Feature selection is crucial for pinpointing relevant features in high-dimensional datasets, mitigating the 'curse of dimensionality,' and enhancing machine learning performance. Traditional feature selection methods for classification use data from all classes to select features for each class.This paper explores feature selection methods that select features for each class separately, using class models based on low-rank generative methods and introducing a signal-to-noise ratio (SNR) feature selection criterion. This novel approach theoretically guarantees true feature recovery under certain assumptions and is shown to outperform some existing feature selection methods on standard classification datasets.