# Project: Using a Deep-Belief Neural Network to Diagnose Breast Cancer

I started learning more about deep-belief networks because of all the latest news surrounding this tool. Basically, they are Restricted Boltzmann Machines stacked together and have been shown to be extremely useful in classifying things.

I followed a tutorial and had to learn a few libraries required for the DBN. And then, I decided to apply this to classify the Wisconsin Breast Cancer (Diagnostic) Data Set to see if it would work on a real life (and extremely important) problem.

One shortcut I used to scale the data was as follows:

Anyway, the results were promising with an accuracy of 94% overall in diagnosing breast cancer with a malignant diagnosis of 97%. This is very good because it means that it’s more likely than not to diagnose a false positive than a false negative.

Here’s the code:

This produces:

```
[DBN] fitting X.shape=(381, 30)
[DBN] layers [30, 500, 500, 2]
[DBN] Fine-tune...
100%
Epoch 1:
loss 0.667588567734
err 0.41875
(0:00:00)
100%
Epoch 2:
loss 0.61961773634
err 0.353125
(0:00:00)
100%
Epoch 3:
loss 0.544265073538
err 0.215625
(0:00:00)
100%
Epoch 4:
loss 0.410316121578
err 0.16875
(0:00:00)
100%
Epoch 5:
loss 0.314362972975
err 0.10625
(0:00:00)
100%
Epoch 6:
loss 0.306012681127
err 0.13125
(0:00:00)
100%
Epoch 7:
loss 0.242035767436
err 0.11875
(0:00:00)
100%
Epoch 8:
loss 0.286982005835
err 0.14375
(0:00:00)
100%
Epoch 9:
loss 0.22955622673
err 0.121875
(0:00:00)
100%
Epoch 10:
loss 0.247347301245
err 0.09375
(0:00:00)
Breast Cancer Wisconsin (Diagnostic) Database
Notes
-----
Data Set Characteristics:
:Number of Instances: 569
:Number of Attributes: 30 numeric, predictive attributes and the class
:Attribute Information:
- radius (mean of distances from center to points on the perimeter)
- texture (standard deviation of gray-scale values)
- perimeter
- area
- smoothness (local variation in radius lengths)
- compactness (perimeter^2 / area - 1.0)
- concavity (severity of concave portions of the contour)
- concave points (number of concave portions of the contour)
- symmetry
- fractal dimension ("coastline approximation" - 1)
The mean, standard error, and "worst" or largest (mean of the three
largest values) of these features were computed for each image,
resulting in 30 features. For instance, field 3 is Mean Radius, field
13 is Radius SE, field 23 is Worst Radius.
- class:
- WDBC-Malignant
- WDBC-Benign
:Summary Statistics:
===================================== ======= ========
Min Max
===================================== ======= ========
radius (mean): 6.981 28.11
texture (mean): 9.71 39.28
perimeter (mean): 43.79 188.5
area (mean): 143.5 2501.0
smoothness (mean): 0.053 0.163
compactness (mean): 0.019 0.345
concavity (mean): 0.0 0.427
concave points (mean): 0.0 0.201
symmetry (mean): 0.106 0.304
fractal dimension (mean): 0.05 0.097
radius (standard error): 0.112 2.873
texture (standard error): 0.36 4.885
perimeter (standard error): 0.757 21.98
area (standard error): 6.802 542.2
smoothness (standard error): 0.002 0.031
compactness (standard error): 0.002 0.135
concavity (standard error): 0.0 0.396
concave points (standard error): 0.0 0.053
symmetry (standard error): 0.008 0.079
fractal dimension (standard error): 0.001 0.03
radius (worst): 7.93 36.04
texture (worst): 12.02 49.54
perimeter (worst): 50.41 251.2
area (worst): 185.2 4254.0
smoothness (worst): 0.071 0.223
compactness (worst): 0.027 1.058
concavity (worst): 0.0 1.252
concave points (worst): 0.0 0.291
symmetry (worst): 0.156 0.664
fractal dimension (worst): 0.055 0.208
===================================== ======= ========
:Missing Attribute Values: None
:Class Distribution: 212 - Malignant, 357 - Benign
:Creator: Dr. William H. Wolberg, W. Nick Street, Olvi L. Mangasarian
:Donor: Nick Street
:Date: November, 1995
This is a copy of UCI ML Breast Cancer Wisconsin (Diagnostic) datasets.
https://goo.gl/U2Uwz2
Features are computed from a digitized image of a fine needle
aspirate (FNA) of a breast mass. They describe
characteristics of the cell nuclei present in the image.
A few of the images can be found at
http://www.cs.wisc.edu/~street/images/
Separating plane described above was obtained using
Multisurface Method-Tree (MSM-T) [K. P. Bennett, "Decision Tree
Construction Via Linear Programming." Proceedings of the 4th
Midwest Artificial Intelligence and Cognitive Science Society,
pp. 97-101, 1992], a classification method which uses linear
programming to construct a decision tree. Relevant features
were selected using an exhaustive search in the space of 1-4
features and 1-3 separating planes.
The actual linear program used to obtain the separating plane
in the 3-dimensional space is that described in:
[K. P. Bennett and O. L. Mangasarian: "Robust Linear
Programming Discrimination of Two Linearly Inseparable Sets",
Optimization Methods and Software 1, 1992, 23-34].
This database is also available through the UW CS ftp server:
ftp ftp.cs.wisc.edu
cd math-prog/cpo-dataset/machine-learn/WDBC/
References
----------
- W.N. Street, W.H. Wolberg and O.L. Mangasarian. Nuclear feature extraction
for breast tumor diagnosis. IS&T/SPIE 1993 International Symposium on
Electronic Imaging: Science and Technology, volume 1905, pages 861-870,
San Jose, CA, 1993.
- O.L. Mangasarian, W.N. Street and W.H. Wolberg. Breast cancer diagnosis and
prognosis via linear programming. Operations Research, 43(4), pages 570-577,
July-August 1995.
- W.H. Wolberg, W.N. Street, and O.L. Mangasarian. Machine learning techniques
to diagnose breast cancer from fine-needle aspirates. Cancer Letters 77 (1994)
163-171.
0: malignant
1: benign
precision recall f1-score support
0 0.97 0.85 0.90 66
1 0.92 0.98 0.95 122
avg / total 0.94 0.94 0.94 188
```