2. Case Study with a Small Neural Net
x2
x3
x1
x4
(I5,O5)
(I6,O6)
(I7,O7)
W1,5
W1,6
W2,5
W2,6
W3,6
W3,5
W4,6
W4,5
W5,7
W6,7
Input Nodes Hidden Nodes Output Nodes
x1
x2
x3
x4
3. Case Study with a Small Neural Net
(I2,O2)
(I3,O3)
(I1,O1)
(I4,O4)
(I5,O5)
(I6,O6)
(I7,O7)
W1,5
W1,6
W2,5
W2,6
W3,6
W3,5
W4,6W4,5
W5,7
W6,7
x1
x2
x3
x4
4. Case Study with a Small Neural Net
(I2,O2)
(I3,O3)
(I1,O1)
(I4,O4)
(I5,O5)
(I6,O6)
(I7,O7)
W1,5
W1,6
W2,5
W2,6
W3,6
W3,5
W4,6W4,5
W5,7
W6,7
x1
x2
x3
x4
5. Input Data Set
x1 x2 x 3 x4 Y
1 5.1 3.5 1.4 0.2 0.0
2 4.9 3.0 1.4 0.2 0.0
3 6.3 3.3 6.0 2.5 1.0
4 5.8 2.7 5.1 1.9 1.0
5 7.1 3.0 5.9 2.1 1.0
6 6.3 2.9 5.6 1.8 1.0
7 6.5 3.0 5.8 2.2 1.0
8 5.0 3.4 1.5 0.2 0.0
9 4.4 2.9 1.4 0.2 0.0
10 4.9 3.1 1.5 0.1 0.0
What you see here, there is a extra column Y which represents a class
that is characterized by the input vector [x1,x2,x3,x4]
Therefore Data Set contains (Xi,Yi)……..(Xn,Yn) tuples where
Each Xi =[x1,x2,x3,x4]
6. Case Study with a Small Neural Net
(I2,O2)
(I3,O3)
(I1,O1)
(I4,O4)
(I5,O5)
(I6,O6)
(I7,O7)
W1,5
W1,6
W2,5
W2,6
W3,6
W3,5
W4,6W4,5
W5,7
W6,7
x1
x2
x3
x4
Therefore Given, A data set consists of P tuples of (X,Y) pairs,
the weights of NN can be found by solving the following minimization problem:
I would not spend much time on discussing the introduction. I would like to go to directly to a case study with A popular machine learning technique Neural networks. And I would explain how optimization comes in practice with machine learning.
I would not spend much time on discussing the introduction. I would like to go to directly to a case study with A popular machine learning technique Neural networks. And I would explain how optimization comes in practice with machine learning.