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Drawing Isogloss Lines

Harald Hammarström

An isogloss is the geographical boundary of a certain linguistic feature,... such as the pronunciation of a vowel, the meaning of a word, or use of some syntactic feature (Wikipedia 8 June 2010) and is widely used in dialectology. There appears to be no objective definition of an isogloss line in the literature, let alone an automated procedure for drawing one (Händler, 1983, Ivi¢, 1964, Schneider, 1988). Thus, dialectologists today draw isogloss lines by hand, based on intuition.

We propose both an objective definition of what an optimal isogloss line is and an effective algorithm for computing the isogloss line given input data. The simplest formulation of the problem is as follows.

Input data:

A 2D grid map with rings, crosses (and empty positions).

Assumptions about a ``Line'':

A line is not necessarily a straight line but, either runs from the west end to the east end on the map, crossing each column at exactly once, or runs from the north end to the south end on the map, crossing each row exactly once. (Without this assumption, trivial solutions that simply encircle the all points of a certain kind, become optimal.)

Terminology:

For any line on the map separating rings and crosses, label (by majority) one of the sides the rings-side and the other the crosses-side

Definition:

The isogloss line is the line that minimizes

Alternative A:

the total number of rings on the crosses side + number of crosses on the rings side

Alternative B:

the average proportion of rings on the crosses side and crosses on the rings side

The two definitions are not equivalent. Although there are exponentially many possible lines in the size of the grid, we will show that polynomial algorithms exist for both definitions of isogloss lines.

We will demonstrate the usefulness of the isogloss drawing algorithm on a dataset of structural features of South American languages.

References

Händler, H. (1983). Das konzept der isoglosse: methodische und terminologische probleme. In Besch, W., editor, Dialektologie. Ein Handbuch zur deutschen und allgemeinen Dialektforschung, volume 1.1 of Handbücher zur Sprach- und Kommunikationswissenschaft, pages 501-528. Berlin/New York: de Gruyter.

Ivi¢, P. (1964). Structure and typology of dialectal differentiation. In Lunt, H. G., editor, Proceedings of the ninth International congress of linguists, Cambridge, Mass., August 27-31, 1962, pages 115-129. The Hague: Mouton.

Schneider, E. W. (1988). Quantitative methods of area delimitation in dialectology: A comparison based on lexical data from georgia and alabama. Journal of English Linguistics, 21(2):175-212.

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Last update: September 20, 2014. erik.tjong.kim.sang(at)meertens.knaw.nl