def loss(X, Y, W):
"""
Calculate error by cosine similarity method
PARAMETERS
==========
X:ndarray(dtype=float,ndim=1)
input vector
Y:ndarray(dtype=float)
output vector
W:ndarray(dtype=float)
Weights
RETURNS
=======
Percentage of error in the actural value and predicted value
"""
sigmoid = Sigmoid()
H = sigmoid.activation(np.dot(X, W).T)
DP = np.sum(np.dot(H, Y))
S = DP/((np.sum(np.square(H))**(0.5))*(np.sum(np.square(Y))**(0.5)))
dissimilarity = 1-S
return dissimilarity*(np.sum(np.square(Y))**(0.5))
def predict(self, X):
"""
Predict the Probabilistic Value of
Input, in accordance with
Logistic Regression Model.
PARAMETERS
==========
X: ndarray(dtype=float,ndim=1)
1-D Array of Dataset's Input.
prediction: ndarray(dtype=float,ndim=1)
1-D Array of Predicted Values
corresponding to each Input of
Dataset.
RETURNS
=======
ndarray(dtype=float,ndim=1)
1-D Array of Probabilistic Values
of whether the particular Input
belongs to class 0 or class 1.
"""
prediction = np.dot(X, self.weights).T
sigmoid = Sigmoid()
return sigmoid.activation(prediction)
def classify(self, X):
"""
Classify the Input, according to
Logistic Regression Model,i.e in this
case, either class 0 or class 1.
PARAMETERS
==========
X: ndarray(dtype=float,ndim=1)
1-D Array of Dataset's Input.
prediction: ndarray(dtype=float,ndim=1)
1-D Array of Predicted Values
corresponding to their Inputs.
actual_predictions: ndarray(dtype=int,ndim=1)
1-D Array of Output, associated
to each Input of Dataset,
Predicted by Trained Logistic
Regression Model.
RETURNS
=======
ndarray
1-D Array of Predicted classes
(either 0 or 1) corresponding
to their inputs.
"""
prediction = np.dot(X, self.weights).T
sigmoid = Sigmoid()
prediction = sigmoid.activation(prediction)
actual_predictions = np.zeros((1, X.shape[0]))
for i in range(prediction.shape[1]):
if prediction[0][i] > 0.5:
actual_predictions[0][i] = 1
return actual_predictions
def derivative(X, Y, W):
"""
Calculate derivative for logarithmic error method.
PARAMETERS
==========
X:ndarray(dtype=float,ndim=1)
input vector
Y:ndarray(dtype=float)
output vector
W:ndarray(dtype=float)
Weights
RETURNS
=======
array of derivates
"""
M = X.shape[0]
sigmoid = Sigmoid()
H = sigmoid.activation(np.dot(X, W).T)
return (1/M)*(np.dot(X.T, (H-Y).T))
def loss(X, Y, W):
"""
Calculate loss by logarithmic error method.
PARAMETERS
==========
X:ndarray(dtype=float,ndim=1)
input vector
Y:ndarray(dtype=float)
output vector
W:ndarray(dtype=float)
Weights
RETURNS
=======
array of logarithmic losses
"""
M = X.shape[0]
sigmoid = Sigmoid()
H = sigmoid.activation(np.dot(X, W).T)
return (1/M)*(np.sum((-Y)*np.log(H)-(1-Y)*np.log(1-H)))
def loss(X, Y, W):
"""
Calculate Mean Squared Log Loss
PARAMETERS
==========
X:ndarray(dtype=float,ndim=1)
input vector
Y:ndarray(dtype=float)
output vector
W:ndarray(dtype=float)
Weights
RETURNS
=======
array of mean of logarithmic losses
"""
M = X.shape[0]
sigmoid = Sigmoid()
H = sigmoid.activations(np.dot(X, W).T)
return np.sqrt((1 / M) * (np.sum(np.log(Y + 1) - np.log(H + 1))))
def Plot(self,
X,
Y,
actual_predictions,
optimizer=GradientDescent,
epochs=25,
zeros=False
):
"""
Plots for Logistic Regression.
PARAMETERS
==========
X: ndarray(dtype=float,ndim=1)
1-D Array of Dataset's Input.
Y: ndarray(dtype=float,ndim=1)
1-D Array of Dataset's Output.
actual_predictions: ndarray(dtype=int,ndim=1)
1-D Array of Output, associated
to each Input of Dataset,
Predicted by Trained Logistic
Regression Model.
optimizer: class
Class of one of the Optimizers like
AdamProp,SGD,MBGD,GradientDescent etc
epochs: int
Number of times, the loop to calculate loss
and optimize weights, will going to take
place.
error: float
The degree of how much the predicted value
is diverted from actual values, given by implementing
one of choosen loss functions from loss_func.py .
zeros: boolean
Condition to initialize Weights as either
zeroes or some random decimal values.
RETURNS
=======
2-D graph of Sigmoid curve,
Comparision Plot of True output and Predicted output versus Feacture.
2-D graph of Loss versus Number of iterations.
"""
Plot = plt.figure(figsize=(8, 8))
plot1 = Plot.add_subplot(2, 2, 1)
plot2 = Plot.add_subplot(2, 2, 2)
plot3 = Plot.add_subplot(2, 2, 3)
# 2-D graph of Sigmoid curve.
x = np.linspace(- max(X[:, 0]) - 2, max(X[:, 0]) + 2, 1000)
plot1.set_title('Sigmoid curve')
plot1.grid()
sigmoid = Sigmoid()
plot1.scatter(X.T[0], Y, color="red", marker="+", label="labels")
plot1.plot(x, 0*x+0.5, linestyle="--", label="Decision bound, y=0.5")
plot1.plot(x, sigmoid.activation(x),
color="green", label='Sigmoid function: 1 / (1 + e^-x)'
)
plot1.legend()
# Comparision Plot of Actual output and Predicted output vs Feacture.
plot2.set_title('Actual output and Predicted output versus Feacture')
plot2.set_xlabel("x")
plot2.set_ylabel("y")
plot2.scatter(X[:, 0], Y, color="orange", label='Actual output')
plot2.grid()
plot2.scatter(X[:, 0], actual_predictions,
color="blue", marker="+", label='Predicted output'
)
plot2.legend()
# 2-D graph of Loss versus Number of iterations.
plot3.set_title("Loss versus Number of iterations")
plot3.set_xlabel("iterations")
plot3.set_ylabel("Cost")
iterations = []
cost = []
self.weights = generate_weights(X.shape[1], 1, zeros=zeros)
for epoch in range(1, epochs + 1):
iterations.append(epoch)
self.weights = optimizer.iterate(X, Y, self.weights)
error = optimizer.loss_func.loss(X, Y, self.weights)
cost.append(error)
plot3.plot(np.array(iterations), np.array(cost))
plt.show()