breast cancer data.doc

breast cancer dataset

		Wisconsin Breast Cancer Database (WBCD)
			January 8, 1991
		    Revised Nomeber 3, 1994

This is a description of the Wisconsin Breast Cancer Database, collected
by Dr. William H. Wolberg, University of Wisconsin Hospitals, Madison.
The actual database is contained in another file (datacum). 
Samples were collected periodically as Dr. Wolberg reported his 
clinical cases. The database therefore reflects this chronological 
grouping of the data. The samples consist of 
visually assessed nuclear features of fine needle aspirates (FNAs) taken from
patients' breasts. Each sample has been assigned a 9-dimensional
vector (attributes 3 to 9 below) by Dr. wolberg. Each component
is in the interval 1 to 10, with value 1 corresponding to a normal 
state and 10 to a most abnormal state. Attribute 1 is 
sample number, while attribute 2 designates whether the sample
is benign or malignant. Malignancy is determined by taking
a sample tissue from the patient's breast and performing a biopsy
on it. A benign diagnosis is confirmed either by biopsy or by periodic
examination, depending on the patient's choice.

All groups are in the same file.  We have separated the groups
with a line beginning with ##### and the number of points in that group.  
There are 11 attributes per data point, with one data point per line.
Attribute are separated by a commas.  The attributes are as follows:
 
   Field         Attribute

   1             Sample code number
   2             Class: 2 for benign, 4 for malignant
   3             Clump Thickness
   4             Uniformity of Cell Size
   5             Uniformity of Cell Shape
   6             Marginal Adhesion
   7             Single Epithelial Cell Size
   8             Bare Nuclei
   9             Bland Chromatin
  10             Normal Nucleoli
  11             Mitoses

We have used attributes 3 to 11 to form a 9-dimensional vector
representing each case as a point in 9-dimensional real space.
This 9-dimensional vector was used to obtain a piecewise-linear
surface or equivalently a neural network to discriminate
between benign and malignant samples. A single plane separation
or equivalently a perceptron gives an accuracy of over 97% and is 
given below.

Note that in Groups 1 to 6 there are 17 samples each with a zero 
component. The zero represents UNAVAILABILITY of that attribute for 
the particular sample and does NOT represent a zero level for that 
attribute. Therefore these 19 samples may be discarded or treated 
in a special way.

If you use the data in any publication, please cite  one or more of
the following:

1. O. L. Mangasarian and W. H. Wolberg: "Cancer diagnosis via linear 
   programming", SIAM News, Volume 23, Number 5, September 1990, pp 1 & 18.

2. William H. Wolberg and O.L. Mangasarian: "Multisurface method of 
   pattern separation for medical diagnosis applied to breast cytology", 
   Proceedings of the National Academy of Sciences, U.S.A., Volume 87, 
   December 1990, pp 9193-9196.

3. O. L. Mangasarian, R. Setiono, and W.H. Wolberg: "Pattern recognition via 
   linear programming: Theory and application to medical diagnosis", in: 
   "Large-scale numerical optimization", Thomas F. Coleman and Yuying Li, 
   editors, SIAM Publications, Philadelphia 1990, pp 22-30.

4. K. P. Bennett & O. L. Mangasarian: "Robust linear programming discrimination
   of two linearly inseparable sets", Optimization Methods and Software 1,
   1992, 23-34 (Gordon & Breach Science Publishers).

5. O. L. Mangasarian: ""Mathematical programming in neural networks",
   ORSA Journal on Computing 5, 1993, 349-360.


                           SINGLE PLANE SEPARATION
			   ----------------------

By using the linear program from Reference 4 above on 
682 samples from  the Wisconsin Breast Cancer Database (WBCD), 
the following typical plane was found:


   w1=(.303, -.0087, .227, .210, .0096, .230, .16, .126, .304,-5.14).

The accuracy on the data using w1 was 97.7%. Normalizing and rounding these
coefficients we have:

   w2=(3, 0, 2, 2, 0,  2, 2, 1, 3,-50)


The accuracy on the data using w2 was 97.5%. The way to use this plane
is as follows:

If w2*x >= 50 then malignant

If w2*x <  50 then benign

Here x is the 9-dimensional vector of features from the WBCD, that is the nine 
last numbers in each row.  

NOTE:   16 points with missing attributes (indicated by a 0)
and 1 outlying point were not used in training. Specifially,
the following 17 points from the 699 points of WBCD  were removed:

4 8 4 5 1 2 0 7 3 1
2 6 6 6 9 6 0 7 8 1
2 1 1 1 1 1 0 2 1 1
2 1 1 3 1 2 0 2 1 1
2 1 1 2 1 3 0 1 1 1
2 5 1 1 1 2 0 3 1 1
2 3 1 4 1 2 0 3 1 1
2 3 1 1 1 2 0 3 1 1
2 3 1 3 1 2 0 2 1 1
4 8 8 8 1 2 0 6 10 1
2 1 1 1 1 2 0 2 1 1
2 5 4 3 1 2 0 2 3 1
2 4 6 5 6 7 0 4 9 1
2 3 1 1 1 2 0 3 1 1
2 1 1 1 1 1 0 1 1 1
2 1 1 1 1 1 0 2 1 1
2 8 4 4 5 4 7 7 8 2

---------------------------------------------------------------------------