Classification of Remotely Sensed Data using Gravitational Symbolic Clustering

Classification of Remotely Sensed Data using Gravitational Symbolic Clustering

2 When dimension d=1
This works by assigning 1-dimensional m number of samples to any one of the 1-dimensional arrays. The one 1-dimensional R bin arrays are used to store the useful information of all the features. The data before reduction requires normalization between 1 to R. The normalized features are assigned to the R arrays. The idea that the first feature is used to determine the column position of the bin to which the sample is to be assigned. If the first sample has the feature values f11, which is normalized between 1 to R. This sample is assigned to a bin having a column value of f11.

If the second sample have the feature values f₂₁. Say if f₁₁ = f₂₁, then the bin to which this sample is assigned also has a column value of f₁₁.

The steps are as follows:
Let S1 be the R 1-dimensional arrays to store updated information of the feature and W is another such R 1-dimensional bin-weight array to update number of samples assigned to each corresponding bin.

Normalize the d dimensional m samples between 1 to R.
The first feature gives the column position of the bin.
As each sample is assigned to a bin the arrays S₁ is updated.

Also the number of nonempty bins is updated in W bin-weight array.

Cluster Coglometrate and Global Coglomerate Strengths
The cluster coglomerate strength (CCS) of cluster C_j is :

Where m_j cluster weight of C_j
X_m Composite object of C_j
D_j max X_i Î C_j D ( X_i , X_m ) or maximum dissimilarity.
s: a suitable positive number and
r: a suitable negative number depends
on the input sample set.

The global coglomerate strength (GCS) of cluster at any level is defined as the sum of all the CCS of all the prevalent clusters at that level. Thus the GCS when cluster C_j is formed, is defined as:

Symbolic Gravitational Clustering Algorithm

1 Agglomerative Method

Reduce the data by choosing an appropriate bin size and threshold. Let the initial number of clusters be equal to number of samples in the reduced data (N) each cluster weighted 1, and CCS =0 and GCS =0.
Using the similarity measure, find all the mutual pairs present in the symbolic data set.
Consider the mutual pairs X_i and X_j Merge the two objects to form a CSOm. Find the CCS 'CCSm' of the clusters consisting of two objects X_i and X_j and also GCS 'GCSm' is also found out.
The cluster threshold CT_i,j is calculated

and global threshold GT_i,j is also calculated :

n_i and n_j are the cluster weights of X_i and X_j respectively.

The two objects are replaced by a CSO if the below two conditions are satisfied :

a) CCSm > CT_i,j
b) GCSm > GT_i,j

Then reduce the number of clusters by one.
Step 3 and 4 is repeated for all the mutual pairs present at that stage.
Determine the Cluster Indicator value for each Pth merging:

Where Max_p+1 and Max_P are the maximum similarities of (P+1)^th and p^th merging respectively.
Iterate steps 2 to 6 until a stage is reached when no replacement of mutual pair occurs.

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