Week 7 Lab (Support Vector Machine) COSC 3337

Description

About The Data We’ll be using the Breast Cancer Wisconsin (Diagnostic) Data Set from kaggle for this lab, but feel free to follow along with your own dataset. The dataset contains a total of 32 columns, with following attribute information: 1) ID number 2) Diagnosis (M = malignant, B = benign) 3‑32) Ten real‑valued features are computed for each cell nucleus: a) radius (mean of distances from center to points on the perimeter) b) texture (standard deviation of gray‑scale values) c) perimeter d) area e) smoothness (local variation in radius lengths) f) compactness (perimeter^2 / area ‑ 1.0) g) concavity (severity of concave portions of the contour) h) concave points (number of concave portions of the contour) i) symmetry j) 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. Our goal will be to predict the diagnosis (benign or malignant). Exploratory Data Analysis Let’s begin by importing some necessary libraries that we’ll be using to explore the data. Our first step is to load the data into a pandas DataFrame. There’s an odd column “Unnamed: 32”, which we’ll go ahead and drop since it’s full of NaN values. We also won’t need the id label, so we can drop that as well. Since a lot of the features in this dataset can be hard to interpret without domain knowledge of cancer or tumor cells, we’ll just do a few visualizations here, but feel free to explore as much as you’d like before constructing a model. <class
’pandas.core.frame.DataFrame’> RangeIndex:
569
entries,
0
to
568 Data
columns
(total
31
columns): 
#


Column


















Non­Null
Count

Dtype

 ­­­

­­­­­­


















­­­­­­­­­­­­­­

­­­­­

 
0


diagnosis















569
non­null



object
 
1


radius_mean













569
non­null



float64 
2


texture_mean












569
non­null



float64 
3


perimeter_mean










569
non­null



float64 
4


area_mean















569
non­null



float64 
5


smoothness_mean









569
non­null



float64 
6


compactness_mean








569
non­null



float64 
7


concavity_mean










569
non­null



float64 
8


concave
points_mean





569
non­null



float64 
9


symmetry_mean











569
non­null



float64 
10

fractal_dimension_mean


569
non­null



float64 
11

radius_se















569
non­null



float64 
12

texture_se














569
non­null



float64 
13

perimeter_se












569
non­null



float64 
14

area_se

















569
non­null



float64 
15

smoothness_se











569
non­null



float64 
16

compactness_se










569
non­null



float64 
17

concavity_se












569
non­null



float64 
18

concave
points_se







569
non­null



float64 
19

symmetry_se













569
non­null



float64 
20

fractal_dimension_se




569
non­null



float64 
21

radius_worst












569
non­null



float64 
22

texture_worst











569
non­null



float64 
23

perimeter_worst









569
non­null



float64 
24

area_worst














569
non­null



float64 
25

smoothness_worst








569
non­null



float64 
26

compactness_worst







569
non­null



float64 
27

concavity_worst









569
non­null



float64 
28

concave
points_worst




569
non­null



float64 
29

symmetry_worst










569
non­null



float64 
30

fractal_dimension_worst

569
non­null



float64 dtypes:
float64(30),
object(1) memory
usage:
137.9+
KB calling .info() we see that there are no missing values in this dataset. There seems to be pretty good distinction between the diagnosis (blue & orange) in most of the atributes above. Majority of our data observations are of the benign class. area_mean could be a good predictor wheather malignant or benign since there is pretty good separation here. Most benign (orange) have area_mean of around 500 or lower. Some strong correlations are present. (very bright squares for example) Pre‑Processing Let’s go ahead and scale our data before training and creating our model Creating our Model We’re now ready to begin creating and training our model. We first need to split our data into training and testing sets. This can be done using sklearn’s train_test_split(X, y, test_size) function. This function takes in your features (X), the target variable (y), and the test_size you’d like (Generally a test size of around 0.3 is good enough). It will then return a tuple of X_train, X_test, y_train, y_test sets for us. We will train our model on the training set and then use the test set to evaluate the model. SVC() Model Evaluation Now that we’ve finished training, we can make predictions off of the test data and evaluate our model’s performance using the corresponding test data. Confusion
matrix 
[[104


