#!/usr/bin/env python
# coding: utf-8

# # 09 - Introduction to Neural Networks
# 
# by [Fabio A. González](http://dis.unal.edu.co/~fgonza/), Universidad Nacional de Colombia
# 
# version 1.0, June 2018
# 
# ## Part of the class [Applied Deep Learning](https://github.com/albahnsen/AppliedDeepLearningClass)
# 
# 
# This notebook is licensed under a [Creative Commons Attribution-ShareAlike 3.0 Unported License](http://creativecommons.org/licenses/by-sa/3.0/deed.en_US). 
# 
# 
# To run this notebook you need to download Pybrain (https://github.com/pybrain/pybrain) and copy the `pybrain` folder to the same folder where this notebook is.
# 
# 

# In[2]:


import pybrain
import numpy as np
import pandas as pd
from matplotlib import pyplot as plt

get_ipython().run_line_magic('matplotlib', 'inline')


# ## Artificial Neuron
# 
# <img src="http://upload.wikimedia.org/wikipedia/commons/thumb/6/60/ArtificialNeuronModel_english.png/600px-ArtificialNeuronModel_english.png" >
# 
# $$o_j^{(n)} = \varphi\left(\sum_{i\; in\; layer (n-1)}w_{ij}o_i^{(n-1)} \right)$$

# ## Step activation function
# <img src="https://c.mql5.com/2/4/act1.png" align="middle">

# ## Logistic activation function
# 
# $$\varphi(x) = \frac{1}{1 - e^{-(x-b)}}$$
# 
# <img width= 300 src="http://upload.wikimedia.org/wikipedia/commons/thumb/b/b5/SigmoidFunction.png/400px-SigmoidFunction.png" align="middle">

# ### Question: How to program an artificial neuron to calculate the *and* function?

# <br>
# <table>
# <tr>
# <th>$X$</th>
# <th>$Y$</th>
# <th>$X$ and $Y$</th>
# </tr>
# <tr>
# <td>0</td>
# <td>0</td>
# <td style="text-align:center">0</td>
# </tr>
# <tr>
# <td>0</td>
# <td>1</td>
# <td style="text-align:center">0</td>
# </tr>
# <tr>
# <td>1</td>
# <td>0</td>
# <td style="text-align:center">0</td>
# </tr>
# <tr>
# <td>1</td>
# <td>1</td>
# <td style="text-align:center">1</td>
# </tr>
# </table>

# ## AND Neural Network
# 
# <img width=500 src="images/2in-neuron.jpg" align="middle">

# In[3]:


from pybrain.tools.shortcuts import buildNetwork
net = buildNetwork(2, 1, outclass=pybrain.SigmoidLayer)
print(net.params)


# In[4]:


def print_pred2(dataset, network):
    df = pd.DataFrame(dataset.data['sample'][:dataset.getLength()],columns=['X', 'Y'])
    prediction = np.round(network.activateOnDataset(dataset),3)
    df['output'] = pd.DataFrame(prediction)
    return df

from pybrain.datasets import UnsupervisedDataSet, SupervisedDataSet
D = UnsupervisedDataSet(2) # define a dataset in pybrain
D.addSample([0,0])
D.addSample([0,1])
D.addSample([1,0])
D.addSample([1,1])
print_pred2(D, net)


# ## AND Neural Network
# <img width=500 src="images/2in-neuron.jpg" align="middle">

# In[5]:


net.params[:] = [ -150, -100,  100]
print_pred2(D, net)


# ### Question: How to program an artificial neuron to calculate the *xor* function?
# <br/>
# <table>
# <tr>
# <th>$X$</th>
# <th>$Y$</th>
# <th>$X$ xor $Y$</th>
# </tr>
# <tr>
# <td>0</td>
# <td>0</td>
# <td style="text-align:center">0</td>
# </tr>
# <tr>
# <td>0</td>
# <td>1</td>
# <td style="text-align:center">1</td>
# </tr>
# <tr>
# <td>1</td>
# <td>0</td>
# <td style="text-align:center">1</td>
# </tr>
# <tr>
# <td>1</td>
# <td>1</td>
# <td style="text-align:center">0</td>
# </tr>
# </table>

# ## Plotting the NN Output

# In[6]:


def plot_nn_prediction(N): 
    # a function to plot the binary output of a network on the [0,1]x[0,1] space
    x_list = np.arange(0.0,1.0,0.025)
    y_list = np.arange(1.0,0.0,-0.025)    
    z = [0.0 if N.activate([x,y])[0] <0.5 else 1.0  for y in y_list for x in x_list]
    z = np.array(z)
    grid = z.reshape((len(x_list), len(y_list)))
    plt.imshow(grid, extent=(x_list.min(), x_list.max(), y_list.min(), y_list.max()),cmap=plt.get_cmap('Greys_r'))
    plt.show()


