Instance-based Learning

Prototypes

The simplest form of learning is memorisation. When an object is observed or the solution to a problem is found, it is stored in memory for future use. Memory can be thought of as a look up table. When a new problem is encountered, memory is searched to find if the same problem has been solved before. If an exact match for the search is required, learning is slow and consumes very large amounts of memory. However, approximate matching allows a degree of generalisation that both speeds learning and saves memory.

For example, if we are shown an object and we want to know if it is a chair, then we compare the description of this new object with descriptions of `typical' chairs that we have encountered before. If the description of the new object is `close' to the description of one of the stored instances then we may call it a chair. Obviously, we must defined what we mean by `typical' and `close'.

To better understand the issues involved in learning prototypes, we will briefly describe three experiments in Instance-based learning (IBL) by Aha, Kibler and Albert (1991). IBL learns to classify objects by being shown examples of objects, described by an attribute/value list, along with the class to which each example belongs.

EXPERIMENT 1

In the first experiment (IB1), to learn a concept simply required the program to store every example. When an unclassified object was presented for classification by the program, it used a simple Euclidean distance measure to determine the nearest neighbour of the object and the class given to it was the class of the neighbour.

This simple scheme works well, and is tolerant to some noise in the data. Its major disadvantage is that it requires a large amount of storage capacity.

EXPERIMENT 2

The second experiment (IB2) attempted to improve the space performance of IB1. In this case, when new instances of classes were presented to the program, the program attempted to classify them. Instances that were correctly classified were ignored and only incorrectly classified instances were stored to become part of the concept.

While this scheme reduced storage dramatically, it was less noise-tolerant than the first.

EXPERIMENT 3

The third experiment (IB3) used a more sophisticated method for evaluating instances to decide if they should be kept or not. IB3 is similar to IB2 with the following additions. IB3 maintains a record of the number of correct and incorrect classification attempts for each saved instance. This record summarised an instance's classification performance. IB3 uses a significance test to determine which instances are good classifiers and which ones are believed to be noisy. The latter are discarded from the concept description. This method strengthens noise tolerance, while keeping storage requirements down.

DISCUSSION

Figure 1 shows the boundaries of an imaginary concept in a two dimensions space. The dashed lines represent the boundaries of the target concept. The learning procedure attempts to approximate these boundaries by nearest neighbour matches. Note that the boundaries defined by the matching procedure are quite irregular. This can have its advantages when the target concept does not have a regular shape.
	
Figure 1. The extension of an IBL concept is shown in solid lines. The dashed lines represent the target concept. A sample of positive and negative examples is shown. Adapted from Aha, Kibler and Albert (1991).

Learning by remembering typical examples of a concept has several other advantages. If an efficient indexing mechanism can be devised to find near matches, this representation can be very fast as a classifier since it reduces to a table look up. It does not require any sophisticated reasoning system and is very flexible. As we shall see later, representations that rely on abstractions of concepts can run into trouble with what appear to be simple concepts. For example, an abstract representation of a chair may consist of a description of the number legs, the height, etc. However, exceptions abound since anything that can be sat on can be thought of as a chair. Thus, abstractions must often be augmented by lists of exceptions. Instance-based representation does not suffer from this problem since it only consists exceptions and is designed to handle them efficiently.

One of the major disadvantages of this style of representation is that it is necessary to define a similarity metric for objects in the universe. This can often be difficult to do when the objects are quite complex.

Another disadvantage is that the representation is not human readable. What does a collection of typical instances tell us about the concept that has been learned?

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