Ng. Jordan Weiss (NJW) is one of the most widely used spectral clustering algorithms. For partitioning data into clusters, this method uses the largest eigenvectors of the normalized affinity matrix derived from the data set. However, this set of features is not always the best selection to represent and reveal the structure of the data. In this paper, we aim to propose a quadratic framework to select the most representative eigenvectors. In this way, we define an objective function which includes two factors. In the first part, the interaction of each pair of eigenvectors is considered. In the second part, the ability of each eigenvector to represent the structure of data is considered separately. Then, we use proposed Tabu Search in [1] to solve this mixed-integer quadratic optimization problem. The experimental results show the success of this method to select relevant eigenvectors.

In this paper, we introduce a novel artificial neural network (NN) to solve the portfolio optimization problem. The proposed NN is called the Mixed Tabu Machine (MTM) since its structure is similar to the Tabu Machine, but includes both discrete and continuous variables. Similar to the Hopfield network, the state of the MTM is updated to find the global minimum energy state. To escape from local minimum states of the energy in the MTM, the state transition mechanism is controlled by a Tabu search in both discrete and continuous search spaces. The experimental results for five standard benchmark data sets show that the MTM can clearly obtain good results in very small computation time. ARTICLE HISTORY