Locally linear representation Fisher criterion based tumor gene expressive data classification

• Based on the class information, an intra-class graph and inter-class graph are constructed.
• In the inter-class graph, the reconstruction error denotes the shortest inter-class distance.
• In the intra-class graph, the reconstruction error means the intra-class data compactness.
• Experiments on some tumor gene expressive data validate LLRFC׳s superiority.

Tumor gene expressive data are characterized by a large amount of genes with only a small amount of observations, which always appear with high dimensionality. So it is necessary to reduce the dimensionality before identifying their genre. In this paper, a discriminant manifold learning method, named locally linear representation Fisher criterion (LLRFC), is applied to extract features from tumor gene expressive data. In LLRFC, an inter-class graph and an intra-class graph are constructed based on their genre information, where any tumor gene expressive data in the inter-class graph should select k nearest neighbors with different class labels and in the intra-class graph the k nearest neighbors for any tumor gene expressive data must be sampled from those with the same class. And then the locally least linear reconstruction is introduced to optimize the corresponding weights in both graphs. Moreover, a Fisher criterion is modeled to explore a low dimensional subspace where the reconstruction errors in the inter-class graph can be maximized and the reconstruction errors in the intra-class graph can be minimized, simultaneously. Experiments on some benchmark tumor gene expressive data have been conducted with some related algorithms, by which the proposed LLRFC has been validated to be efficient.