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Transient noise appearing in the data from gravitational‐wave detectors frequently causes problems, such as instability of the detectors and overlapping or mimicking gravitational‐wave signals. Because transient noise is considered to be associated with the environment and instrument, its classification would help to understand its origin and improve the detector's performance. In a previous study, an architecture for classifying transient noise using a time–frequency 2D image (spectrogram) is proposed, which uses unsupervised deep learning combined with variational autoencoder and invariant information clustering. The proposed unsupervised‐learning architecture is applied to the Gravity Spy dataset, which consists of Advanced Laser Interferometer Gravitational‐Wave Observatory (Advanced LIGO) transient noises with their associated metadata to discuss the potential for online or offline data analysis. In this study, focused on the Gravity Spy dataset, the training process of unsupervised‐learning architecture of the previous study is examined and reported. [ABSTRACT FROM AUTHOR]

In the data obtained by laser interferometric gravitational wave detectors, transient noise with non-stationary and non-Gaussian features occurs at a high rate. This often results in problems such as detector instability and the hiding and/or imitation of gravitational-wave signals. This transient noise has various characteristics in the time–frequency representation, which is considered to be associated with environmental and instrumental origins. Classification of transient noise can offer clues for exploring its origin and improving the performance of the detector. One approach for accomplishing this is supervised learning. However, in general, supervised learning requires annotation of the training data, and there are issues with ensuring objectivity in the classification and its corresponding new classes. By contrast, unsupervised learning can reduce the annotation work for the training data and ensure objectivity in the classification and its corresponding new classes. In this study, we propose an unsupervised learning architecture for the classification of transient noise that combines a variational autoencoder and invariant information clustering. To evaluate the effectiveness of the proposed architecture, we used the dataset (time–frequency two-dimensional spectrogram images and labels) of the Laser Interferometer Gravitational-wave Observatory (LIGO) first observation run prepared by the Gravity Spy project. The classes provided by our proposed unsupervised learning architecture were consistent with the labels annotated by the Gravity Spy project, which manifests the potential for the existence of unrevealed classes. [ABSTRACT FROM AUTHOR]

We discuss various aspects of the post-Newtonian approximation in general relativity. After presenting the foundation based on the Newtonian limit, we show a method to derive post-Newtonian equations of motion for relativistic compact binaries based on a surface integral approach and the strong field point particle limit. As an application we derive third post-Newtonian equations of motion for relativistic compact binaries which respect the Lorentz invariance in the post-Newtonian perturbative sense, admit a conserved energy, and are free from any ambiguity. [ABSTRACT FROM AUTHOR]