Dongjin Lee

Mai Lan Tran, Dongjin Lee, Jae-Hun Jung

Common AI music composition algorithms based on artificial neural networks are to train a machine by feeding a large number of music pieces and create artificial neural networks that can produce music similar to the input music data. This approach is a blackbox optimization, that is, the underlying composition algorithm is, in general, not known to users. In this paper, we present a way of machine composition that trains a machine the composition principle embedded in the given music data instead of directly feeding music pieces. We propose this approach by using the concept of {\color{black}{Overlap}} matrix proposed in \cite{TPJ}. In \cite{TPJ}, a type of Korean music, so-called the {\it Dodeuri} music such as Suyeonjangjigok has been analyzed using topological data analysis (TDA), particularly using persistent homology. As the raw music data is not suitable for TDA analysis, the music data is first reconstructed as a graph. The node of the graph is defined as a two-dimensional vector composed of the pitch and duration of each music note. The edge between two nodes is created when those nodes appear consecutively in the music flow. Distance is defined based on the frequency of such appearances. Through TDA on the constructed graph, a unique set of cycles is found for the given music. In \cite{TPJ}, the new concept of the {\it {\color{black}{Overlap}} matrix} has been proposed, which visualizes how those cycles are interconnected over the music flow, in a matrix form. In this paper, we explain how we use the {\color{black}{Overlap}} matrix for machine composition. The {\color{black}{Overlap}} matrix makes it possible to compose a new music piece algorithmically and also provide a seed music towards the desired artificial neural network. In this paper, we use the {\it Dodeuri} music and explain detailed steps.

Kwanghyuk Park, Xinjuan Chen, Dongjin Lee et al.

In this paper, we introduce the finite difference weighted essentially non-oscillatory (WENO) scheme based on the neural network for hyperbolic conservation laws. We employ the supervised learning and design two loss functions, one with the mean squared error and the other with the mean squared logarithmic error, where the WENO3-JS weights are computed as the labels. Each loss function consists of two components where the first component compares the difference between the weights from the neural network and WENO3-JS weights, while the second component matches the output weights of the neural network and the linear weights. The former of the loss function enforces the neural network to follow the WENO properties, implying that there is no need for the post-processing layer. Additionally the latter leads to better performance around discontinuities. As a neural network structure, we choose the shallow neural network (SNN) for computational efficiency with the Delta layer consisting of the normalized undivided differences. These constructed WENO3-SNN schemes show the outperformed results in one-dimensional examples and improved behavior in two-dimensional examples, compared with the simulations from WENO3-JS and WENO3-Z.

Dongjin Lee, Kijung Shin

Consider multiple seasonal time series being collected in real-time, in the form of a tensor stream. Real-world tensor streams often include missing entries (e.g., due to network disconnection) and at the same time unexpected outliers (e.g., due to system errors). Given such a real-world tensor stream, how can we estimate missing entries and predict future evolution accurately in real-time? In this work, we answer this question by introducing SOFIA, a robust factorization method for real-world tensor streams. In a nutshell, SOFIA smoothly and tightly integrates tensor factorization, outlier removal, and temporal-pattern detection, which naturally reinforce each other. Moreover, SOFIA integrates them in linear time, in an online manner, despite the presence of missing entries. We experimentally show that SOFIA is (a) robust and accurate: yielding up to 76% lower imputation error and 71% lower forecasting error; (b) fast: up to 935X faster than the second-most accurate competitor; and (c) scalable: scaling linearly with the number of new entries per time step.