Mining high-dimensional business data is a challenging problem. This paper proposes a novel approach to address the problems including (1) the curse of dimensionality and (2) the meaningfulness of the similarity measure in the high dimension space. The solution of this study is to build a generalized multiple kernel machine (GMKM) on a low-dimensional subspace. The representative subspace is created by the locally consistent matrix factorization (an improved variation of non-negative matrix factorization). The strengths of our system are two-fold: (1) GMKM takes products of kernels-corresponding to a tensor product of feature spaces. This leads to a richer and much higher dimensional feature representation, which is powerful in identifying relevant features and their apposite kernel representation. (2) Locally consistent matrix factorization finds a compact low-dimensional representation for data, which uncovers underlying information and simultaneously respects the intrinsic geometric structure of data manifold. Our system robustly outperforms traditional multiple kernel machines, and dimensionality reduction methods.