An innovative linear unsupervised space adjustment by keeping low-level spatial data structure

A novel objective function has been introduced for solving the problem of space adjustment when supervisor is unavailable. In the introduced objective function, it has been tried to minimize the difference between distributions of the transformed original and test-data spaces. The local structural information presented in the original space is preserved by optimizing the mentioned objective function. We have proposed two techniques to preserve the structural information of original space: (a) identifying those pairs of examples that are as close as possible in original space and minimizing the distance between these pairs of examples after transformation and (b) preserving the naturally occurring clusters that are presented in original space during transformation. This cost function together with its constraints has resulted in a nonlinear objective function, used to estimate the weight matrix. An iterative framework has been employed to solve the problem of optimizing the objective function, providing a suboptimal solution. Next, using orthogonality constraint, the optimization task has been reformulated into the Stiefel manifold. Empirical examination using real-world datasets indicates that the proposed method performs better than the recently published state-of-the-art methods.