# 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 .

### Raster-Based Index Model

An illustration of a raster-based index model. First, the cell values of each input grid are converted into the standardized scale of 0.0 to 1.0. Second, the index values in the output grid are calculated by summing the products of each grid multiplied by its assigned weight.

For example, the index value of 0.28 is calculated from: .

## Other Index Methods

In this index model represents paired comparison for determining criterion weights is sometimes called direct assessment. An alternative to direct assessment is trade-off weighting. Tradeoff weighting determines the criterion weights by asking participants to state how much of one criterion they are willing to give up obtaining a given improvement in another criterion. In other words, trade-off weighting is based on the degree of compromise one is willing to make between two criteria when an ideal combination of the two criteria is not attainable. Although realistic in some real-world applications, trade-off weighting has shown to be more difficult to understand and use than direct assessment.

Data aggregation refers to the derivation of the index value. Weighted linear combination calculates the index value by summing the weighted criterion values. One alternative is to skip the computation entirely and assign the lowest value, the highest value, or the most frequent value among the criteria to the index value.