ارايه‌ي مدلي براي كمينه‌سازي مجموع متوسط فواصل درون‌خوشه‌يي در طبقه‌بندي مشتريان

PRESENTING A MODEL FOR MINIMIZING THE MEAN SUM OF DISTANCES WITHIN CLUSTERS IN CUSTOMER SEGMENTATION

در سال‌هاي اخير اهميت داده‌ها به‌عنوان منابع داراي پتانسيل اطلاعاتي بسيار بالا به‌نحو گسترده‌يي مورد توجه قرار گرفته شده است. داده‌كاوي با استخراج و كشف سريع و دقيق اطلاعاتِ با ارزش و پنهان از پايگاه داده‌ها به‌منظور تصميم گيري و پشتيباني تصميم از جمله اموري است كه هر كشور، سازمان و شركتي به‌منظور توسعه علمي، فني و اقتصادي خود به آن نياز دارد. با توجه به ضرورت استفاده از فنون داده‌كاوي ــ خصوصاً خوشه‌بندي ــ در اين نوشتار يك مدل رياضي براساس رويكرد خوشه‌بندي ارايه‌ مي‌شود كه در خوشه‌بندي مشتريان شركت صنعتي پارس‌خزر كاربرد دارد. مسيله‌ي خوشه‌بندي به‌صورت مدل رياضي با هدف كمينه‌سازي مجموع متوسط فواصل درون‌خوشه‌يي در طبقه‌بندي مشتريان فرمول بندي مي‌شود كه در تمامي موارد آزمايش شده، با بهبود‌بخشي شديد در فواصل درون‌خوشه‌يي همراه است. عملكرد اين شيوه در يك مسيله‌ي واقعي آزموده شده و تحليل نتايج حاكي از كارايي محاسبات اين شيوه است.

In recent years, data importance is widely considered as a resource with high information potential. Data mining is a process of extracting and refining knowledge from a large database. The extracted information can be used to predict, classify, model, and characterize the data being mined. It is an intelligent method of discovering unknown or unexplored relationships within a large database. It uses the principles of pattern recognition and machine learning to discover knowledge, and various statistical and visualization techniques to present the knowledge in a comprehensible form. Data mining with extraction, and rapid and precise discovery of valuable and hidden information from data bases, is used for decision making and decision support. It is a technique that every country, organization and company requires in order for scientific, technological and economic development. Nowadays, considering the strong competition condition of companies and organizations to gain new customers and maintain previous customers, the volume of customer information and dramatically complex interaction with customers, data mining has been a pioneer for acquisition profitability in customer relationships, considering the necessity to use data mining, especially clustering. In this paper, the first concept of clustering and its applications is considered, then a review about data mining mathematical concepts and clustering, including: minimizing the sums of squares within clustering, components related to p-dimension Euclidean space, minimizing the distances of the mean squared sum within clustering, number of clusters, minimizing the total distance within clustering, and minimizing the maximum distance within clusters, is addressed. A model of “minimizing the mean sum of distances within clusters in customer segmentation” is proposed. The proposed model is formulated as a mathematical model with the objective of minimizing the mean sum of distances within clusters. Then, the model is compared with the “minimizing the distances mean squared sum within clustering” model using MATLAB 7.5.0 (R2007b). The proposed method does not depend on any initial positions for the cluster centers and does not allow any empirically adjustable parameters. In the tested cases, the model has improved the distances within clusters. Finally, the performance of the model is tested on a real problem for classification of the Parskhazar Industry customers. Experiments reveal that the proposed model has efficient yield.