Under the commonalities found in the goals of two areas, neural network compression and feature selection for dimension reduction, this research focused on finding a new method to address both issues: a method that can lead to easier feature selection, and an enhancement in the capacity of information flow control of neural network compression techniques, especially clustering based compression. Specifically, this research focused on creating a novel and effective framework to transform the weight matrix between the input layer and the first hidden layer in neural networks to be optimal. In other words, a method that can make the weight matrix's structure itself optimal for information extraction. By proposing a simple, yet powerful weight clipping + GMM based method called an In-and-Out Weight Box that can intrinsically act similar to filtering while increasing the possibility of getting better results in compression, the main aim of research was found to be satisfied. Using Glioma Grading data from the UCI Repository for checking performance of the In-and-Out Weight box in fitting neural networks, it was found that significantly better compression results can be achieved in terms of weight sharing via clustering. This research also suggests a new feature selection method based on the In-and-Out Weight box constraint called IOW-FI, which can lead to solving limitations or problems of filtering techniques such as setting the number of components to be selected as efficient features or considering joint distributions of feature space.