1] 
[

3

63]] True
Positives(TP)
=

104 True
Negatives(TN)
=

63 False
Positives(FP)
=

1 False
Negatives(FN)
=

3 













precision



recall

f1­score


support 










B






0.97





0.99





0.98






105 










M






0.98





0.95





0.97







66 



accuracy


























0.98






171 


macro
avg






0.98





0.97





0.98






171 weighted
avg






0.98





0.98





0.98






171 Hyperparameter Tuning Finding the right parameters (like what C or gamma values to use) is a tricky task, but luckily we can be a little lazy and just try a bunch of combinations and see what works best. This idea of creating a ‘grid’ of parameters and just trying out all the possible combinations is called a Gridsearch, this method is common enough that Scikit‑learn has this functionality built in with GridSearchCV. The CV stands for cross‑validation. GridSearchCV takes a dictionary that describes the parameters that should be tried and a model to train. The grid of parameters is defined as a dictionary, where the keys are the parameters and the values are the settings to be tested. Let’s go ahead and try a few different parameters to see which of them is the best set to use. You should add refit=True and choose verbose to whatever number you want. The higher the number, the more verbose.(verbose just means the text output describing the process). What fit does is a bit more involved than usual. First, it runs the same loop with cross‑validation to find the best parameter combination. Once it has the best combination, it runs fit again on all data passed to fit (without cross‑validation), to build a single new model using the best parameter setting. Note: This process may take a while. The more parameters we test, the longer it may take since it has to try all different combinations inorder to find the best set. Fitting
5
folds
for
each
of
25
candidates,
totalling
125
fits [CV]
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backend
SequentialBackend
with
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workers. [Parallel(n_jobs=1)]:
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score=0.633,
total=


0.0s [CV]
C=100,
gamma=1,
kernel=rbf
……………………………….. [CV]
……….
C=100,
gamma=1,
kernel=rbf,
score=0.633,
total=


0.0s [CV]
C=100,
gamma=0.1,
kernel=rbf
……………………………… [CV]
……..
C=100,
gamma=0.1,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=100,
gamma=0.1,
kernel=rbf
……………………………… [CV]
……..
C=100,
gamma=0.1,
kernel=rbf,
score=0.963,
total=


0.0s [CV]
C=100,
gamma=0.1,
kernel=rbf
……………………………… [CV]
……..
C=100,
gamma=0.1,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.1,
kernel=rbf
……………………………… [CV]
……..
C=100,
gamma=0.1,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.1,
kernel=rbf
……………………………… [CV]
……..
C=100,
gamma=0.1,
kernel=rbf,
score=0.987,
total=


0.0s [CV]
C=100,
gamma=0.01,
kernel=rbf
…………………………….. [CV]
…….
C=100,
gamma=0.01,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.01,
kernel=rbf
…………………………….. [CV]
…….
C=100,
gamma=0.01,
kernel=rbf,
score=0.938,
total=


0.0s [CV]
C=100,
gamma=0.01,
kernel=rbf
…………………………….. [CV]
…….
C=100,
gamma=0.01,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.01,
kernel=rbf
…………………………….. [CV]
…….
C=100,
gamma=0.01,
kernel=rbf,
score=0.949,
total=


0.0s [CV]
C=100,
gamma=0.01,
kernel=rbf
…………………………….. [CV]
…….
C=100,
gamma=0.01,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.001,
kernel=rbf
……………………………. [CV]
……
C=100,
gamma=0.001,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=100,
gamma=0.001,
kernel=rbf
……………………………. [CV]
……
C=100,
gamma=0.001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.001,
kernel=rbf
……………………………. [CV]
……
C=100,
gamma=0.001,
kernel=rbf,
score=1.000,
total=


0.0s [CV]
C=100,
gamma=0.001,
kernel=rbf
……………………………. [CV]
……
C=100,
gamma=0.001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=100,
gamma=0.001,
kernel=rbf
……………………………. [CV]
……
C=100,
gamma=0.001,
kernel=rbf,
score=0.987,
total=


0.0s [CV]
C=100,
gamma=0.0001,
kernel=rbf
…………………………… [CV]
…..
C=100,
gamma=0.0001,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=100,
gamma=0.0001,
kernel=rbf
…………………………… [CV]
…..
C=100,
gamma=0.0001,
kernel=rbf,
score=0.988,
total=


0.0s [CV]
C=100,
gamma=0.0001,
kernel=rbf
…………………………… [CV]
…..
C=100,
gamma=0.0001,
kernel=rbf,
score=1.000,
total=


0.0s [CV]
C=100,
gamma=0.0001,
kernel=rbf
…………………………… [CV]
…..
C=100,
gamma=0.0001,
kernel=rbf,
score=0.987,
total=


0.0s [CV]
C=100,
gamma=0.0001,
kernel=rbf
…………………………… [CV]
…..
C=100,
gamma=0.0001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=1000,
gamma=1,
kernel=rbf
………………………………. [CV]
………
C=1000,
gamma=1,
kernel=rbf,
score=0.637,
total=


0.0s [CV]
C=1000,
gamma=1,
kernel=rbf
………………………………. [CV]
………
C=1000,
gamma=1,
kernel=rbf,
score=0.637,
total=


