On the Persistence of Clustering Solutions and True Number of Clusters in a Dataset

Typically clustering algorithms provide clustering solutions with prespecified number of clusters. The lack of a priori knowledge on the true number of underlying clusters in the dataset makes it important to have a metric to compare the clustering solutions with different number of clusters. This article quantifies a notion of persistence of clustering solutions that enables comparing solutions with different number of clusters. The persistence relates to the range of data-resolution scales over which a clustering solution persists; it is quantified in terms of the maximum over two-norms of all the associated cluster-covariance matrices. Thus we associate a persistence value for each element in a set of clustering solutions with different number of clusters. We show that the datasets where natural clusters are a priori known, the clustering solutions that identify the natural clusters are most persistent - in this way, this notion can be used to identify solutions with true number of clusters. Detailed experiments on a variety of standard and synthetic datasets demonstrate that the proposed persistence-based indicator outperforms the existing approaches, such as, gap-statistic method, $X$-means, $G$-means, $PG$-means, dip-means algorithms and information-theoretic method, in accurately identifying the clustering solutions with true number of clusters. Interestingly, our method can be explained in terms of the phase-transition phenomenon in the deterministic annealing algorithm, where the number of distinct cluster centers changes (bifurcates) with respect to an annealing parameter

Fixed-time Distributed Optimization under Time-Varying Communication Topology

This paper presents a method to solve distributed optimization problem within a fixed time over a time-varying communication topology. Each agent in the network can access its private objective function, while exchange of local information is permitted between the neighbors. This study investigates first nonlinear protocol for achieving distributed optimization for time-varying communication topology within a fixed time independent of the initial conditions. For the case when the global objective function is strictly convex, a second-order Hessian based approach is developed for achieving fixed-time convergence. In the special case of strongly convex global objective function, it is shown that the requirement to transmit Hessians can be relaxed and an equivalent first-order method is developed for achieving fixed-time convergence to global optimum. Results are further extended to the case where the underlying team objective function, possibly non-convex, satisfies only the Polyak-\L ojasiewicz (PL) inequality, which is a relaxation of strong convexity.Comment: 25 page

透明導電膜を必要としないタンデム型色素増感太陽電池の構造最適化と効率の向上

九州工業大学博士学位論文（要旨）学位記番号：生工博甲第253号 学位授与年月日平成28年3月25

Speed Control of Separately Excited DC Motor using Neuro Fuzzy Technique

This paper uses NEURO FUZZY TECHNIQUE in estimating speed and controlling it for a separately excited DC motor. The rotor speed of the dc motor can be made to follow an arbitrarily selected trajectory. The purpose is to achieve accurate trajectory control of the speed of saperately excited DC Motor, especially when the motor and load parameters are unknown. Such a neuro fuzzy control scheme consists of two parts. One is the neural identifier which is used to estimate the motor speed error (state error or state error derivative). The second is the fuzzy logic controller which is used to generate a control signal for a chopper & speed control of separately excited DC Motor. The purpose of this technique is to achieve accurate trajectory control of the speed. Such a control scheme consists of two parts. One is the neural identifier which is used to estimate the motor speed. The other is the neural fuzzy logic controller which is used to generate the control signal (fuzzy output)