br where S shows the mean values
where µS0 shows the mean values of pixels in the area of a cell and S(u, v) pixel value in the area of a cell.
where σ shows the divergence from the mean distance given by the Distance variable. Mathematically, σ and Distance are computed by the follow-ing equations:
where P is the perimeter. The value of the circularity is ranging between and 1. If the nucleus circularity is equal to 1, then it is considered to be circular, otherwise elongated in shape. • Roundness: Malignancy tends to change the MK-2206 in the nucleus which disfigure the shape of the nucleus. This leads to changes in nucleus circularity and roundness. Roundness measures the distance between the border of the malignant cell to the center of the area. Mathematically, it can be computed by the following equation: 1 − σ
• Standard Deviation:
In order to perform a proper classification of benign and malig-nant cells, the feature vector is constructed from both morpho-logical and texture based features.
Due to the complexity of the problem and for automated processing, the knowledge of significant features is unknown in advance. Therefore, many relevant feature sets are established for better representation of the domain. In hypothesis, additional features should give more perceptive control over the data, but in practice, more features lead to slowing down the learning pro-
(8) cess. Similarly, one of the disadvantages of unnecessary features results in over-fitting by the classifier. In the proposed approach, the GA based feature selection technique is used for the selection of optimal features. The GA is one of the popular types of EA, and it is commonly used in a variety of computer vision applications, which are based on natural selection of features. GA works with space of feature population, where a chain of iterative processes (9) is executed for the creation of a new generation. GA builds up a chronological population of time-based solutions presented by chromosomes to achieve satisfactory results . A fitness func-tion calculates the significance of the answer in the evaluation (10) phase. Mutation and crossover are the two essential functions and have a crucial impact on the value of fitness. Chromosomes with higher fitness values are chosen for the next generation based on roulette wheel techniques . Similarly, in the mutation process, some of the genes are randomly updated. Crossover is a genetic function that combines separated features from subsets pair into a new subset. Offspring is replaced with the preceding population using the variety or exclusivity substitution approach to generate a new population in the future generation . Different GA based feature selection algorithms are presented in the literature. In the proposed approach, Chain-like Agent Genetic Algorithm (CAGA) is used because of its simplicity, accuracy, and efficiency. The CAGA approach implements a chain-like agent structure as a population structure [36,37]. This population structure is more straightforward as compared to other agent structures. Similarly, it is efficient computationally which successfully avoids early convergence. The introduction of genetic operators such as (11) adaptive mutation and crossovers in the CAGA efficiently search for the global optima and maintain the population diversity. Moreover, a competitive selection approach is used to increase the searching ability through dynamic neighboring selection. Fig. 3 shows different features that are extracted from segmented
(12) breast cytology images. The features matrix is created from the extracted features, which is then passed through CAGA for the optimal features selection. CAGA is used for the optimal features selection and global numerical optimization problem, which result in a satisfactory (13) classification with higher accuracy. The CAGA is the combination of both dynamic neighboring genetic operators and chain-like agent structure to acquire a higher optimization capability. In the chain-like agent structure, an agent signifies a candidate solution to the problem of optimization. The evolution takes place through (14) the interaction of agents. Similarly, with genetic operators, the neighboring agents compete and collaborate with their peers to improve the performance.
In the CAGA environment, all agents are connected in one chain, known as agent chain, which is represented by L, as shown (15) in Fig. 4. In Fig. 4, circles represent agents while the label inside the circle shows the position of the agent in the chain. The agent can communicate with both back and forward neighbors . The chain begins with the first agent given by node (1, 1) (where 1 represents one-dimensional agent structure) and communi-