1. A biometric authentication device comprising: an input device providing a biometric information input unit configured to input biometric information; a storage providing a retention unit configured to retain the biometric information input from the biometric information input unit; a processor providing a merging unit configured to merge new biometric information input from the biometric information input unit and the biometric information retained in the retention unit; a feature extraction unit configured to extract feature information of the biometric information input from the biometric information input unit, or feature information of biometric information merged by the merging unit; a classification unit configured to classify the biometric information on the basis of the feature information extracted by the feature extraction unit; a merging reliability degree calculation unit configured to calculate a degree of reliability of the biometric information input from the biometric information input unit, or a degree of reliability of the biometric information merged by the merging unit; a classification reliability degree calculation unit configured to calculate a degree of reliability of classification of the biometric information classified by the classification unit; a control unit configured to analyze the degree of reliability of biometric information on the basis of the degree of reliability of merging and the degree of reliability of classification, and to issue a re-input instruction for the biometric information or an identification process instruction for performing matching with biometric information prestored in a storage unit in accordance with whether the degree of reliability of merging is equal to or larger than a specified threshold value or smaller than the specified threshold value, and whether the degree of reliability of classification is equal to or larger than a specified threshold value or smaller than the specified threshold value; an identification unit configured to execute the identification process for performing matching with the biometric information stored in the storage unit according to the identification process instruction issued by the control unit; and a notification unit configured to notify a user of the re-input instruction according to the re-input instruction issued by the control unit.