generalization

In the previous post I discussed some aspects of learning a concept from examples. We will now connect it to….

 

Generalization

Generalization is the ability to learn a concept or a class from a set of examples. In short, generalization is our way of capturing sameness or similarity between objects.

By “objects” we understand all kinds of entities, including physical objects, abstractions, experiences and so on that are elements of the class or belong to the concept of interest.

For instance, we can learn a concept of a bicycle with the objects being bicycles, as well as we can learn a concept of driving with the ‘objects’ being driving experiences.

Generalization is a truly remarkable skill of an intelligent mind. It is one of the basic principles of learning.

We are able to learn a general rule and apply it when needed. We are able to classify or categorize not only physical objects, but also ideas, abstractions, events, behaviors, approaches and people. We are able to recognize patterns from examples, determine the essence and categorize experiences.

Generalization is being used daily on all levels in your life. You can apply skills and abilities in the new context exactly because generalization is at work.  It is really powerful.

  • Isn’t that remarkable that once you know how to walk, you are soon able to run?
  • Isn’t that remarkable that once you can drive an individual car, you can drive (nearly) all other cars?
  • Isn’t that remarkable that once you know how to cook a few meals, you can cook a totally new meal, never tried before?
  • Isn’t that remarkable that once you know how to orient yourself with a map, you can follow maps in arbitrary situations?
  • Isn’t that remarkable that once you know a programming or human language, you can learn a different language much faster?

The stages of concept learning

A quilt by Inge Duin

Imagine that you are to learn how to recognize a particular object or to learn a concept. The stages of learning a concept are in fact the stages of generalization. These are:

  1. Typical examples. Study, observation or experimentation with a number of typical examples of the given class.
  2. Finding the patterns: seeing the differences and perceiving similarities. This is made possible because of our ability to compare.
  3. Concept creation. A first mental formulation of a concept of an object/class/notion. Grasping the basic essence. This is made possible because of our ability to reflect.
  4. Atypical examples. Study of atypical, uncommon and otherwise strange examples from the class. Refining of the concept.
  5. Borderline cases. Exploration of the negative examples (i.e. examples from outside of the class), especially of the borderline cases.
  6. Re-definition of the concept.
  7. Abstraction. A new level of understanding. The essence is found.

Abstraction may develop without your conscious intent. It happens naturally when you reach a good understanding of  the class or concept of interest. Such an understanding is built when you engage in active learning, i.e. thinking, experimentation, reflection and evaluation. Abstraction occurs when you develop a mental image/sound or internal feeling of the class.

Some researchers think that such a class representation relies on a single prototype or a set of prototypes that somehow capture the idea of the class. Sometimes a prototype can be defined by a set of features, but it is usually much more than that. Features offer a limited scope and may vary from example to example.

A prototype  is meant to be an internal representation of the class. It likely combines visual, auditory, olfactory and kinesthetic modalities. Moreover, such a representation includes an emotional component, i.e. feelings that the concept evokes in you or emotionally strong events that took place when you had a related experience. In addition, such a representation may be equipped with a graph of structural dependencies and be hierarchical in order to reflect levels of importance or degree of detail.

Recognition

Testing is the next step after you have derived a concept of a class. It is called recognition. A good recognition does not necessarily prove that you have created an accurate and factual concept. The quality of your recognition depends on the quality of examples you consider for testing, i.e. whether they are a mixture of easy (typical) and challenging ones (border cases).

There are two types of errors you can make, called false positive and false negative errors. False positive are examples that you recognize as belonging to the class of interest while in fact they are not the member of that class. An example is an orange recognized as a ball by a child. After noticing such boundary examples you need to update your concept so that you will exclude such cases in the future (e.g fruits are not balls).

The second type of error is the false negative error which occurs when you miss to name a particular object as a member of the class, while in fact it belongs there . This suggests that you have not included a sufficient variety of examples when you were building your concept.

Concept learning is an ongoing process

If you think you learned a concept, you are wrong. We are living in a developing world and this asks us to continuously update, reformulate or even abandon our concepts by taking new developments and personal experiences into account. For instance, the concept of a telephone or TV you learned, say 20-40 years ago, is really outdated by now. Or the concept of friendship (which refers here to the class of friendship experiences) you developed in your childhood is not going to serve you in your thirties or later. You need to update your concepts by more recent examples.

Concept learning and recognition run in cycles

The concepts you develop are never fixed. They are solid, however, in the sense that they are built from concrete examples leading to specific representations of the classes. But, they are subjected to change.

In fact, you are always in the process of concept learning, recognition and concept re-learning, even though you don’t follow it consciously. These two stages are intertwined and you run them in cycles. You learn a concept and you test it. As long as your examples do not contradict your concept or challenge you with novel perceptions, your concept remains unchanged. If, however, you find a surprising example, you will decide whether the concept should to be re-learned or not.

You need to pay attention to noticing these interesting examples and be ready and prepared to modify your learned concept. At some point you will see that novel examples occur for which your concept definition does not work well. These are the moments in which you observe how your false positive or false negative errors increase. So, you are encouraged to include such examples in the concept formation process.

In addition, you may mentally weight your examples depending on some importance factor (that you define for yourself) or the time you collected them. Perhaps, you may even neglect early examples as they are not relevant any longer. For instance, concerning the concept of friendship, you may like to include examples of your friends from your primary school but they may have a much less weight than the examples from your last years of life.

Summary

Generalization supports us in learning on all levels. The use of generalization requires an open mind, however, able and prepared to question and redefine the derived concepts, if needed. Any concept we learn in our life is temporary. We change and the world changes as well. This means that our general rules, concepts and learned ideas are in operation until e.g. we find a surprise or a contradiction. This is a sign that points us to reformulation of the concept or perhaps even abandoning it.

What is essential is the meta ability of a conscious mind to pay attention and to notice outliers. As long as we remain flexible in our learning, open to questioning and re-learning, we will use generalization well.

Practise generalization with a conscious effort.

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Top photo courtesy Fe Langdon, available under the Creative Commons license on Flickr.
The middle image shows a beautiful quilt by Inge Duin. See www.ingeduin.nl for more details.

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