Feature space

A feature space is a mathematical space that determines an object through its measured values in relation to its special properties or features.

In the context of artificial intelligence, the term is used in pattern recognition .

In empirical social research , the term is used to classify measurement results and to methodically control the classification or type formation.

In artificial intelligence

Concept of pattern recognition

Pattern recognition examines automatic classification , i.e. how objects can be automatically classified into classes. In order to distinguish objects, one first determines a number of features in which they differ as strongly as possible. Then you measure these features for each object to be classified and write the measurement results in a vector, the so-called feature vector . This gives a vector for each object with as many entries as there are features. Each of these vectors denotes a point in feature space; the feature space thus has as many dimensions as features are considered. We are now looking for a function that divides the feature space into several classes, a so-called classifier .

Types of feature spaces

The feature spaces commonly used in pattern recognition are multi-dimensional real vector spaces :

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The dimension d of the space corresponds to the number of features examined and can be very large.

In empirical social research

The idea of the property space was introduced by Paul F. Lazarsfeld into the methodology of empirical social research.

As in the usual spatial conception, in which certain spatial coordinates are assigned to each location, a number of characteristic dimensions can be assigned to each object of investigation in social research, based on each of which a certain measured value or a certain measurement category can be assigned. The simplest type of characteristic is a dichotomous attribute. In contrast to the usual room concept, more than three features and different scale types can be used in the feature space. The IBM punch card, which was used for a long time for statistical evaluations, contained 80 columns with 12 lines each, which allowed each respondent in an opinion poll to be classified in a dichotomous attribute range of up to 960 values.

The idea of the feature space is particularly helpful in reducing the amount of data and reducing it to a manageable number of classes or categories. It allows you to check which reductions are theoretically and practically sensible.

In addition, it serves as a "substructure" of previously theoretically formed or found typologies. This means that a typology and its possible classification are checked for consistency and completeness on the basis of the specified characteristics. The result may be that the list of specified features is insufficient and that it should be supplemented or reduced.

Individual evidence

^ Allen H. Barton: The Concept of Property-Space in Social Research. In: Paul F. Lazarsfeld, Morris Rosenberg, (eds.): The Language of Social Research. A Reader in the Methodology of Social Research. The Free Press, New York. Collier-Macmillan Ltd. London, 1955. pp. 40 ff.

[1] Allen H. Barton: The Concept of Property-Space in Social Research. In: Paul F. Lazarsfeld, Morris Rosenberg, (eds.): The Language of Social Research. A Reader in the Methodology of Social Research. The Free Press, New York. Collier-Macmillan Ltd. London, 1955. pp. 40 ff.