  In this work, we propose to use a local clustering approach based on the
sparse solution technique to study the medical image, especially the lung
cancer image classification task. We view images as the vertices in a weighted
graph and the similarity between a pair of images as the edges in the graph.
The vertices within the same cluster can be assumed to share similar features
and properties, thus making the applications of graph clustering techniques
very useful for image classification. Recently, the approach based on the
sparse solutions of linear systems for graph clustering has been found to
identify clusters more efficiently than traditional clustering methods such as
spectral clustering. We propose to use the two newly developed local clustering
methods based on sparse solution of linear system for image classification. In
addition, we employ a box spline-based tight-wavelet-framelet method to clean
these images and help build a better adjacency matrix before clustering. The
performance of our methods is shown to be very effective in classifying images.
Our approach is significantly more efficient and either favorable or equally
effective compared with other state-of-the-art approaches. Finally, we shall
make a remark by pointing out two image deformation methods to build up more
artificial image data to increase the number of labeled images.
