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111 KiB
111 KiB
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In [2]:
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
Data¶
Breast cancer wisconsin (diagnostic) dataset¶
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
worst/largest values) of these features were computed for each image,
resulting in 30 features. For instance, field 0 is Mean Radius, field
10 is Radius SE, field 20 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.
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/
.. topic:: 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.
In [3]:
df = pd.read_csv('../DATA/cancer_tumor_data_features.csv')
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df.head()
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In [5]:
from sklearn.preprocessing import StandardScaler
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scaler = StandardScaler()
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scaled_X = scaler.fit_transform(df)
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scaled_X
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- Calculate Covariance Matrix
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# Because we scaled the data, this won't produce any change.
# We've left if here because you would need to do this for unscaled data
scaled_X -= scaled_X.mean(axis=0)
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scaled_X
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In [18]:
# Grab Covariance Matrix
covariance_matrix = np.cov(scaled_X, rowvar=False)
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# Get Eigen Vectors and Eigen Values
eigen_values, eigen_vectors = np.linalg.eig(covariance_matrix)
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# Choose som number of components
num_components=2
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# Get index sorting key based on Eigen Values
sorted_key = np.argsort(eigen_values)[::-1][:num_components]
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# Get num_components of Eigen Values and Eigen Vectors
eigen_values, eigen_vectors = eigen_values[sorted_key], eigen_vectors[:, sorted_key]
In [24]:
# Dot product of original data and eigen_vectors are the principal component values
# This is the "projection" step of the original points on to the Principal Component
principal_components=np.dot(scaled_X,eigen_vectors)
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principal_components
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In [29]:
plt.figure(figsize=(8,6))
plt.scatter(principal_components[:,0],principal_components[:,1])
plt.xlabel('First principal component')
plt.ylabel('Second Principal Component')
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In [33]:
from sklearn.datasets import load_breast_cancer
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# REQUIRES INTERNET CONNECTION AND FIREWALL ACCESS
cancer_dictionary = load_breast_cancer()
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cancer_dictionary.keys()
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In [37]:
cancer_dictionary['target']
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In [38]:
plt.figure(figsize=(8,6))
plt.scatter(principal_components[:,0],principal_components[:,1],c=cancer_dictionary['target'])
plt.xlabel('First principal component')
plt.ylabel('Second Principal Component')
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