Comparison of Matrix Dimensionality Reduction Methods in Uncovering Latent Structures in the Data

Phase identification is the problem of determining what phase(s) that a load is connected to in a power distribution<br>system. However, real world sensor measurements used for phase identification have some level of noise that can hamper the ability to identify phase connections using data driven methods. Knowing the phase connections is important to keep the distribution system balanced so that parts of the system aren’t overloaded which can lead to inefficient operations, accelerated component degradation, and system destruction at worst. We use Singular Value Decomposition (SVD) with the optimal Singular Value Hard Threshold (SVHT) as part of a feature engineering pipeline to denoise data matrices of voltage magnitude measurements. This approach results in a reduction in frobenius error and an increase in average phase identification accuracy over a year of time series data. K-medoids clustering is used on the denoised voltage magnitude measurements to perform phase identification.<br>

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Time-Series Data Analysis Using Sliding Window Based SVD for Motion Evaluation

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2017.p1240 ◽

2017 ◽

Vol 21 (7) ◽

pp. 1240-1250

Author(s):

Yinlai Jiang ◽

Isao Hayashi ◽

Shuoyu Wang ◽

Kenji Ishida ◽

◽

...

Keyword(s):

Time Series ◽

Time Series Data ◽

Sliding Window ◽

Singular Values ◽

Singular Value ◽

Series Data ◽

Singular Vectors ◽

Walking Difficulty ◽

The Right ◽

Value Decomposition

A method based on singular value decomposition (SVD) is proposed for extracting features from motion time-series data observed with various sensing systems. Matrices consisting of the sliding window (SW) subsets of time-series data are decomposed, yielding singular vectors as the patterns of the motion, and the singular values as a scalar, by which the corresponding singular vectors describe the matrices.The sliding window based singular value decomposition was applied to analyze acceleration during walking. Three levels of walking difficulty were simulated by restricting the right knee joint in the measurement. The accelerations of the middles of the shanks and the back of the waist were measured and normalized before the SW-SVD was performed.The results showed that the first singular values inferred from the acceleration data of the restricted side (the right shank) significantly related to the increase of the restriction among all the subjects while there were no common trends in the singular values of the left shank and the waist. The SW-SVD was suggested to be a reliable method to evaluate walking disability. Furthermore, a 2D visualization tool is proposed to provide intuitive information about walking difficulty which can be used in walking rehabilitation to monitor recovery.

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DESIGN OF 2-D DIGITAL FILTERS BASED ON THE OPTIMAL DECOMPOSITION OF MAGNITUDE SPECIFICATIONS

Journal of Circuits System and Computers ◽

10.1142/s0218126693000447 ◽

1993 ◽

Vol 03 (03) ◽

pp. 733-756 ◽

Cited By ~ 7

Author(s):

T.-B. DENG ◽

M. KAWAMATA ◽

T. HIGUCHI

Keyword(s):

Singular Value Decomposition ◽

Digital Filters ◽

Matrix Decomposition ◽

Decomposition Methods ◽

Singular Value ◽

The Other ◽

Design Technique ◽

One Dimensional ◽

Rms Error ◽

Value Decomposition

The optimal decomposition (OD) technique for decomposing 2-D magnitude specifications into 1-D ones is proposed. Differing from the conventional matrix decomposition methods such as the singular value decomposition (SVD), the OD of a 2-D magnitude specification matrix results in 1-D magnitude specifications which are always non-negative while the root mean-squared (rms) error in decomposition is minimum. Therefore, the OD is more suitable for designing 2-D digital filters (2DDFs) through designing one-dimensional digital filters (1DDFs) than the conventional matrix decomposition methods. Based on the OD, the problem of designing a recursive 2DDF can be reduced to one of designing a pair of 1DDFs, one 1-input/multi-output, and the other multi-input/ 1-output. Consequently, 2DDFs can easily be obtained by designing 1DDFs using the well-established 1-D design techniques. Three design examples are presented to illustrate that this OD-based 2DDF design technique is extremely efficient.

