Page 286 - Contributed Paper Session (CPS) - Volume 2

CPS1857 Nicholas J. et al.
regression models for the i-th observation (i = 1, 2, ..., n), p-varieties, and
the j-land types categorical (j = {1, 2, 3, 4}) in every subset, which can be
formulated as:
= + + ⋯ + (4)
⃗

1 1
2 2
The estimator of regression coefficient for the j-land types can be
formulated as:
= ( ) (′) (5)
⃗
⃗
−1
′

where
11 21 … 1 1
12 22 … 2
⃗
= [ ⋮ ⋮ ⋱ ⋮ ] ; and = [ ⋮ 2 ]
1 2 …
denotes the independent variable. In this research, four different
independent variables () will be used to define the parameter to classify
the land types: band 1 ( ), band 2 ( ), band 3 ( ), NDVI ( ), and SAVI
3
1
2
4
( ). denotes the dependent variable. There will be five categorical land
5
types which will be represented by the limited multi-dependent variable
, , , , and . They are taken from the value of either 0 or 1 (Table
1
5
2
4
3
1). The value of 0 means that the response is zero. Conversely, the value
of 1 means that the response has a significant value. We assume that
1
is impervious defined as (1, 0, 0, 0, 0), is green land defined as (0, 1, 0,
2
0, 0), is water defined as (0, 0, 1, 0, 0), and is soil land defined as (0,
4
3
0, 0, 1, 0) [4].

Table 1. The Limited Multi Dependent for Four Land Types
Category of Land Types
4
1
3
2
Impervious 1 0 0 0
⋮ ⋮ ⋮ ⋮ ⋮
Green Land 0 1 0 0
⋮ ⋮ ⋮ ⋮ ⋮
Water 0 0 1 0
⋮ ⋮ ⋮ ⋮ ⋮
Soil Land 0 0 0 1
⋮ ⋮ ⋮ ⋮ ⋮

3. Calculate the error value for every observation and classes in each

subset. The error itself can be formulated as [4]:
= − (6)
⃗

4. Calculate for the median square of error of each subset and define [2]:
2

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