روش خوشه ضرب و شتم جدید مبتنی بر بهینه سازی کلونی مورچه فازی با ابزار های ترکیبی برای حوزه های مداوم

The kernelized fuzzy c-means algorithm uses kernel methods to improve the clustering performance of the well known fuzzy c-means algorithm by mapping a given dataset into a higher dimensional space non-linearly. Thus, the newly obtained dataset is more likely to be linearly seprable. However, to further improve the clustering performance, an optimization method is required to overcome the drawbacks of the traditional algorithms such as, sensitivity to initialization, trapping into local minima and lack of prior knowledge for optimum paramaters of the kernel functions. In this paper, to overcome these drawbacks, a new clustering method based on kernelized fuzzy c-means algorithm and a recently proposed ant based optimization algorithm, hybrid ant colony optimization for continuous domains, is proposed. The proposed method is applied to a dataset which is obtained from MIT–BIH arrhythmia database. The dataset consists of six types of ECG beats including, Normal Beat (N), Premature Ventricular Contraction (PVC), Fusion of Ventricular and Normal Beat (F), Artrial Premature Beat (A), Right Bundle Branch Block Beat (R) and Fusion of Paced and Normal Beat (f). Four time domain features are extracted for each beat type and training and test sets are formed. After several experiments it is observed that the proposed method outperforms the traditional fuzzy c-means and kernelized fuzzy c-means algorithms.

Electrical activity of the heart is measured by a noninvasive method called the electrocardiogram (ECG). ECG is a very important tool for the diagnosis of the heart beat abnormalities. If there exists an abnormality in usual behavior of the heart, the measured ECG signal deviates from its normal shape which helps the physician to diagnose this abnormality. However, it is really difficult to diagnose an abnormality in a long term ECG record which consists of thousands of ECG beats. For this reason, supplementary tools for automatically diagnosis of the heart beat abnormalities are proposed. These tools use both the signal processing and pattern recognition methods. Pattern recognition methods can be categorized into two groups according to their learning procedure. Supervised learning, requires prior labeling of the training data to create a model of the given dataset. A supervised learning algorithm analyses the given training dataset and creates an output. This output is then compared with the desired output (label) and an error or feedback signal is created. Algorithm then updates itself according to this feedback signal in order to create a model of the given dataset. Once the algorithm is terminated the obtained model should generalize the training data such that when an unknown input pattern is given to the model it should be classified correctly. However, unsupervised learning does not need a prior labeling. It creates clusters from a given dataset according to a similarity measure which is usually a distance function. After the clustering process, similar patterns are grouped in the same cluster and dissimilar patterns are grouped in different clusters. Probably the most popular clustering algorithm is the hard c-means (or k-means) algorithm which assigns a data point in a given dataset to exactly one cluster. Such an assignment can be inadequate because some data points can be in a location which is almost equally distant from two or more cluster centers. By forcing such a point to exactly one cluster, the similarity of this point to other clusters is totally ignored. For this reason, fuzzy clustering methods are proposed. In fuzzy clustering methods a data point can belong to more than one cluster with different degrees of membership which is useful especially when the clusters overlap each other. Actually, this is the case for most of the real world problems, as in the ECG beat clustering problem. In real world problems, there is often no sharp boundary between clusters so that, the fuzzy clustering methods are usually better suited for these kind of problems when compared to the crisp methods. Generally speaking, in ECG classification algorithms, a similarity measure is used to measure the distances between the query beat and the templates in the database. The smaller the distance is, the more similar the template to the query [1]. However, as stated above, in many cases a data point can be in a location which is almost equally distant to more than one cluster center. In such a situation, fuzzy clustering methods could prevent the misclassification of a query beat by utilizing the membership values of the datapoints to each cluster. Based on the above considerations, recently a number of studies which use fuzzy clustering algorithms for ECG beat classification are proposed. One of these fuzzy clustering algorithms is the fuzzy c-means (FCM) algorithm [2]. After a clustering process, the FCM algorithm gives two outputs namely, the cluster centers and a fuzzy partition matrix which contains the membership values of each datapoint to these clusters. The obtained cluster centers or the membership values are then utilized for classification. Özbay et al. [3] utilizes the membership values obtained by using FCM algorithm to train a multilayer perceptron (MLP) for classification of ten types of ECG beats. In more recent studies, Ceylan et al. [4] and Özbay [5] use type-2 fuzzy c-means algorithm in a similar manner. Another study which utilizes membership values for ECG beat classification is proposed by Yeh et al. [6]. In this study, four morphological features out of nine are selected with a method called Range-Overlap Method (ROM) and then clustered by fuzzy c-means algorithm. Different from the above studies, Haseena et al. [7] use cluster centers as input to a neural network for classification of eight types of ECG beats.

In this study, it is aimed to show that, the clustering performance of the KFCM algorithm can be improved by using an optimization method. For this purpose, a recently proposed ant-based algorithm, hybrid ant colony optimization for continuous domains (HACO), is used. HACO optimizes both the kernel function parameter (here σ values) and cluster centers, which in turn minimizes the objective function of the traditional KFCM algorithm. The proposed method is applied to an ECG beat classification system. It is shown that, the proposed method outperforms traditional FCM and KFCM algorithms. However, it needs to be further improved. As stated before in classification stage, in order to minimize the effect of the classifier to the classification performance and to compare traditional algorithms with the proposed method more accurately, a simple but stable classifier is used. It is thought that, replacing the classification stage by a more complex classifier scheme such as an artificial neural network, the classification results can be further improved. Future directions include the design of this classifier stage to improve the generalization capability of the proposed ECG beat classification system.