Page 285 - Contributed Paper Session (CPS) - Volume 2

CPS1857 Nicholas J. et al.
0 it can be said that an area is covered by a building. The NDVI calculation
formula is as follows [3]:

(NIR − Red) (1)
NDVI =
(NIR + Red)
NDVI value empirically is still less stable for classifying vegetation because
it is influenced by a variety of factors such as soil color, soil moisture, and
saturation effects of high density vegetation. The Soil Adjusted Vegetation
Index (SAVI) method was developed as the improvement of NDVI when
vegetation cover is low on a soil. The SAVI calculation formula is as follows [3]:

(NIR − Red)
SAVI = ∗ (1 + L)
(NIR + Red + L) (2)

where NIR denotes every pixels in the band 5 of Landsat 8 imagery. RED
denotes every pixels in the band 4 of Landsat 8 imagery and L denotes the soil
calibration factor, that usually calculated as 0.5 which indicates the land cover
is not fully covered by the vegetation [3].

2.2 Least Median of Squares Regression
The existance of outliers in linear regression models can be a problem
because outliers can cause the formation of regression parameter models to
be less accurate. Classical least squares regression consists of minimizing the
sum of the squared residuals. Many authors have produced more robust
versions of this estimator by replacing the square by something else, such as
the absolute value [2]. One of the methods suggested to perform robust
regression models is Least Median of Squares (LMS) regression [2]. The LMS
regression is a different approach to calculate the robust regression by
replacing the sum with the median of the squared residuals [2]. This method
predicts the regression models by minimizing the value of the square errors
of the ℎ observation. The method is suitable for data with outliers. The LMS
estimator is defined as follows [2]:

= arg min () (3)
̂

where () denotes the median square of error for ℎ observation
( ). In general, the algorithm for applying the LMS regression method
2
ℎ
can be summarized in the following steps [2]:
1. Determine the size of the subset and the number of subset according
to the number of classes. In this research, we will use four subset that
indicates the four land types (impervious, green, water, and soil land.
2. We will take the subset of size from the -sized example and find the
estimated regression coefficient for each subset to generate the
⃗
274 | I S I W S C 2 0 1 9