Minimum Number Of Misclassifications Research Articles

BitProb: Probabilistic Bit Signatures for Accurate Application Identification

Network traffic classification finds its applications in a variety of network management tasks such as quality of service, security monitoring, traffic engineering, etc. Deep Packet Inspection is one of the methods to identify applications. With the number of proprietary protocols on the rise and network protocols using bit level information for encoding, recently it has been shown that bit level signatures are effective for identifying applications. In this paper, we propose BitProb which generates probabilistic bit signatures for traffic classification. It uses the probability of a bit at a particular position being either 0 or 1 and generates a space efficient signature represented as a state transition machine. Subsequently, it uses the overall probability of an ${n}$ bit binary string extracted from a network flow to identify which application generated the flow. We experiment with three datasets covering twenty protocols (text, binary and proprietary) and show that BitProb classifies network flows with high accuracy and has a minimum number of misclassifications.

Improvement of CPU time of Linear Discriminant Function based on MNM criterion by IP

Revised IP-OLDF (optimal linear discriminant function by integer programming) is a linear discriminant function to minimize the number of misclassifications (NM) of training samples by integer programming (IP). However, IP requires large computation (CPU) time. In this paper, it is proposed how to reduce CPU time by using linear programming (LP). In the first phase, Revised LP-OLDF is applied to all cases, and all cases are categorized into two groups: those that are classified correctly or those that are not classified by support vectors (SVs). In the second phase, Revised IP-OLDF is applied to the misclassified cases by SVs. This method is called Revised IPLP-OLDF. In this research, it is evaluated whether NM of Revised IPLP-OLDF is good estimate of the minimum number of misclassifications (MNM) by Revised IP-OLDF. Four kinds of the real data—Iris data, Swiss bank note data, student data, and CPD data—are used as training samples. Four kinds of 20,000 re-sampling cases generated from these data are used as the evaluation samples. There are a total of 149 models of all combinations of independent variables by these data. NMs and CPU times of the 149 models are compared with Revised IPLP-OLDF and Revised IP-OLDF. The following results are obtained: 1) Revised IPLP-OLDF significantly improves CPU time. 2) In the case of training samples, all 149 NMs of Revised IPLP-OLDF are equal to the MNM of Revised IP-OLDF. 3) In the case of evaluation samples, most NMs of Revised IPLP-OLDF are equal to NM of Revised IP-OLDF. 4) Generalization abilities of both discriminant functions are concluded to be high, because the difference between the error rates of training and evaluation samples are almost within 2%. Therefore, Revised IPLP-OLDF is recommended for the analysis of big data instead of Revised IP-OLDF. Next, Revised IPLP-OLDF is compared with LDF and logistic regression by 100-fold cross validation using 100 re-sampling samples. Means of error rates of Revised IPLP-OLDF are remarkable fewer than those of LDF and logistic regression.

Improvement of CPU time of Linear Discriminant Function based on MNM criterion by IP

Revised IP-OLDF (optimal linear discriminant function by integer programming) is a linear discriminant function to minimize the number of misclassifications (NM) of training samples by integer programming (IP). However, IP requires large computation (CPU) time. In this paper, it is proposed how to reduce CPU time by using linear programming (LP). In the first phase, Revised LP-OLDF is applied to all cases, and all cases are categorized into two groups: those that are classified correctly or those that are not classified by support vectors (SVs). In the second phase, Revised IP-OLDF is applied to the misclassified cases by SVs. This method is called Revised IPLP-OLDF.In this research, it is evaluated whether NM of Revised IPLP-OLDF is good estimate of the minimum number of misclassifications (MNM) by Revised IP-OLDF. Four kinds of the real data—Iris data, Swiss bank note data, student data, and CPD data—are used as training samples. Four kinds of 20,000 re-sampling cases generated from these data are used as the evaluation samples. There are a total of 149 models of all combinations of independent variables by these data. NMs and CPU times of the 149 models are compared with Revised IPLP-OLDF and Revised IP-OLDF. The following results are obtained: 1) Revised IPLP-OLDF significantly improves CPU time. 2) In the case of training samples, all 149 NMs of Revised IPLP-OLDF are equal to the MNM of Revised IP-OLDF. 3) In the case of evaluation samples, most NMs of Revised IPLP-OLDF are equal to NM of Revised IP-OLDF. 4) Generalization abilities of both discriminant functions are concluded to be high, because the difference between the error rates of training and evaluation samples are almost within 2%. Therefore, Revised IPLP-OLDF is recommended for the analysis of big data instead of Revised IP-OLDF. Next, Revised IPLP-OLDF is compared with LDF and logistic regression by 100-fold cross validation using 100 re-sampling samples. Means of error rates of Revised IPLP-OLDF are remarkable fewer than those of LDF and logistic regression.

Error-Free and Best-Fit Extensions of Partially Defined Boolean Functions

In this paper, we address a fundamental problem related to the induction of Boolean logic: Given a set of data, represented as a set of binary “true n -vectors” (or “positive examples”) and a set of “false n -vectors” (or “negative examples”), we establish a Boolean function (or an extension) f , so that f is true (resp., false) in every given true (resp., false) vector. We shall further require that such an extension belongs to a certain specified class of functions, e.g., class of positive functions, class of Horn functions, and so on. The class of functions represents our a priori knowledge or hypothesis about the extension f , which may be obtained from experience or from the analysis of mechanisms that may or may not cause the phenomena under consideration. The real-world data may contain errors, e.g., measurement and classification errors might come in when obtaining data, or there may be some other influential factors not represented as variables in the vectors. In such situations, we have to give up the goal of establishing an extension that is perfectly consistent with the given data, and we are satisfied with an extension f having the minimum number of misclassifications. Both problems, i.e., the problem of finding an extension within a specified class of Boolean functions and the problem of finding a minimum error extension in that class, will be extensively studied in this paper. For certain classes we shall provide polynomial algorithms, and for other cases we prove their NP-hardness.

Neural networks using a logistics sigmoid function: linear classifier bounds and global nonattainability

Simple examples clearly demonstrate that highly consistent data lead to solution nonattainability, in neural networks utilizing a logistics sigmoid function. Solution attainability requires a high degree of inconsistency. Bounds are obtained on the optimal value of the mean-square error of a one-layer neural network, in terms of the minimum number of misclassifications obtained from three linear classification problems, and conditions are given that imply solution attainability and nonattainability