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Acquisition of Embodied Knowledge on Gesture Motion by Singular Value Decomposition

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2011.p1011 ◽

2011 ◽

Vol 15 (8) ◽

pp. 1011-1018 ◽

Cited By ~ 5

Author(s):

Isao Hayashi ◽

◽

Yinlai Jiang ◽

Shuoyu Wang ◽

Keyword(s):

Time Series ◽

Singular Value Decomposition ◽

Time Series Data ◽

Singular Spectrum Analysis ◽

Singular Value ◽

Series Data ◽

Embodied Knowledge ◽

Interval Time Series ◽

Nonverbal Information ◽

Value Decomposition

Communication is classified in terms of verbal and nonverbal information. We discuss an acquisition method of knowledge from nonverbal information. In particular, a gesture is an efficient form of nonverbal communication as well as in verbal ways, and we formulate here a method that measures similarity and estimation between gestures. A gesture includes human embodied knowledge, and therefore the visible bodily actions can communicate particular messages. However, we have infinite patterns for gesture, determined by personality. Recently, the singular spectrum analysis method is utilized as an attractive method. In this paper, we propose a new method for acquiring embodied knowledge from time-series data on gestures using singular value decomposition. The motion behavior is categorized into several clusters with similarity and estimation between interval time-series data. We discuss the usefulness of the proposed method using an example of gesture motion.

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Denoising with Singular Value Decomposition for Phase Identification in Power Distribution Systems

10.36227/techrxiv.15102072.v1 ◽

2021 ◽

Author(s):

Nicholas Zaragoza ◽

Vittal Rao

Keyword(s):

Singular Value Decomposition ◽

Power Distribution ◽

Distribution System ◽

Distribution Systems ◽

Time Series Data ◽

Singular Value ◽

Identification Accuracy ◽

Series Data ◽

Phase Identification ◽

Value Decomposition

Phase identification is the problem of determining what phase(s) that a load is connected to in a power distribution<br>system. However, real world sensor measurements used for phase identification have some level of noise that can hamper the ability to identify phase connections using data driven methods. Knowing the phase connections is important to keep the distribution system balanced so that parts of the system aren’t overloaded which can lead to inefficient operations, accelerated component degradation, and system destruction at worst. We use Singular Value Decomposition (SVD) with the optimal Singular Value Hard Threshold (SVHT) as part of a feature engineering pipeline to denoise data matrices of voltage magnitude measurements. This approach results in a reduction in frobenius error and an increase in average phase identification accuracy over a year of time series data. K-medoids clustering is used on the denoised voltage magnitude measurements to perform phase identification.<br>

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A Survey of Singular Value Decomposition Methods for Distributed Tall/Skinny Data

2020 IEEE/ACM 11th Workshop on Latest Advances in Scalable Algorithms for Large-Scale Systems (ScalA) ◽

10.1109/scala51936.2020.00009 ◽

2020 ◽

Author(s):

Drew Schmidt

Keyword(s):

Singular Value Decomposition ◽

Decomposition Methods ◽

Singular Value ◽

Value Decomposition

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LSTM-Guided Coaching Assistant for Table Tennis Practice

Sensors ◽

10.3390/s18124112 ◽

2018 ◽

Vol 18 (12) ◽

pp. 4112 ◽

Cited By ~ 6

Author(s):

Se-Min Lim ◽

Hyeong-Cheol Oh ◽

Jaein Kim ◽

Juwon Lee ◽

Jooyoung Park

Keyword(s):

Time Series ◽

State Space ◽

Time Series Data ◽

State Space Model ◽

Skill Assessment ◽

Series Data ◽

High Dimensional ◽

Table Tennis ◽

Space Model ◽

Low Dimensional

Recently, wearable devices have become a prominent health care application domain by incorporating a growing number of sensors and adopting smart machine learning technologies. One closely related topic is the strategy of combining the wearable device technology with skill assessment, which can be used in wearable device apps for coaching and/or personal training. Particularly pertinent to skill assessment based on high-dimensional time series data from wearable sensors is classifying whether a player is an expert or a beginner, which skills the player is exercising, and extracting some low-dimensional representations useful for coaching. In this paper, we present a deep learning-based coaching assistant method, which can provide useful information in supporting table tennis practice. Our method uses a combination of LSTM (Long short-term memory) with a deep state space model and probabilistic inference. More precisely, we use the expressive power of LSTM when handling high-dimensional time series data, and state space model and probabilistic inference to extract low-dimensional latent representations useful for coaching. Experimental results show that our method can yield promising results for characterizing high-dimensional time series patterns and for providing useful information when working with wearable IMU (Inertial measurement unit) sensors for table tennis coaching.

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