# ## Plotting the NN Output

# In[7]:


net.params[:] = [-20, -50, 50]
plot_nn_prediction(net)


# <br/>
# <br/>
# ## Answer: It is impossible with only one neuron!
# <br/>
# <br/>   

#   
# ## We need to use more than one neuron....

# ## Multilayer Neural Network
# <img src="http://www.cs.nott.ac.uk/~gxk/courses/g5aiai/006neuralnetworks/images/ffnet.jpg">

# ## Learning an XOR NN

# In[8]:


Dtrain = SupervisedDataSet(2,1) # define a dataset in pybrain
Dtrain.addSample([0,0],[0])
Dtrain.addSample([0,1],[1])
Dtrain.addSample([1,0],[1])
Dtrain.addSample([1,1],[0])

from pybrain.supervised.trainers import BackpropTrainer

net = buildNetwork(2, 2, 1, hiddenclass=pybrain.SigmoidLayer, outclass=pybrain.SigmoidLayer)
T = BackpropTrainer(net, learningrate=0.1, momentum=0.9)
T.trainOnDataset(Dtrain, 1000)
print_pred2(D, net)


# ## XOR NN Output Plot

# In[9]:


plot_nn_prediction(net)


# ## The Little Red Riding Hood Neural Network
# 
# <img src="http://themaleharem.com/wp-content/uploads/2014/06/Walter-crane-little-red-riding-hood-meets-the-wolf-in-the-woods.jpg">

# ## LRRH Network Architecture
# 
# <img src="images/lrrh_net.jpg">

# ## Training
# 

# In[10]:


from pybrain.tools.validation import Validator

validator =  Validator()
Dlrrh = SupervisedDataSet(4,4) 
Dlrrh.addSample([1,1,0,0],[1,0,0,0])
Dlrrh.addSample([0,1,1,0],[0,0,1,1])
Dlrrh.addSample([0,0,0,1],[0,1,1,0])
df = pd.DataFrame(Dlrrh['input'],columns=['Big Ears', 'Big Teeth', 'Handsome', 'Wrinkled'])
print (df.join(pd.DataFrame(Dlrrh['target'],columns=['Scream', 'Hug', 'Food', 'Kiss'])))
net = buildNetwork(4, 3, 4, hiddenclass=pybrain.SigmoidLayer, outclass=pybrain.SigmoidLayer)


# ## Backpropagation

# In[11]:


T = BackpropTrainer(net, learningrate=0.01, momentum=0.99)
scores = []
for i in range(1000):
    T.trainOnDataset(Dlrrh, 1)
    prediction = net.activateOnDataset(Dlrrh)
    scores.append(validator.MSE(prediction, Dlrrh.getField('target')))
plt.ylabel('Mean Square Error')
plt.xlabel('Iteration')
plt.plot(scores)


# ## Learning as optimization
# 
# General optimization problem:
# 
# $$\min_{f\in H}L(f,D)$$
# 
# with $H$: hypothesis space, $D$:training data, $L$:loss/error

# ## Example, least squares linear regression:
# $$\min_{f\in H}L(f,D)$$
# * Hypothesis space:
# $f(x)=w^{T}x$
# * Data: $D = \{(x_1, t_1), \dots , (x_n, t_n)\}$
# * Least squares loss: 
# $$L(f, D)=-\sum_{t_i \in D}(t_{i} - f(x_i))^2$$

# ## Example, logistic regression:
# $$\min_{f\in H}L(f,D)$$
# * Hypothesis space:
# $f(x)=P(C_{+}|x)=\sigma(w^{T}x)$
# * Data: $D = \{(x_1, t_1), \dots , (x_n, t_n)\}$
# * Cross-entropy error: 
# $$E(f,D)=-\ln p(D|f)=-\sum_{t_i \in D}(t_{n}\ln y_{n}+(1-t_{n})\ln(1-y_{n}))$$

# ## Gradient descent
# 
# <img src="https://s3-ap-south-1.amazonaws.com/av-blog-media/wp-content/uploads/2017/03/06100746/grad.png">

# ## Prediction

# In[12]:


def lrrh_input(vals):
    return pd.DataFrame(vals,index=['big ears', 'big teeth', 'handsome', 'wrinkled'], columns=['input'])

def lrrh_output(vals):
    return pd.DataFrame(vals,index=['scream', 'hug', 'offer food', 'kiss cheek'], columns=['output'])


# In[13]:


in_vals = [0, 0, 0, 0]
lrrh_input(in_vals)


# In[14]:


lrrh_output(net.activate(in_vals))