A robust semi-supervised method using the mode filter has been presented for learning with partially-labeled training data including label errors. The mode filter has been originally developed for smoothing images contaminated with impulsive noises. However it needs nonlinear optimization which is usually solved with iterative methods. In this paper, we propose a direct solution method with full search of solution spaces. This direct method outperforms the iterative algorithm in classification rates and computational speeds. Additional iterations of the mode filter raise up the classification rates. We extend the mode filter by introducing weights based on the isolation degree of data, and show the effectiveness of this extension.