We assume that each instance can be represented as a vector of feature values and that all relevant aspects are represented by this vector. This is sometimes called an abstraction because we filter out unnecessary information and represent a real-world phenomena with a vector. For example, representing the entire works of Leo Tolstoy as a vector of word frequencies is an abstraction. We make no pretense that this abstraction will serve any more than a very particular limited application. We may learn something about Tolstoy's use of language and perhaps elicit some information regarding the sentiment and subject of Tolstoy's writing. However, we are unlikely to gain any significant insights into the broad canvas of the 19th century Russia portrayed in these works. A human reader, or a more sophisticated algorithm, will gain these insights not from the counting of each word but by the structure that these words are part of.
We can think of structured features in a similar...