Andri Mirzal

Andri Mirzal

This paper discusses clustering and latent semantic indexing (LSI) aspects of the singular value decomposition (SVD). The purpose of this paper is twofold. The first is to give an explanation on how and why the singular vectors can be used in clustering. And the second is to show that the two seemingly unrelated SVD aspects actually originate from the same source: related vertices tend to be more clustered in the graph representation of lower rank approximate matrix using the SVD than in the original semantic graph. Accordingly, the SVD can improve retrieval performance of an information retrieval system since queries made to the approximate matrix can retrieve more relevant documents and filter out more irrelevant documents than the same queries made to the original matrix. By utilizing this fact, we will devise an LSI algorithm that mimicks SVD capability in clustering related vertices. Convergence analysis shows that the algorithm is convergent and produces a unique solution for each input. Experimental results using some standard datasets in LSI research show that retrieval performances of the algorithm are comparable to the SVD's. In addition, the algorithm is more practical and easier to use because there is no need to determine decomposition rank which is crucial in driving retrieval performance of the SVD.

Andri Mirzal

This paper proposes uni-orthogonal and bi-orthogonal nonnegative matrix factorization algorithms with robust convergence proofs. We design the algorithms based on the work of Lee and Seung [1], and derive the converged versions by utilizing ideas from the work of Lin [2]. The experimental results confirm the theoretical guarantees of the convergences.

Andri Mirzal

A convergent algorithm for nonnegative matrix factorization with orthogonality constraints imposed on both factors is proposed in this paper. This factorization concept was first introduced by Ding et al. with intent to further improve clustering capability of NMF. However, as the original algorithm was developed based on multiplicative update rules, the convergence of the algorithm cannot be guaranteed. In this paper, we utilize the technique presented in our previous work to develop the algorithm and prove that it converges to a stationary point inside the solution space.

Andri Mirzal

We present a converged algorithm for Tikhonov regularized nonnegative matrix factorization (NMF). We specially choose this regularization because it is known that Tikhonov regularized least square (LS) is the more preferable form in solving linear inverse problems than the conventional LS. Because an NMF problem can be decomposed into LS subproblems, it can be expected that Tikhonov regularized NMF will be the more appropriate approach in solving NMF problems. The algorithm is derived using additive update rules which have been shown to have convergence guarantee. We equip the algorithm with a mechanism to automatically determine the regularization parameters based on the L-curve, a well-known concept in the inverse problems community, but is rather unknown in the NMF research. The introduction of this algorithm thus solves two inherent problems in Tikhonov regularized NMF algorithm research, i.e., convergence guarantee and regularization parameters determination.

Andri Mirzal, Shinichiro Yoshii, Masashi Furukawa

Time delays are components that make time-lag in systems response. They arise in physical, chemical, biological and economic systems, as well as in the process of measurement and computation. In this work, we implement Genetic Algorithm (GA) in determining PID controller parameters to compensate the delay in First Order Lag plus Time Delay (FOLPD) and compare the results with Iterative Method and Ziegler-Nichols rule results.