have been already filled in the cluster column of are 
found within its vicinity and when only one kind of the 
cluster numbers is allocated to them,the cell is 
recognized to belong to the same cluster. The cluster 
number is registered in the cluster column of the cell, 
step 3. When there are more than two kinds of the 
clusters in its vicinity, the cell is considered to be 
located on the bottom of the valley, that is, the 
boundary between the clusters, the cluster number of the 
mountain nearest to the cell is registered in the 
cluster column of the cell. 
Radius of the vicinity. From the same reason as the 
histogram space was quantumized in its generation , the size 
of the vicinity,that is,the radius drv of the hyper-sphere 
should vary according to the distance from the origin. 
The radius drv of the vicinity should be reasonably 
described as followings, 
drv(x)=a*drq(x) (9) 
where a is a constant deciding the size of the vicinity. The 
constant a should be rather larger than one. Otherwise,any 
other cells except oneself under consideration would not be 
found within the vicinity. 
The searching time. It is basically possible 
sequentially by checking all the distance between the cell 
and ones with higher frequence to find whether there may be 
any other cells within the vicinity or not. When the cell 
is especially stored in lower part of the MDH table, there 
is a great problem of searching time because the number of 
the cells to be compared with is rather large. To reduce 
the searching time, a key k presented by the following 
eq.(10) is introduced to our system. 
By checking whether its key may be in the following range 
or not, 
Z xi-SQRT(N) * drv <= k <= Z xi + SQRT(N ) * drv (11) 
i i 
the cell can be known of the potential presence in its 
vicinity. 
Clustering process. For the simplicy, a diagram is shown 
in Fig.(3) to demonstrate the procedure of the cluster 
analysis when the histogram space is one dimensional. The 
small figures on the shoulders and capital ones inside the 
figure show the processing order and the allocated cluster 
numbers, respectively. The diagram teaches us that the one 
dimensional histogram is classified into two clusters 1 and 
2 through 15 processes. 1st and 4th processes generate new 
clusters and 15th process discovers the bottom of the 
valley. 
Threshold of the radius. When the cluster analysis is 
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