Data Range

Create a function to compress data into a specific range of values.

We'll cover the following

Chapter Goals:

  • Learn how to compress data values to a specified range

A. Range scaling

Apart from standardizing data, we can also scale data by compressing it into a fixed range. One of the biggest use cases for this is compressing data into the range [0, 1]. This allows us to view the data in terms of proportions, or percentages, based on the minimum and maximum values in the data.

The formula for scaling based on a range is a two-step process. For a given data value, x, we first compute the proportion of the value with respect to the min and max of the data dmin and dmax, respectively).

xprop=x−dmindmax−dminx_{prop} = \frac{x - d_{min}}{d_{max} - d_{min}}

The formula above computes the proportion of the data value, xprop. Note that this only works if not all the data values are the same (i.e. dmax ≠ dmin).

We then use the proportion of the value to scale to the specified range, [rmin, rmax]. The formula below calculates the new scaled value, xscale.

xscale=xprop⋅(rmax−rmin)+rminx_{scale} = x_{prop} \cdot (r_{max} - r_{min}) + r_{min}

B. Range compression in scikit-learn

The scikit-learn library provides a variety of transformers, modules that perform transformations on data. While in the previous chapter we used a single function, scale, to perform the data standardization, the remaining chapters will focus on using these transformer modules.

The MinMaxScaler transformer performs the range compression using the previous formula. Specifically, it scales each feature (column) of the data to a given range (where the default range is [0, 1]).

The code below shows how to use the MinMaxScaler (with the default range and a custom range).

The MinMaxScaler object contains a function called fit_transform, which allows it to take in the input data array and then output the scaled data. The function is a combination of the object's fit and transform functions, where the former takes in an input data array and the latter transforms a (possibly different) array based on the data from the input to the fit function.

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# predefined data
print('{}\n'.format(repr(data)))
from sklearn.preprocessing import MinMaxScaler
default_scaler = MinMaxScaler() # the default range is [0,1]
transformed = default_scaler.fit_transform(data)
print('{}\n'.format(repr(transformed)))
custom_scaler = MinMaxScaler(feature_range=(-2, 3))
transformed = custom_scaler.fit_transform(data)
print('{}\n'.format(repr(transformed)))

Now lets run the fit and transform functions separately and compare them with the fit_transform function. fit takes in an input data array and transform transforms a (possibly different) array based on the data from the input to the fit function.

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# predefined new_data
print('{}\n'.format(repr(new_data)))
from sklearn.preprocessing import MinMaxScaler
default_scaler = MinMaxScaler() # the default range is [0,1]
transformed = default_scaler.fit_transform(new_data)
print('{}\n'.format(repr(transformed)))
default_scaler = MinMaxScaler()  # new instance
default_scaler.fit(data)  # different data value fit
transformed = default_scaler.transform(new_data)
print('{}\n'.format(repr(transformed)))

The code above scales the new_data array to the range [0, 1], based on the (column-wise) minimum and maximum values from the data array in the original code example.

Time to Code!

The coding exercise in this chapter uses MinMaxScaler (imported in backend) to complete the ranged_data function.

The function will compress the input NumPy array, data, into the range given by value_range.

Set min_max_scaler equal to MinMaxScaler initialized with value_range for the feature_range keyword argument.

Set scaled_data equal to min_max_scaler.fit_transform applied with data as the only argument. Then return scaled_data.

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def ranged_data(data, value_range):
  # CODE HERE
  pass

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