0.0s [CV]
C=1000,
gamma=1,
kernel=rbf
………………………………. [CV]
………
C=1000,
gamma=1,
kernel=rbf,
score=0.637,
total=


0.0s [CV]
C=1000,
gamma=1,
kernel=rbf
………………………………. [CV]
………
C=1000,
gamma=1,
kernel=rbf,
score=0.633,
total=


0.0s [CV]
C=1000,
gamma=1,
kernel=rbf
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………
C=1000,
gamma=1,
kernel=rbf,
score=0.633,
total=


0.0s [CV]
C=1000,
gamma=0.1,
kernel=rbf
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…….
C=1000,
gamma=0.1,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=1000,
gamma=0.1,
kernel=rbf
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…….
C=1000,
gamma=0.1,
kernel=rbf,
score=0.963,
total=


0.0s [CV]
C=1000,
gamma=0.1,
kernel=rbf
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…….
C=1000,
gamma=0.1,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
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gamma=0.1,
kernel=rbf
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gamma=0.1,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
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gamma=0.1,
kernel=rbf
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C=1000,
gamma=0.1,
kernel=rbf,
score=0.987,
total=


0.0s [CV]
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gamma=0.01,
kernel=rbf
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……
C=1000,
gamma=0.01,
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score=0.950,
total=


0.0s [CV]
C=1000,
gamma=0.01,
kernel=rbf
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……
C=1000,
gamma=0.01,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=1000,
gamma=0.01,
kernel=rbf
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……
C=1000,
gamma=0.01,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
C=1000,
gamma=0.01,
kernel=rbf
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……
C=1000,
gamma=0.01,
kernel=rbf,
score=0.937,
total=


0.0s [CV]
C=1000,
gamma=0.01,
kernel=rbf
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……
C=1000,
gamma=0.01,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=1000,
gamma=0.001,
kernel=rbf
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…..
C=1000,
gamma=0.001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=1000,
gamma=0.001,
kernel=rbf
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…..
C=1000,
gamma=0.001,
kernel=rbf,
score=0.963,
total=


0.0s [CV]
C=1000,
gamma=0.001,
kernel=rbf
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…..
C=1000,
gamma=0.001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=1000,
gamma=0.001,
kernel=rbf
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…..
C=1000,
gamma=0.001,
kernel=rbf,
score=0.949,
total=


0.0s [CV]
C=1000,
gamma=0.001,
kernel=rbf
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…..
C=1000,
gamma=0.001,
kernel=rbf,
score=0.975,
total=


0.0s [CV]
C=1000,
gamma=0.0001,
kernel=rbf
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….
C=1000,
gamma=0.0001,
kernel=rbf,
score=0.950,
total=


0.0s [CV]
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gamma=0.0001,
kernel=rbf
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….
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gamma=0.0001,
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score=0.975,
total=


0.0s [CV]
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gamma=0.0001,
kernel=rbf
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….
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gamma=0.0001,
kernel=rbf,
score=1.000,
total=


0.0s [CV]
C=1000,
gamma=0.0001,
kernel=rbf
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….
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gamma=0.0001,
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score=0.975,
total=


0.0s [CV]
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gamma=0.0001,
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….
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gamma=0.0001,
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score=0.987,
total=


0.0s [Parallel(n_jobs=1)]:
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1.0s
finished GridSearchCV(estimator=SVC(), 












param_grid={‘C’:
[0.1,
1,
10,
100,
1000], 
























’gamma’:
[1,
0.1,
0.01,
0.001,
0.0001], 
























’kernel’:
[‘rbf’]}, 












verbose=3) You can inspect the best parameters found by GridSearchCV using the bestparams attribute, and the best estimator using the best_estimator_ attribute. Here we see that the best set of parameters from the ones we specified are 10 for c value, 0.01 for gamma, and ‘rbf’ for the kernel. {‘C’:
10,
’gamma’:
0.01,
’kernel’:
’rbf’} Then you can re‑run predictions on this grid object just like you would with a normal model. [[105


