## 1 Introduction
Their advantage is that they are computationally light, but they neglect the inter-feature dependence. Therefore, the selected feature subset inevitably contains some redundant features. To overcome this problem, filter methods based on subset evaluation, also known as subset evaluation methods (SEMs), have been proposed [4]. However, these methods involve two critical issues: search strategy and evaluation criterion, which are typically encountered in wrapper and embedded methods. Finding the optimal subset from a high-dimensional dataset is an NP-hard problem, which cannot be solved optimally with an exhaustive search in a reasonable amount of time. Hence, some alternative search strategies (e.g., heuristic search [14], complete search [15], and random search [16]) have been used for the FS process. Although these search strategies significantly enhance the efficiency of the FS process, the absence of robust and precise evaluation criteria presents a considerable challenge in accurately identifying the optimal feature subset. Recently, evaluation criteria based on relevance and redundancy analysis have gained increasing attention. Among these criteria, mutual information (MI) stands out as a powerful measure of relevance, capturing both linear and non-linear relationships between features and the target class. MI quantifies the amount of information obtained about one variable through the other, making it an ideal tool for assessing the relevance of features in the context of FS. Presently, typical SEMs include MIM [17], JMI [18], CIFE [19], CMIM [20], JMIM [21], MIFS [22], mRMR [23], and maxMIFS [24]. Despite these methods possessing certain advantages in unveiling complex relationships between features and the target class, as well as among the features themselves, they also confront significant challenges, such as failing to accurately capture the maximum relevance between features and the target class and the minimum redundancy in the selected feature subset, not being able to automatically determine the optimal number of features, and overly depending on meticulous parameter calibration. In this paper, we propose an FS algorithm based on maximum conditional MI and a greedy algorithm to search for the optimal feature subset in high-dimensional datasets. The algorithm is evaluated by comparing it to existing classical filter methods on three pig gene microarray datasets. The significant contributions of this paper are as follows:  
1. Proposal of an accurate evaluation criterion based on MI for the maximum relevant no-redundant (MRNR) feature subset along with a detailed proof process. This criterion proves effective in practical contexts to identify whether a feature subset is an MRNR feature subset. 2. Introduction of a greedy search strategy based on maximum conditional MI to efficiently search for the MRNR feature subset with the minimum size. This strategy can automatically determine the number of features in the subset without the need for any wrapper method. 3. Introducing two evaluation metrics, relevance and redundancy, to assess the feature quality of FS methods. These metrics provide a comprehensive analysis of the selected feature subset's quality and its potential impact on classification performance. For the convenience of the reader, Abbreviations table lists the abbreviations used in this paper.