5. Colored FCM

landscape image. This image includes many objects in different colors, and these colors are

Figure 5. FCM algorithm results. (a) Original image; (b) FCM Cluster No:1; (c) FCM Cluster No:2; and (d) FCM Cluster

FCM algorithm includes iterative procecesses. For the given image at the end of the 55 iteration steps, clustering processes are completed for the given threshold value which is 10<sup>5</sup> for FCM

generally indented in these objects.

Figure 4. Flow chart of the FCM algorithm.

24 Recent Applications in Data Clustering

distance change.

No:3.

Colored Image Fuzzy C-Mean (C-FCM) involves color-based clustering using fuzzy sets. This 3D method is firstly given by Kutbay and Hardalaç [17] as Robust Colored Image FCM (RCI-FCM), but this presented method is different from RCI-FCM. In RCI-FCM, distances are calculated for each R, G and B channels, but in this method, the mean distance is calculated for RGB color spaces. This method represents the RGB color formed images in FCM, which uses FCM-based algorithm in colored images. The membership function calculates the centroids of the clusters for each R, G and B color spaces. After calculation of Euclidian distance for each channel, the mean distance could be calculated shown in equivalence (10).

$$d\_{i\mathcal{k}(R,G,\mathcal{B})}^2 = \operatorname{mean}(\left| \left| \mathbf{x}\_{\mathcal{k}(R)} - \boldsymbol{\upsilon}\_{i(R)} \right| \right|, \left| \left| \mathbf{x}\_{\mathcal{k}(G)} - \boldsymbol{\upsilon}\_{i(G)} \right| \right|, \left| \left| \mathbf{x}\_{\mathcal{k}(B)} - \boldsymbol{\upsilon}\_{i(B)} \right| \right|) \tag{10}$$

Membership for each cluster can be calculated in the following formula (11).

$$\mu\_{ik(R,G,B)}^{\*} = \left\{ \sum\_{j=1}^{c} \left( \frac{d\_{ik(R,G,B)}}{d\_{jk(R,G,B)}} \right)^{2/(m-1)} \right\}^{-1} \forall i \in [1,c] \text{ and } k \in [1,n] \tag{11}$$

where u<sup>∗</sup> ik Rð Þ ;G;<sup>B</sup> represents the membership degree for mean distance for each color. In this representation for each item, cluster's membership can be calculated and statistically membership could be defined for each cluster.

New cluster center can be calculated in the following equivalence (12) for each cluster:

$$\boldsymbol{\sigma}\_{i(R,G,B)}^{\*} = \frac{\sum\_{k=1}^{n} \boldsymbol{\mu}\_{ik(R,G,B)}^{\mathrm{m}} \boldsymbol{\chi}\_{k(R,G,B)}}{\sum\_{k=1}^{n} \boldsymbol{\mu}\_{ik(R,G,B)}^{\mathrm{m}}} \quad \forall i \in [1, c] \tag{12}$$

where u<sup>∗</sup> ik Rð Þ ;G;<sup>B</sup> is the membership function of each RGB color pixel. This function calculates for each R, G and B colors, for the each RGB space representation. c denotes the clusters for each npixel, and dik Rð Þ ;G;<sup>B</sup> explains the distance between pixel xk and the centroid vi for i th number cluster for each color domain. v<sup>∗</sup> i Rð Þ ;G;<sup>B</sup> represents the centers of the clusters for each RGB pixel value into the c-cluster. C-FCM algorithm's flow chart is shown in Figure 6. The proposed method aims to create c3 cluster for the given stopping criteria. New cluster centroids are calculated from the results of the membership function for all RGB colors.

C-FCM algorithm flow chart is shown in Figure 6. The flowchart shows the C-FCM algorithm for colored images. For each iteration step, RGB distances are calculated and cluster centers are calculated. After updating the cluster centers in the given threshold value, each item will be assigned into the given cluster.

Figure 7 represents the C-FCM algorithm, which is applied for the given original image shown in Figure 7a. For each color, pixels assigned into two cluster. For RGB color space 2<sup>3</sup> cluster are created for this image. These clusters can be given in eight clusters as in Figure 4b–i, respectively.

C-FCM algorithm includes iterative procecesses. For the given image at the end of the 26 iteration steps, clustering processes are completed for the given threshold value which is 10<sup>5</sup>

Genetic algorithm is very popular method in evolutionary computation processes. This method is firstly developed by Holland in 1975 [18]. This algorithm includes natural evolutionary processes. This method optimizes a population of the structure by using a set of

This method maintains a population of structures and these structures consisting of individuals. Each individual is evaluated by a function named as fitness function. These processes

In genetic algorithms (GAs), each individual represents a candidate solution in binary form. This individual called as chromosome. After an initial population is generated, randomly

For genetic algorithm examination, the following terms are useful for describing the concept of genetic algorithms. These are gene, chromosome, population (mass), reproduction process,

Gen is a unit that carries partial information. By bringing together these units, the chromosomal sequence that forms the solution cluster comes into play; for this reason, the genome

Chromosomes are structures that contain the information of the problem solving. Population is formed by the combination of chromosomes. At the initiative of the designer, what informa-

The population is called the heap of possible solutions. In the GA process, the population size remains constant, but the bad chromosomes separate from the stack. The size of the heap is a very important concept, which must be well established, as the overcrowded heap increases the time of possible heuristic approach, while the small heap may cause no possible solution at

The reproduction process is the process of selecting the sequences to be transferred from the current stack to the next stack. The sequences carried are genetically the most appropriate sequences. The requirement for transition is whether the level of conformity specified has been

The fitness value, in genetic algorithms, which specifies which index will transfer the next generation, which index will be lost. Conformity value reflects the purpose of the problem.

Bandyopadhyay and Maulik [19] attempted to use GA to automatically determine the number

th cluster using genetic

Partitional Clustering

27

http://dx.doi.org/10.5772/intechopen.75836

of clusters K in 2002. The GA clustering aims assigning the data into k

includes selection, recombination and mutation processes.

crossover and mutation processes are executed for each iteration step.

for C-FCM distance change.

6. Genetic clustering

evolutionary operators.

and conformity value.

all.

achieved.

processes.

decides well how to code it.

tion is to be found on the chromosome.

Figure 6. Flow chart of the C-FCM algorithm.

Figure 7. C-FCM algorithm results. (a)Original image; (b)–(i). C-FCM Cluster No:1–8.

C-FCM algorithm includes iterative procecesses. For the given image at the end of the 26 iteration steps, clustering processes are completed for the given threshold value which is 10<sup>5</sup> for C-FCM distance change.
