Python Tutorial : Transforming features for better clusterings
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Let's look now at another dataset: the Piedmont wines dataset. We have 178 samples of red wine from the Piedmont region of Italy. The features measure chemical composition (like alcohol content) and visual properties like color intensity. The samples come from 3 distinct varieties of wine.
Let's take the array of samples and use KMeans to find 3 clusters. There are three varieties of wine, so let's use pandas crosstab to check the cluster label - wine variety correspondence. As you can see, this time things haven't worked out so well. The KMeans clusters don't correspond well with the wine varieties.
The problem is that the features of the wine dataset have very different variances. The variance of a feature measures the spread of its values. For example, the malic acid feature has a higher variance than the od280 feature, and this can also be seen in their scatter plot. The differences in some of the feature variances is enormous, as seen here, for example, in the scatter plot of the od280 and proline features.
In KMeans clustering, the variance of a feature corresponds to its influence on the clustering algorithm. To give every feature a chance, the data needs to be transformed so that features have equal variance. This can be acheived with the StandardScaler from scikit-learn. It transforms every feature to have mean 0 and variance 1. The resulting "standardized" features can be very informative. Using standardized od280 and proline, for example, the three wine varieties are much more distinct.
Let's see the StandardScaler in action. First, import StandardScaler from sklearn.preprocessing. Then create a StandardScaler object, and fit it to the samples. The transform method can now be used to standardize any samples, either the same ones,
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