Takashi Imai

Ryohei Umatani, Takashi Imai, Kaoru Kawamoto et al.

In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the dynamics in various time series. To address this problem, we propose a novel model-based time series clustering method with mixtures of linear Gaussian state space models, which have high flexibility. The proposed method uses a new expectation-maximization algorithm for the mixture model to estimate the model parameters, and determines the number of clusters using the Bayesian information criterion. Experiments on a simulated dataset demonstrate the effectiveness of the method in clustering, parameter estimation, and model selection. The method is applied to real datasets commonly used to evaluate time series clustering methods. Results showed that the proposed method produces clustering results that are as accurate or more accurate than those obtained using previous methods.

Masahiro Kato, Yuki Ikeda, Kentaro Baba et al.

In this study, we propose a method for identifying potential customers in targeted marketing by applying learning from positive and unlabeled data (PU learning). We consider a scenario in which a company sells a product and can observe only the customers who purchased it. Decision-makers seek to market products effectively based on whether people have loyalty to the company. Individuals with loyalty are those who are likely to remain interested in the company even without additional advertising. Consequently, those loyal customers would likely purchase from the company if they are interested in the product. In contrast, people with lower loyalty may overlook the product or buy similar products from other companies unless they receive marketing attention. Therefore, by focusing marketing efforts on individuals who are interested in the product but do not have strong loyalty, we can achieve more efficient marketing. To achieve this goal, we consider how to learn, from limited data, a classifier that identifies potential customers who (i) have interest in the product and (ii) do not have loyalty to the company. Although our algorithm comprises a single-stage optimization, its objective function implicitly contains two losses derived from standard PU learning settings. For this reason, we refer to our approach as double PU learning. We verify the validity of the proposed algorithm through numerical experiments, confirming that it functions appropriately for the problem at hand.

Ryoichi Ishizuka, Takashi Imai, Kaoru Kawamoto

In this paper, we propose a novel method of model-based time series clustering with mixtures of general state space models (MSSMs). Each component of MSSMs is associated with each cluster. An advantage of the proposed method is that it enables the use of time series models appropriate to the specific time series. This not only improves clustering and prediction accuracy but also enhances the interpretability of the estimated parameters. The parameters of the MSSMs are estimated using stochastic variational inference, a subtype of variational inference. The proposed method estimates the latent variables of an arbitrary state space model by using neural networks with a normalizing flow as a variational estimator. The number of clusters can be estimated using the Bayesian information criterion. In addition, to prevent MSSMs from converging to the local optimum, we propose several optimization tricks, including an additional penalty term called entropy annealing. To our best knowledge, the proposed method is the first computationally feasible one for time series clustering based on general (possibly nonlinear, non-Gaussian) state space models. Experiments on simulated datasets show that the proposed method is effective for clustering, parameter estimation, and estimating the number of clusters.