Scientific and therapeutic advances in perinatology and neonatology have improved the survival prospects of preterm and extremely-low-birth-weight infants. Infants’ cries are a valuable noninvasive tool for monitoring their neurologic health, especially if they are premature. Automatic acoustic analysis and data mining are employed in this study to determine the discriminative features of preterm and full-term infant cries. The use of machine learning for recognizing sounds in a newborn's cry language has received less attention than previous methods for analyzing the sounds. Moreover, to extract appropriate features from infant cries, adequate knowledge and appropriate signal descriptors are required. Accordingly, to analyze infant cry language, we propose an approach that uses fractal descriptors to extract discriminant features from spectrograms of windowed signals, followed by iterative neighborhood component analysis (iNCA) to select appropriate features. Additionally, the improved deep support vector machine (DeepSVM) is used to classify the infants’ crying types and their meanings. The proposed method is verified using a newborn sound dataset. According to the classification of five types of crying perception based on various characteristics, 98.34% of all crying perceptions have been recognized. Although there are many classes examined, the feature extraction method based on the fractal method and our optimal classification have a much higher diagnostic accuracy compared with similar methods for analyzing baby crying language. The proposed method can overcome many problems associated with analyzing babies’ crying sounds and understanding their language, such as uncertainty and unusual errors in classification.