## 1 Introduction  
Data mining and pattern recognition are critical components of many fields and represent essential classification processes. Popular algorithms include the Support Vector Machine (SVM) [1, 2], Dense Neural Network (DNN) [3, 4], Deep Learning [5, 6, 7], K-nearest neighbor (k-NN) [8, 9, 10], and Naive Bayes [11, 12, 13]. In particular, Deep Learning is a widely used to solve a variety of problems, such as Alzheimer's Disease classification [14, 15, 16, 17]. In contemporary times, the challenges associated with classification have become increasingly complex and diverse. This is particularly true when dealing with non-conforming binary formats, which are low-level binary data. Therefore, it remains challenging to use recognition or classification techniques and implement a classifier that can directly handle the aforementioned data type. However, classifier-based cellular automata (CA) successfully handle the complex problem of binary pattern classification tasks using a simple CA rule. For example, image compression [18], image classification [20], image encryption [21, 22], and texture recognition [23, 24], especially for pattern classification [25], have been proposed as highly reliable classifier methods based on elementary cellular automata (CAC). These methods play a role in non-conforming and conforming patterns for binary data. The primary objective of this research is to employ the \"network-reduction\" technique to improve the ability of the cellular automata-based classifier to handle increasingly complex and challenging issues [26]. Despite its utilization of basic cellular automata rule matrices and the concept of two-class classification akin to SVM, the classification performance of CAC remains encumbered by two key issues. Firstly, the data with ambiguity impact the rule ordering process to generate the rule matrices from the decision of the genetic algorithm (GA) by a random boundary cutting point without a statistical background for classification using only random values does not produce effective results in the classification model. Secondly, when working with high-dimensional data, the rule ordering procedure that utilizes GA may become trapped in a local optimal solution [27] because GA is limited when dealing with high-dimensional problems [28]. One alternative to GA is butterfly optimization, which has been shown to improve usage in a number of applications, including feature selection [29; 30] and enhancing the BOA utilizing a mutualism scheme [31]. Butterfly optimization performs better than classical optimization. In this paper, we proposed an efficient classification called cellular automata-based with a variance decision table (CAV) using the percentage coefficient of variation (\(\%CV\)). This study makes three critical contributions to the literature. First, we created an initial rule matrix based on finding the edge using the periodic boundary condition instead of zero constants (null boundary condition) to reduce data redundancy and demonstrate the proper form of the data for a more precise classification. Secondly, besides the ability to classify data patterns instead of random intersections by using a meta-heuristic algorithm, coefficients of variation were used to determine the relationships between classes, giving the data pattern more clarity and reducing the solution area from two-variable solutions to only a single variable that was less reliant on the search algorithm's ability. Finally, an efficient butterfly optimization algorithm (m-MBOA) was implemented instead of a genetic algorithm. We evaluated CAV using well-known classification algorithms in RapidMiner studio [32] and used 15 datasets for classification tasks from an OpenML repository [33]. This study is divided into six parts: the introduction in Section 1, related work on the proposed cellular automata classifier, and a novel butterfly optimization algorithm (m-MBOA) (Section 2). Section 3 expands on our proposed CAV method. Section 4 contains a comparison of experimental results.