Abstract With the improvement of communication and identification and determination of people identity problems for achieving the information, transfer the money and controlling the import and exporting the people of country and different places become important topics to invest in. Biometrics is methods to automatically verify or identify individuals using their physiological or behavioral characteristics. The necessity for personal identification in the fields of private and secure systems made face recognition one of the main fields among other biometric technologies. The importance of face recognition rises from the fact that a face recognition system does not require the cooperation of the individual while the other systems need such cooperation. Feature extraction methods try to reduce the feature dimensions Used in the classification step. There are especially two methods used in Pattern recognition to reduce the feature dimensions; Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA). These algorithms transform the input image data into a 1-D vector, which ignores the underlying data structure so these methods suffer from curse of dimensionality and often leads us to the small sample size problem. For solving these problems we proposed a new algorithm MDA that transform the image into a tensor with its own order. MDA with optimizing the new criterion, DTC, achieves multiple subspaces that the number of these subspaces determined with the order of the tensor. Performance of this algorithm is evaluated with 3 standard databases. With the respect to these results, our proposed algorithms improve the face recognition accuracy and the time of finding these optimum results and also avoiding the curse of dimensionality and the SSS problem. | 
