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Equally, the data items associated to the cell σ i + r− 1 ( t + 1) will be the data item
with the greater distance:
σ i + r− 1 ( t +1)= σ i + r− 1 ( t ) f d (
x i ,
x i +1 ) <d (
x i ,
x i + r− 1 )
(3)
σ i +1 ( t )
t r ise
These rules keep together data with similar values in the feature vectors. Fig. 2
depicts the states which the tape can evolve depending on the data items
considered.
... σ i σ i +1 ... σ i + r 1 ...
... σ i σ i +1 ... σ i + r 1 ...
d ( x i , x i +1 ) <d ( x i , x i + r 1 )
d ( x i , x i + r 1 ) <d ( x i , x i +1 )
... σ i σ i +1 ... σ i + r 1 ...
... σ i σ i + r 1 ... σ i +1 ...
Fig. 2. A tape state can evolve to two different states depending on the distances
between data item associated to the reference cell σ i and the cells σ i +1 and σ i + r 1
By increasing systematically the range r of the rules, the number of contiguous
cells belonged to data items on the same cluster also increases. After a few
iterations, the system converges to a final state where all the cells associated
to data items of the same cluster are contiguous. The items in each cluster can
be easily detected by comparing the distance between each cell and the next
one (i.e. the chainmap diagram). When that distance is much greater than the
previous ones, the new cell corresponds to a new cluster.
3 Experimental Results
We have tested the proposed algorithm with both synthetic and real data like
the well-known Iris dataset. In the sequel we describe and comment the results.
3.1 Clustering Results with Synthetic Data
The synthetic dataset used for experimental purposes is shown in Fig. 3. It is
composed of 4 two-dimensional classes. Each class contains 20 data items.
After initializing the cellular automata linear lattice by depositing at random
the individual data items, one at each cell or site, the cellular automata rules
explained in section 2 start to act.
Fig. 4 displays the successive states of the automata lattice. Each line shows
the tape's state in each iteration. We have assigned a different grey level to each
cluster shown in the Fig. 3: black corresponds to the cluster represented with
circles, dark grey to the triangles, light grey to the stars and white to the squares.
 
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