On account of an increase in the human-computer interface applications, the study of automatic personality perception has become more and more prevalent than speech signal processing in recent years. These studies have shown that personality traits derived from psychology theories mainly affect acoustic features. However, some obstacles remain in the automatic personality perception classification, and the most important one is to extract the features related to each personality trait. Previous studies have shown that the personality effect differs from one acoustic feature to the others. Additionally, there are many features one can extract from speech signals. Curse of dimensionality in features also makes the classification difficult. This paper aimed to introduce and examine a novel and efficient automatic feature extraction method to classify the well-known big five personality traits. In this regard, three data augmentation methods for increasing data samples were examined. Afterwards, 6,373 statistical features were extracted from the nonverbal features of the SSPNet Speaker Personality Corpus. Finally, an innovative stacked asymmetric auto-encoder was utilized to extract useful features automatically to improve classification results. Compared with the conventional stacked auto-encoder and convolutional neural network, the proposed method exhibited an average improvement of 12.40%(10.14%) and 14.36%(1.42%) in terms of the unweighted average recall (accuracy), respectively. In comparison with other published works, classification results also revealed a notable average enhancement (11.78%) for unweighted average recall for all five traits and an average improvement of 5.1% for accuracy in two out of five personality traits.