Shaik Khaleel Ahamed ¹, M. M. Naidu ¹, C. Subba Rami Reddy ²

Affiliations
1 C.S.E. Department, S.V.U. College of Engineering, S. V. University, Tirupati – 517501, Andhra Pradesh, IN
2 Statistics Department, S. V. University, Tirupati - 517501, Andhra Pradesh, IN

Abstract

Background/Objectives: Outliers are extreme observations which deviate significantly from the normal observations. Their presence distorts the end results of scientific study. In Data Envelopment Analysis (DEA), most influential observations are outliers. Identification of outliers and their deletion is important in DEA problems. Deletion of an extreme observation results in contraction of the production possibility set. Methods/Analysis: This study identifies outliers as these extreme observations whose absence results in significant contraction of the production possibility set. Data Envelopment Analysis is based on solving linear programming problems to assess the efficiency scores of Decision Making Units (DMUs). The present study can estimate efficiency scores of DMUs with and without outliers. Deletion of outliers provides smaller targets to the inefficient DMUs. Findings: For identification of outliers super efficiency, problems can be solved for extremely efficient DMUs, which results in the largest dimension of the contracted Production Possibility Set (PPS). The present study provides many dimensions of the contracted PPset, solving Banker, Charnes and Cooper (BCC 1984) linear programming problems. Sum of these dimensions can be viewed as histogram that closely envelops the contracted Production Possibility Set. Larger is the sum of all dimensions, more influential is the decision making unit. To identify outliers in DEA in this study a statistical test is outlined. Application/Improvements: The methodology outlined can be used for DMUs competing with each other in a competitive environment employing similar inputs to produce similar outputs.

Keywords

Data Envelopment Analysis, Outliers, Super Efficiency

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C. Madhusudhana Rao ¹, M. M. Naidu ²

Affiliations
1 Department of Computer Science and Engineering, Sri Venkateswara University (SVU) College of Engineering, Tirupati – 517502, Andhra Pradesh, IN
2 School of Computing, Veltech Dr. RR and Dr. SR University, Avadi, Chennai – 600062, Tamil Nadu, IN

Abstract

Objectives: This study proposes a model for generating synthetic network flows inserting malicious fragments randomly and a new metric for measuring the performance of an Anomaly Network Intrusion Detection System (ANIDS). Method: A simulation model is developed for generating synthetic network flows inserting malicious fragments that reflect Denial of Service (DoS) and Probe attacks. An ANIDS shall maximize true positives and true negatives which is equivalent to minimizing Type-I and Type-II errors. The geometric mean of True Positive Rate (TPR) and True Negative Rate (TNR) is proposed as a metric, namely, Geometric Mean Accuracy Index (GMAI) for measuring the performance of any proposed ANIDS. Findings: The task of detecting anomalous network flows by inspecting at fragment level boils down to discrete binary classification problem. The Receiver Operating Characteristic (ROC) curve considers False Positive Rates (FPR) and True Positive Rate (TPR) only. It does not reflect the minimization of Type-I and Type-II errors. Maximizing GMAI is the reflection of minimizing 1-GMAI which is equivalent to minimizing Type-I and Type-II errors. Further, the GMAI can be employed as service level for evaluating acceptance sampling based ANIDS. The domain of DoS and Probe attacks, mostly employed by the intruders at fragment level is studied. A conceptual simulation model is developed for generating synthetic network flows incorporating malicious fragments randomly from the domain of DoS and Probe attacks. The conceptual model is translated into operational model (a set computer programs) and synthetic network flows are generated. Using the operational model, the 1000 synthetic network flows are generated for each percentage of anomalous flows varying from 0.1 to 0.9 and employing discrete uniform probability distribution for selecting a fragment for transforming it into malicious. The generated network flows for each percentage of anomalous flows are represented graphically as histogram. It is found that they follow discrete uniform distribution. Hence, the model is validated. Applications: The simulation model can be used for generating synthetic networks flows for evaluating ANIDS. The GMAI can be used as service level for evaluating a discrete binary classifier irrespective of domain.

Keywords

Anomalous Flows, Geometric Mean Accuracy Index, Network Intrusion Detection Systems, Synthetic Network Flows, Simulation Model

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