One interesting aspect of these features is that the compactness feature is not actually a new measurement, but a function of the previous two features: area and perimeter. It is often very useful to derive new combined features. Trying to create new features is generally called feature engineering. It is sometimes seen as less glamorous than algorithms, but it often matters more for performance (a simple algorithm on well-chosen features will perform better than a fancy algorithm on not-so-good features).

In this case, the original researchers computed the compactness, which is a typical feature for shapes. It is also sometimes called roundness. This feature will have the same value for two kernels, one of which is twice as big as the other one, but with the same shape. However, it will have different values for kernels that are very round (when the feature is close to 1) when compared to kernels that are elongated (when the feature is closer to zero).

The goals of a good feature are to simultaneously vary with what matters (the desired output) and be invariant with what does not. For example, compactness does not vary in size, but varies in shape. In practice, it might be hard to achieve both objectives perfectly, but we want to approximate this ideal.

You will need to use background knowledge to design good features. Fortunately, for many problem domains, there is already a vast amount of possible features and feature types that you can build upon. In terms of images, all of the previously mentioned features are typical, and computer vision libraries will compute them for you. In text-based problems, too, there are standard solutions that you can mix and match (we will also look at this in Chapter 4, Classification I - Detecting Poor Answers). When possible, you should use your knowledge of the problem to design a specific feature or to select, from literature, the ones that are more applicable to the data at hand.

Even before you have data, you must decide which data is worthwhile to collect. Then, you hand all your features to the machine to evaluate and compute the best classifier.

A natural question is whether we can select good features automatically. This problem is known as feature selection. There are many methods that have been proposed for this problem, but in practice, very simple ideas work best. For the small problems we are currently exploring, it does not make sense to use feature selection, but if you had thousands of features, then throwing out most of them might make the rest of the process much faster.