Pattern

Classification

using 2-D Cellular Automata

N-dimensional gridof cells

Each cell in of the finite number of

states

Cells constituting the neighbour of

the cell in consideration

Collection of rulesdetermining the

state of the cell in the next instant

Cellular Automata -A discrete dynamical system that consists of :

Behind every complex

behavior lies simple logic-

Cellular Automata

Purely local

decisions

parallelism

Nomodeling

constraints

Works well with less

data

Collective behavior ofsimple cells

• finds application in effective pattern classificationCellular Automata

Meaningful interpretation of voluminous data-DATA CLASSIFICATION

Presented algorithm maps data set instance to pixel position ( 2-dimensional in this case)- PATTERN CLASSFICATION

Pattern classification was proposed as an application of Sweeper’s Algorithm(SA)

Combined use of SA and Majority rule as an attempt to classify iris dataset - define regions (patterns) corresponding to distinct disjoint classes of the dataset.

Classification AlgorithmStep 1 : Mapping instances to pattern

• x = average (sepal length, sepal width) x 100

• y = average (petal length, petal width) x 100

Mapping instances to

pixel position

• M(x, y) =

Matrix, ‘M’ formation • Mset (x, y)=

• Mversi(x, y) =

• Mvir(x, y) =

Divide matrix

M, into 3

1, setosa2, versicolor3, virginica0, otherwise

1, M(x,y)=10, otherwise

2, M(x,y)=20, otherwise

3, M(x,y)=30, otherwise

Setosa.bmp

Versicolor.bmp

Virginica.bmpAn instance

(5.1, 3.5, 1.4, 0.2) -Setosa

x = (5.1 + 3.5)/2 × 100 = 430

y = (1.4 + 0.2 )/2 × 100 = 80

M(430,80) = 1

Example

Classification AlgorithmStep 2 : Application of Sweeper’s Algorithm

Sweeper’s Algorithm

Null boundary, 9 neighborhood, hybrid 2-D CA

Given a destination point (x , y)

Consider an axis passing through the point dividing the 2-D search region into two ( refer figure alongside)

Rotate the axis through an angle of rotation,45 degrees in this case, forming 4 such set of regions

In each iteration apply hybrid rules to each of these sets of regions, aimed at bringing the marked pixels a step

closer to the axis

As a result, after certain number of iterations, all marked pixels accumulate around the destination point.

Setosa.bmp

Combined.bmp

Virginica.bmp

Versicolor.bmp

Write to ‘combined.bmp’ image file

Combine corresponding matrices into one: M‘ = Mset + Mversi + Mvir

Apply Sweeper’s Algorithm (application of hybrid 2-D CA

rules to ‘sweep’ points near to a single destination point) to each

.bmp image files with

Centroid of pixels in white as destination, for each image

Classification Algorithm Step 2 continued …

Majority Rule:Next state of cell =

(applied to each pixel)

• Moore neighborhood

• Null boundary

• Uniform• Here, ni is the numbers of neighbors of class ‘I’.

Assign different colors :

Verification:

• Map instance to pixel

• Check for the color assigned to the corresponding element (pixel) in matrix

• If match , increase counter

• Efficiency = (total number of matches /total number of instances)x 100

Conclusion:• Linear and non-linear

instance space classifier

0 : n1 + n2 + n3 = 01 : n1 > n2 and n1 > n3

2 : n2 > n1 and n2 > n3

3 : n3 > n1 and n3 > n2

Rand(1, 2): n1 = n2 > n3

Rand(1, 3): n1 = n3 > n2

Rand(2, 3): n2 = n3 > n1

Rand(1, 2, 3): n1 = n2 =n3 ≠ 0

M’i,j = 1setosa

M’i,j = 2versicolor

M’i,j = 3viriginica

Classification AlgorithmStep 3 : Application of Majority Rule

Efficiency :Efficiency in the range of

97.6± 1.5

Efficiency nearly the same even with lesser value for k

Efficiency = 100% when classify setosa and versicolor compared

to 99± 3.2 in voting rule

Complexity:2-dimensional grid in scale of

hundred

45 iterations of Sweeper’s Algorithm and nearly 200iterations of Majority rule

cosumes nearly 21 mins. cputime in a serial processor

• With ‘k’ = number of instances from each class, as the training set• 5 simulations for each value of ‘k’• Averaging the efficiencyfor all k , we obtain graph as :

• An efficient linear as well as non-linear classifier (with efficiency nearly 97.6 ± 1.5 %)

• Sweeper preserves the pattern of region a class occupies

• Maps attributes to 2-dimensional grid resulting in loss of information, yet efficient.

• Generalize the algorithm for any data set

• Reduce time complexity

• Optimize sweeper’s algorithm for minimum number of iterations

• Optimum selection of destination point to improvise the algorithm

THANK

YOU