# The Index Model in Application in GIS Image Classification: Weighted Linear Combination Method (Vector Based and Raster Based) (Especially for GATE-Geospatial 2022)

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## Index Model

An index model calculates the index value for each unit area and produces a ranked map based on the index values. An index model is like a binary model in that both involve multi-criteria evaluation and both depend on map overlay operations in data processing. But an index model produces for each unit area an index value rather than a simple yes or no.

Selected variables are evaluated at two levels

• Relative importance, assigning a weight
• Observed values are evaluated and given scores.

## The Weighted Linear Combination Method

The primary consideration in developing an index model, either vector-or raster-based, is the method for computing the index value. Weighted linear combination is a common method for computing the index value. Following the analytic hierarchy process proposed by Saaty, weighted linear combination involves evaluation at three levels.

First, the relative importance of each criterion, or factor, is evaluated against other criteria. Many studies have used expert derived paired comparison for evaluating criteria. This method involves performing ration estimates for each pair of criteria.

Second, data for each criterion are standardized. A common method for data standardization is linear transformation. For example, the following formula can convert interval or ration data into a standardized scale of 0.0 to 1.0:

Where is the standardized value for the original value is the lowest original value, and is the highest original value.

### Vector-Based Index Model

An illustration of a vector-based index model. First the Suit and Type values of the two input maps are standardized from 0.0 to 1.0. Second, the two maps are overlaid. Third, a weight of 0.4 is assigned to the map with Suit and a weight of 0.6 to the map with Type. Finally, the index values are calculated for each polygon the output by summing the weighted values. For example, Polygon 4 has an index value of .