Naoya Takeishi

Anomaly detection from multivariate time-series with sparse representation.

Anomaly detection from sensor data is an important data mining application for efficient and secure operation of complicated systems. In this study, we propose a novel anomaly detection method for multivariate time-series to capture relationships of variables and time-domain correlations simultaneously, without assuming any generative models of signals. The supposed framework in this study is a semi-supervised anomaly detection where we seek unusual parts of test data compared with reference data. The proposed method is based on feature extraction with sparse representation and relationship learning with dimensionality reduction. Our idea comes from the similarity between a sparse feature matrix extracted from multivariate time-series and a term-document matrix. We conducted experiments with synthetic and simulated data, and confirmed that the proposed method successfully detected anomalies in multivariate time-series signals. Especially, it demonstrated superior performance with anomalies in which only relationships of time-series patterns are changed from reference data (multivariate anomalies).

Subspace dynamic mode decomposition for stochastic Koopman analysis

The analysis of nonlinear dynamical systems based on the Koopman operator is attracting attention in various applications. Dynamic mode decomposition (DMD) is a data-driven algorithm for Koopman spectral analysis, and several variants with a wide range of applications have been proposed. However, popular implementations of DMD suffer from observation noise on random dynamical systems and generate inaccurate estimation of the spectra of the stochastic Koopman operator. In this paper, we propose subspace DMD as an algorithm for the Koopman analysis of random dynamical systems with observation noise. Subspace DMD first computes the orthogonal projection of future snapshots to the space of past snapshots and then estimates the spectra of a linear model, and its output converges to the spectra of the stochastic Koopman operator under standard assumptions. We investigate the empirical performance of subspace DMD with several dynamical systems and show its utility for the Koopman analysis of random dynamical systems.

Bayesian Dynamic Mode Decomposition

Dynamic mode decomposition (DMD) is a data-driven method for calculating a modal representation of a nonlinear dynamical system, and has been utilized in various fields of science and engineering. In this talk, we introduce reformulations of DMD, namely probabilistic DMD and Bayesian DMD, with which we can explicitly incorporate observation noises, conduct posterior inference on DMD-related quantities and consider extensions of DMD in a systematic way. Furthermore, we introduce two examples of application: Bayesian sparse DMD and mixtures of probabilistic DMD.

Fast estimation of asteroid shape and motion for spacecraft navigation

In this paper, we consider fast simultaneous estimation problem of the geometric shape of the asteroid and the relative motion of the spacecraft. In asteroid exploration missions, the information of asteroid shape and motion is needed to find suitable landing sites and navigate the spacecraft safely. In the previous HAYABUSA mission, large part of the estimation was performed manually by ground operators. We propose an efficient automatic estimation method using the image feature matching and matrix decomposition based fast 3D reconstruction techniques. Preliminary experiment results are also shown.

A Data-Driven Health Monitoring Method for Satellite Housekeeping Data Based on Probabilistic Clustering and Dimensionality Reduction

In the operation of artificial satellites, it is very important to monitor the health status of the systems and detect any symptoms of anomalies in the housekeeping data as soon as possible. Recently, the data-driven approach to the system monitoring problem, in which statistical machine learning techniques are applied to the large amount of measurement data collected in the past, has attracted considerable attention. In this paper, we propose a new data-driven health monitoring and anomaly detection method for artificial satellites based on probabilistic dimensionality reduction and clustering, taking into consideration the miscellaneous characteristics of the spacecraft housekeeping data. We applied our method to the telemetry data of the small demonstration satellite 4 (SDS-4) of the Japan Aerospace Exploration Agency (JAXA) and evaluated its effectiveness. The results show that the proposed system provides satellite operators with valuable information for understanding the health status of the system and inferring the causes of anomalies.

Simultaneous estimation of shape and motion of an asteroid for automatic navigation

In an asteroid exploration and sample return mission, accurate estimation of the shape and motion of the target asteroid is essential for selecting a touchdown site and navigating a spacecraft during touchdown operation. In this work, we present an automatic estimation method for the shape and motion of an asteroid, which is planned to be tested in future exploration missions including Japanese Hayabusa-2 [1]. Our task is to estimate the shape and rotation axis of the asteroid, as well as positions of the spacecraft from optical images. The proposed method is based on the expectation conditional-maximization (ECM) framework that consists of an auxiliary particle filter and nonlinear optimization techniques. One of our technical contributions is the estimation of the direction of rotation axis of the asteroid from monocular camera images, which are taken by the moving spacecraft. We conducted two experiments with synthetic data and an asteroid mock-up to show the validity of the proposed method and to present the numerical accuracy.

Dynamic Grouped Mixture Models for Intermittent Multivariate Sensor Data

For secure and efficient operation of engineering systems, it is of great importance to watch daily logs generated by them, which mainly consist of multivariate time-series obtained with many sensors. This work focuses on challenges in practical analyses of those sensor data: temporal unevenness and sparseness. To handle the unevenly and sparsely spaced multivariate time-series, this work presents a novel method, which roughly models temporal information that still remains in the data. The proposed model is a mixture model with dynamic hierarchical structure that considers dependency between temporally close batches of observations, instead of every single observation. We conducted experiments with synthetic and real dataset, and confirmed validity of the proposed model quantitatively and qualitatively.