Learning the parts of objects have drawn more attentions in computer science recently, and they have been playing the important role in computer applications such as object recognition, self-driving cars, and image processing, etc… However, the existing research such as traditional non-negative matrix factorization (NMF), principal component analysis (PCA), and vector quantitation (VQ) has not been discovering the ground-truth bases which are basic components representing objects. On this thesis, I am proposed to study on pattern recognition enhancement combined non-negative matrix factorization (NMF) with automatic relevance determination (ARD). The main point of this research is to propose a new technique combining the algorithm Expectation Maximization (EM) with Automatic Relevance Determination (ARD) to discover the ground truth basis of datasets, and then to compare my new proposed technique to the others such as: traditional NMF, sparseness constraint and graph embedding in pattern recognition problems to verify if my method has over performance in accuracy rate than the others. Particularly, the new technique will be tested on variety of datasets from simple to complex one, from synthetic datasets to real ones. To compare the performance, I split these datasets into 10 random partitions as the training and the testing sets called 10-fold cross validation, and then use the technique called Euclidean algorithm to classify them and test their accuracy. As the result, my proposed method has higher accuracy than the others, and it is good to use in pattern recognition problems with missing data.