0] 
[

2

64]] 













precision



recall

f1­score


support 










B






0.98





1.00





0.99






105 










M






1.00





0.97





0.98







66 



accuracy


























0.99






171 


macro
avg






0.99





0.98





0.99






171 weighted
avg






0.99





0.99





0.99






171 Nice! We got a slightly better improvement using these parameters, though our original accuracy was already very good. Keep this grid search in mind when you need to do hyperparameter tuning. It can save you a lot of time. Congrats! You now know how to use SVM and hyperparameter tuning in sklearn. Try using this on your own dataset and refer back to this lecture if you get stuck. id diagnosis radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavi 0 842302 M 17.99 10.38 122.80 1001.0 0.11840 0.27760 1 842517 M 20.57 17.77 132.90 1326.0 0.08474 0.07864 2 84300903 M 19.69 21.25 130.00 1203.0 0.10960 0.15990 3 84348301 M 11.42 20.38 77.58 386.1 0.14250 0.28390 4 84358402 M 20.29 14.34 135.10 1297.0 0.10030 0.13280 5 rows × 33 columns radius_mean texture_mean perimeter_mean area_mean smoothness_mean compactness_mean concavity_mean concave points_mean 0 1.097064 ‑2.073335 1.269934 0.984375 1.568466 3.283515 2.652874 2.532475 1 1.829821 ‑0.353632 1.685955 1.908708 ‑0.826962 ‑0.487072 ‑0.023846 0.548144 2 1.579888 0.456187 1.566503 1.558884 0.942210 1.052926 1.363478 2.037231 3 ‑0.768909 0.253732 ‑0.592687 ‑0.764464 3.283553 3.402909 1.915897 1.451707 4 1.750297 ‑1.151816 1.776573 1.826229 0.280372 0.539340 1.371011 1.428493 5 rows × 30 columns In
[1]: import numpy as np import pandas as pd import matplotlib.pyplot as plt import seaborn as sns In
[2]: from matplotlib import rcParams rcParams[‘figure.figsize’] = 15, 5 sns.set_style(‘darkgrid’) In
[3]: breast_cancer_df = pd.read_csv(‘data.csv’) breast_cancer_df.head() Out[3]: In
[4]: breast_cancer_df.drop(labels=[‘Unnamed:
32’, ‘id’], axis=1, inplace=True) In
[5]: breast_cancer_df.info() In
[6]: sns.pairplot(breast_cancer_df, hue=’diagnosis’, vars=[‘radius_mean’, ‘texture_mean’, ‘perimeter_mean’, ‘area_ 




































’smoothness_mean’, ‘compactness_mean’, ‘concavity_mean’, 




































’concave
points_mean’, ‘symmetry_mean’, ‘fractal_dimension_mean’]) plt.show() In
[7]: sns.countplot(x=breast_cancer_df[‘diagnosis’]) plt.show() In
[8]: sns.scatterplot(x = ‘area_mean’, y = ‘smoothness_mean’, hue = ‘diagnosis’, data = breast_cancer_df) plt.show() In
[9]: plt.figure(figsize=(20,10)) sns.heatmap(breast_cancer_df.corr(), annot=True) plt.show() In
[10]: from sklearn.preprocessing import StandardScaler #
all
columns
except
’Outcome’ X = breast_cancer_df.drop(‘diagnosis’, axis=1) y = breast_cancer_df[‘diagnosis’] #
create
our
scaler
object scaler = StandardScaler() #
use
our
scaler
object
to
transform/scale
our
data
and
save
it
into
X_scaled X_scaled = scaler.fit_transform(X) #
reassign
X
to
a
new
DataFrame
using
the
X_scaled
values. X = pd.DataFrame(data=X_scaled, columns=X.columns) In
[11]: X.head() Out[11]: In
[12]: from sklearn.model_selection import train_test_split X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=101) In
[13]: from sklearn.svm import SVC #
instantiate
the
model
with
default
parameters model = SVC() #
fit/train
 model.fit(X_train,y_train) Out[13]: In
[14]: predictions = model.predict(X_test) In
[15]: from sklearn.metrics import confusion_matrix cm = confusion_matrix(y_test, predictions) print(‘Confusion
matrix\n\n’, cm) print(‘\nTrue
Positives(TP)
=
’, cm[0,0]) print(‘\nTrue
Negatives(TN)
=
’, cm[1,1]) print(‘\nFalse
Positives(FP)
=
’, cm[0,1]) print(‘\nFalse
Negatives(FN)
=
’, cm[1,0]) In
[16]: from sklearn.metrics import classification_report print(classification_report(y_test,predictions)) In
[17]: param_grid = {‘C’: [0.1,1, 10, 100, 1000], ‘gamma’: [1,0.1,0.01,0.001,0.0001], ‘kernel’: [‘rbf’]} In
[19]: from sklearn.model_selection import GridSearchCV grid = GridSearchCV(SVC(),param_grid,refit=True,verbose=3) In
[20]: grid.fit(X_train,y_train) Out[20]: In
[21]: grid.best_params_ Out[21]: In
[23]: grid_predictions = grid.predict(X_test) In
[24]: print(confusion_matrix(y_test,grid_predictions)) print(classification_report(y_test,grid_predictions))