Computing technologies pervade physical spaces and human lives, and produce a vast amount of data that is available for analysis. However, there is a growing concern that potentially sensitive data may become public if the collected data are not appropriately sanitized before being released for investigation. Although there are more than a few privacy-preserving methods available, they are not efficient, scalable or have problems with data utility, and/or privacy. This paper addresses these issues by proposing an efficient and scalable nonreversible perturbation algorithm, PABIDOT, for privacy preservation of big data via optimal geometric transformations. PABIDOT was tested for efficiency, scalability, resistance, and accuracy using nine datasets and five classification algorithms. Experiments show that PABIDOT excels in execution speed, scalability, attack resistance and accuracy in large-scale privacy-preserving data classification when compared with two other, related privacy-preserving algorithms.