916696	0

In [ ]: