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1. Clustering-based Mode Reduction for Markov Jump Systems

   Du, Zhe; Ozay, Necmiye; Balzano, Laura (January 2022, Conference on Learning for Decision and Control)

   While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. 

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2. Clustering-based Mode Reduction for Markov Jump Systems

   Du, Zhe; Ozay, Necmiye; Balzano, Laura (January 2022, Learning for Decision and Control)

   While Markov jump systems (MJSs) are more appropriate than LTI systems in terms of modeling abruptly changing dynamics, MJSs (and other switched systems) may suffer from the model complexity brought by the potentially sheer number of switching modes. Much of the existing work on reducing switched systems focuses on the state space where techniques such as discretization and dimension reduction are performed, yet reducing mode complexity receives few attention. In this work, inspired by clustering techniques from unsupervised learning, we propose a reduction method for MJS such that a mode-reduced MJS can be constructed with guaranteed approximation performance. Furthermore, we show how this reduced MJS can be used in designing controllers for the original MJS to reduce the computation cost while maintaining guaranteed suboptimality. 

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3. Mode Clustering for Markov Jump Systems

   Du, Zhe; Ozay, Necmiye; Balzano, Laura (January 2019, IEEE CAMSAP 2019)

   In this work, we consider the problem of mode clustering in Markov jump models. This model class consists of multiple dynamical modes with a switching sequence that determines how the system switches between them over time. Under different active modes, the observations can have different characteristics. Given the observations only and without knowing the mode sequence, the goal is to cluster the modes based on their transition distributions in the Markov chain to find a reduced-rank Markov matrix that is embedded in the original Markov chain. Our approach involves mode sequence estimation, mode clustering and reduced-rank model estimation, where mode clustering is achieved by applying the singular value decomposition and k-means. We show that, under certain conditions, the clustering error can be bounded, and the reduced-rank Markov chain is a good approximation to the original Markov chain. Through simulations, we show the efficacy of our approach and the application of our approach to real world scenarios. Index Terms—Switched model, Markov chain, clustering 

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4. Allan Variance-based Granulation Technique for Large Temporal Databases

   Sinanaj, Lorina; Haeri, Hossein; Gao, Liming; Maddipatla, Satya Prasad; Chen, Cindy; Jerath, Kshitij; Beal, Craig; Brennan, Sean (October 2021, 13th International Conference on Knowledge Management and Information Systems)

   null (Ed.)

   decrease query response time with limited main memory and storage space, data reduction techniques that preserve data quality are needed. Existing data reduction techniques, however, are often computationally expensive and rely on heuristics for deciding how to split or reduce the original dataset. In this paper, we propose an effective granular data reduction technique for temporal databases, based on Allan Variance (AVAR). AVAR is used to systematically determine the temporal window length over which data remains relevant. The entire dataset to be reduced is then separated into granules with size equal to the AVAR-determined window length. Data reduction is achieved by generating aggregated information for each such granule. The proposed method is tested using a large database that contains temporal information for vehicular data. Then comparison experiments are conducted and the outstanding runtime performance is illustrated by comparing with three clustering-based data reduction methods. The performance results demonstrate that the proposed Allan Variance-based technique can efficiently generate reduced representation of the original data without losing data quality, while significantly reducing computation time. 

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5. Topology Preserving Data Reduction for Computing Persistent Homology

   https://doi.org/10.1109/BigData50022.2020.9378216  

   Malott, Nicholas O.; Sens, Aaron M.; Wilsey, Philip A. (December 2020, International Workshop on Big Data Reduction)

   An emerging method for data analysis is called Topological Data Analysis (TDA). TDA is based in the mathematical field of topology and examines the properties of spaces under continuous deformation. One of the key tools used for TDA is called persistent homology which considers the connectivity of points in a d-dimensional point cloud at different spatial resolutions to identify topological properties (holes, loops, and voids) in the space. Persistent homology then classifies the topological features by their persistence through the range of spatial connectivity. Unfortunately the memory and run-time complexity of computing persistent homology is exponential and current tools can only process a few thousand points in R3. Fortunately, the use of data reduction techniques enables persistent homology to be applied to much larger point clouds. Techniques to reduce the data range from random sampling of points to clustering the data and using the cluster centroids as the reduced data. While several data reduction approaches appear to preserve the large topological features present in the original point cloud, no systematic study comparing the efficacy of different data clustering techniques in preserving the persistent homology results has been performed. This paper explores the question of topology preserving data reductions and describes formally when and how topological features can be mischaracterized or lost by data reduction techniques. The paper also performs an experimental assessment of data reduction techniques and resilient effects on the persistent homology. In particular, data reduction by random selection is compared to cluster centroids extracted from different data clustering algorithms. 

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