Acoustic feature transformation is widely used to reduce dimensionality and improve speech recognition performance. In this letter we focus on dimensionality reduction methods that minimize the average classification error. Unfortunately, minimization of the average classification error may cause considerable overlaps between distributions of some classes. To mitigate risks of considerable overlaps, we propose a dimensionality reduction method that minimizes the maximum classification error. We also propose two interpolated methods that can describe the average and maximum classification errors. Experimental results show that these proposed methods improve speech recognition performance.