Non-Negative Matrix Factorization (NMF) is a part-based image representation method. It comes from the intuitive idea that entire face image can be constructed by combining several parts. In this paper, we propose a framework for face recognition by finding localized, part-based representations, denoted “ Iterative weighted Non-smooth Non-Negative Matrix Factorization” (IWNS-NMF). A new cost function is proposed in order to incorporate sparsity which is controlled by a specific parameter and weights of feature coefficients. This method extracts highly localized patterns, which generally improves the capability of face recognition. After extracting patterns by IWNS-NMF, we use principle component analysis to reduce dimension for classification by linear SVM. The Recognition rates on ORL, YALE and JAFFE datasets were 97. 5, 93. 33 and 87. 8%, respectively. Comparisons to the related methods in the literature indicate that the proposed IWNS-NMF method achieves higher face recognition performance than NMF, NS-NMF, Local NMF and SNMF.

Machine learning has been widely used over the past decades due to its wide range of applications. In most machine learning applications such as clustering and classification, data dimensions are large and the use of data reduction methods is essential. Non-Negative Matrix Factorization reduces data dimensions by extracting latent features from large dimensional data. Non-Negative Matrix Factorization only considers how to model each feature vector in the decomposed matrices and ignores the relationships between feature vectors. The relationships between feature vectors provide better Factorization for machine learning applications. In this paper, a new method based on Non-Negative Matrix Factorization is proposed to reduce the dimensions of the data, which sets constraints on each feature vector pair using distance-based criteria. The proposed method uses the Frobenius norm as a cost function to create update rules. The results of experiments on the data sets show that the proposed multiplicative update rules converge rapidly and give better results than other algorithms.

Rice classification and detection of its quality as a main field in the modern agriculture is attracted many researchers in recent years. This problem is a major issue in the scientific and commercial fields associated with modern agriculture. Different processing techniques in recent years are applied to recognize various types of agricultural products. There are also several color-based and texture-based features to achieve the desired results in this classification procedure. In this paper, the problem of rice categorization and quality detection is considered using sparse Non-Negative Matrix Factorization algorithm. This technique includes Non-Negative Matrix Factorization method with sparsity constraint to achieve dictionaries that represent the structural content of rice variety. Also, these dictionaries are corrected in such a way to yield the dictionaries with least coherence values to each other. The results of the proposed classifier based on the learned models are compared with the results obtained from the neural network and support vector machine classifiers. Simulation results show that the proposed method based on the combinational features is able to identify the type of rice grain and determine its quality with high accuracy rate.

Classification of ECG arrhythmia along with medical knowledge can lead to proper decision-making on the patientchr('39')s condition. Also, classification of arrhythmia types is one of the challenging issues due to the need for detailed analysis of the extracted feature from ECG signal. Therefore, addressing this field using signal processing techniques can be very important. In this paper, various types of morphological features are used to determine the type of ECG arrhythmia. Sparse structured principal component analysis and sparse Non-Negative Matrix Factorization algorithms are used to learn the over-complete models based on the characteristics of each data category. Also, the wavelet packet transform coefficients are calculated in different decomposition level to learn over-complete dictionaries. The results of this categorization are compared with the results of the classification based on the neural network, support vector machine another methods presented in this processing field. The simulation results show that the proposed method based on the selected combinational features and learning the over-complete dictionaries can be able to classify the types of ECG arrhythmia precisely.

Community detection is a significant issue in extracting valuable information and ‎understanding complex network structures. Non-Negative Matrix Factorization (NMF) methods ‎are the most remarkable topics in community detection. The modularized tri-factor NMF ‎‎(Mtrinmf) method was proposed as a new class of NMF methods that combines the modularized ‎information with tri-factor NMF. It has high computational complexity due to its dependence on ‎the choice of the initial value of the parameter and the number of communities (c). In other ‎words, the Mtrinmf method should search among different c candidates to find correct c. In this ‎paper, a novel hybrid adaptive Mtrinmf (Hamtrinmf) method is proposed to improve the ‎performance of Mtrinmf and reduce the computational complexity efficiently. In the proposed ‎method, computational complexity reduction is made by selecting the right c candidates and ‎tuning parameter. For this purpose, a hybrid algorithm including singular value decomposition ‎‎(SVD) and relative eigenvalue gap (REG) algorithms is suggested to estimate the set of c ‎candidates. Next, the Tpmtrinmf model is proposed to improve the performance of community ‎detection via employing a self-tuning β parameter. Moreover, experimental results confirm the ‎efficiency of the Hamtrinmf method with respect to other reference methods on artificial and ‎real-world networks.‎

Classification of brain tumors using MRI images along with medical knowledge can lead to proper decision-making on the patient's condition. Also, classification of benign or malignant tumors is one of the challenging issues due to the need for detailed analysis of tumor tissue. Therefore, addressing this field using image processing techniques can be very important. In this paper, various types of texture-based and statistical-based features are used to determine the type of brain tumor and different types of features are applied in this classification procedure. Sparse Non-Negative Matrix Factorization algorithm is used to learn the over-complete models based on the characteristics of each data category. Also, sparse structured principal component analysis algorithm is applied to reduce the dimension of training data. The classification process is carried out based on the calculated energy of the sparse coefficients. Also, the results of this categorization are compared with the results of the classification based on the neural network and support vector machine. The simulation results show that the proposed method based on the selected combinational features and learning the over-complete dictionaries can be able to classify the types of brain tumors precisely.