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
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