Here we will talk about an important piece of machine learning: the extraction of quantitative features from data. By the end of this section you will
In addition, we will go over several basic tools within scikit-learn which can be used to accomplish the above tasks.
Recall that data in scikit-learn is expected to be in two-dimensional arrays, of size n_samples $\times$ n_features.
Previously, we looked at the iris dataset, which has 150 samples and 4 features
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from sklearn.datasets import load_iris
iris = load_iris()
print(iris.data.shape)
These features are:
Numerical features such as these are pretty straightforward: each sample contains a list of floating-point numbers corresponding to the features
What if you have categorical features? For example, imagine there is data on the color of each iris:
color in [red, blue, purple]
You might be tempted to assign numbers to these features, i.e. red=1, blue=2, purple=3 but in general this is a bad idea. Estimators tend to operate under the assumption that numerical features lie on some continuous scale, so, for example, 1 and 2 are more alike than 1 and 3, and this is often not the case for categorical features.
In fact, the example above is a subcategory of "categorical" features, namely, "nominal" features. Nominal features don't imply an order, whereas "ordinal" features are categorical features that do imply an order. An example of ordinal features would be T-shirt sizes, e.g., XL > L > M > S.
One work-around for parsing nominal features into a format that prevents the classification algorithm from asserting an order is the so-called one-hot encoding representation. Here, we give each category its own dimension.
The enriched iris feature set would hence be in this case:
Note that using many of these categorical features may result in data which is better represented as a sparse matrix, as we'll see with the text classification example below.
When the source data is encoded has a list of dicts where the values are either strings names for categories or numerical values, you can use the DictVectorizer class to compute the boolean expansion of the categorical features while leaving the numerical features unimpacted:
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measurements = [
{'city': 'Dubai', 'temperature': 33.},
{'city': 'London', 'temperature': 12.},
{'city': 'San Francisco', 'temperature': 18.},
]
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from sklearn.feature_extraction import DictVectorizer
vec = DictVectorizer()
vec
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vec.fit_transform(measurements).toarray()
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vec.get_feature_names()
Another common feature type are derived features, where some pre-processing step is applied to the data to generate features that are somehow more informative. Derived features may be based in feature extraction and dimensionality reduction (such as PCA or manifold learning), may be linear or nonlinear combinations of features (such as in polynomial regression), or may be some more sophisticated transform of the features.
As an example of how to work with both categorical and numerical data, we will perform survival predicition for the passengers of the HMS Titanic.
We will use a version of the Titanic (titanic3.xls) from here. We converted the .xls to .csv for easier manipulation but left the data is otherwise unchanged.
We need to read in all the lines from the (titanic3.csv) file, set aside the keys from the first line, and find our labels (who survived or died) and data (attributes of that person). Let's look at the keys and some corresponding example lines.
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import os
import pandas as pd
titanic = pd.read_csv(os.path.join('datasets', 'titanic3.csv'))
print(titanic.columns)
Here is a broad description of the keys and what they mean:
pclass Passenger Class
(1 = 1st; 2 = 2nd; 3 = 3rd)
survival Survival
(0 = No; 1 = Yes)
name Name
sex Sex
age Age
sibsp Number of Siblings/Spouses Aboard
parch Number of Parents/Children Aboard
ticket Ticket Number
fare Passenger Fare
cabin Cabin
embarked Port of Embarkation
(C = Cherbourg; Q = Queenstown; S = Southampton)
boat Lifeboat
body Body Identification Number
home.dest Home/DestinationIn general, it looks like name, sex, cabin, embarked, boat, body, and homedest may be candidates for categorical features, while the rest appear to be numerical features. We can also look at the first couple of rows in the dataset to get a better understanding:
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titanic.head()
We clearly want to discard the "boat" and "body" columns for any classification into survived vs not survived as they already contain this information. The name is unique to each person (probably) and also non-informative. For a first try, we will use "pclass", "sibsp", "parch", "fare" and "embarked" as our features:
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labels = titanic.survived.values
features = titanic[['pclass', 'sex', 'age', 'sibsp', 'parch', 'fare', 'embarked']]
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features.head()
The data now contains only useful features, but they are not in a format that the machine learning algorithms can understand. We need to transform the strings "male" and "female" into binary variables that indicate the gender, and similarly for "embarked".
We can do that using the pandas get_dummies function:
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pd.get_dummies(features).head()
This transformation successfully encoded the string columns. However, one might argue that the class is also a categorical variable. We can explicitly list the columns to encode using the columns parameter, and include pclass:
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features_dummies = pd.get_dummies(features, columns=['pclass', 'sex', 'embarked'])
features_dummies.head(n=16)
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data = features_dummies.values
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import numpy as np
np.isnan(data).any()
With all of the hard data loading work out of the way, evaluating a classifier on this data becomes straightforward. Setting up the simplest possible model, we want to see what the simplest score can be with DummyClassifier.
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from sklearn.model_selection import train_test_split
from sklearn.preprocessing import Imputer
train_data, test_data, train_labels, test_labels = train_test_split(
data, labels, random_state=0)
imp = Imputer()
imp.fit(train_data)
train_data_finite = imp.transform(train_data)
test_data_finite = imp.transform(test_data)
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np.isnan(train_data_finite).any()
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from sklearn.dummy import DummyClassifier
clf = DummyClassifier('most_frequent')
clf.fit(train_data_finite, train_labels)
print("Prediction accuracy: %f"
% clf.score(test_data_finite, test_labels))
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# %load solutions/10_titanic.py