A multiscale neural network
Tiphaine Champetier - Team biocomp
21st March 2017
Neural Network
What for?
Classification
Features vector
Class / Label / Category
Perceptron
Linear combination of
inputs
Neural Network
Compute a more complex
function
Foward propagation
\bold{x}
x_{1}
x_{2}
x_{3}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
a^{(1)}
}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
a^{(1)}
}
W^{(1)}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(1)}
}
W^{(1)}
\color{Green}{
\bold{
z^{(2)}
}}
=
\bold{
W^{(1)}.
\color{red}{a^{(1)}}
}
\color{Green}{z^{(2)}_{i}}
=\sum_{j}
W^{(1)}_{ij}.
\color{Red}{a^{(1)}_{j}}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
W^{(1)}
\color{Red}{
\bold{
a^{(2)}
}}
=
g(
\bold{
\color{Green}{z^{(2)}}
}
)
\color{Red}{a^{(2)}_{j}}
=g(
\color{Green}{z^{(2)}_{i}}
)
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
z^{(3)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
W^{(1)}
W^{(2)}
\color{Green}{
\bold{
z^{(3)}
}}
=
\bold{
W^{(2)}.
\color{red}{a^{(2)}}
}
\color{Green}{z^{(3)}_{i}}
=\sum_{j}
W^{(2)}_{ij}.
\color{Red}{a^{(2)}_{j}}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
z^{(3)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
g()
g()
g()
g()
W^{(1)}
W^{(2)}
\bold{
a^{(3)}}
\color{Red}{
\bold{
a^{(3)}
}}
=
g(
\bold{
\color{Green}{z^{(3)}}
}
)
\color{Red}{a^{(3)}_{j}}
=g(
\color{Green}{z^{(3)}_{i}}
)
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
z^{(3)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
g()
g()
g()
g()
W^{(1)}
W^{(2)}
W^{(3)}
\bold{
z^{(4)}}
\bold{
a^{(3)}}
\color{Green}{
\bold{
z^{(4)}
}}
=
\bold{
W^{(3)}.
\color{red}{a^{(3)}}
}
\color{Green}{z^{(4)}_{i}}
=\sum_{j}
W^{(3)}_{ij}.
\color{Red}{a^{(3)}_{j}}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
z^{(3)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
g()
g()
g()
g()
g()
g()
g()
W^{(1)}
W^{(2)}
\color{Red}{
\bold{
a^{(4)}
}}
=
g(
\bold{
\color{Green}{z^{(4)}}
}
)
\color{Red}{a^{(4)}_{j}}
=g(
\color{Green}{z^{(4)}_{i}}
)
W^{(3)}
\bold{
z^{(4)}}
\bold{
a^{(4)}}
\bold{
a^{(3)}}
\bold{x}
=
x_{1}
x_{2}
x_{3}
\bold{
z^{(2)}}
\bold{
a^{(2)}}
\bold{
z^{(3)}}
\bold{
a^{(1)}
}
g()
g()
g()
g()
g()
g()
g()
g()
g()
g()
g()
W^{(1)}
W^{(2)}
\bold{
\hat{y}
}
\hat{y}_{1}
\hat{y}_{2}
\hat{y}_{3
}
\hat{y}_{c}
=
\frac{\exp(a_{c}^{(4)})}{\sum_{j}\exp(a_{j}^{(4)})}
W^{(3)}
\bold{
z^{(4)}}
\bold{
a^{(4)}}
\bold{
a^{(3)}}
Softmax function
\hat{y}_{c}
probability of the sample
to belong to class c
Convolutional neural network
Convolution
Architecture of the feature extractor
Filter combining
Filter combining
Global architecture
Pooling / Sub-sampling
Why a neural network for image analysis ?
The mustiscale neural network
Softmax function
Classification accuracies
Binary phenotype classification
Multi-label classification of organelles
Multi-label Classification and prediction of MoA
Thank you !
deck
By Tiphaine Champetier
