Singular Spectrum Analysis: A New Tool in Time Series Analysis (Language of Science)

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SoftwareX Available online 6 April Author links open overlay panel M. Leles a b J. Mozelli a d H. Under a Creative Commons license. Abstract The Singular Spectrum Analysis SSA is powerful method, capable of working with arbitrary statistical process and it is adaptive to the underlaying data. Keywords Singular spectrum analysis. Recommended articles Citing articles 0. Published by Elsevier B. An example of cough events simulated by a volunteer.

Two peaks at around 60 s and s represent the cough events. The blue curve repre- sents the respiratory curve, while the red curve represents the anomaly score calculated by Equation An example of breathing stop simulated by a volunteer. The red curve represents the respiratory curve, while the blue curve represents the anomaly score calculated by Equation On the other hand, gradual increase of respiratory period was not clearly detected by this method.

Real-time anomaly detection was tested as shown in Figure 5. The red curve represents the anomaly score.

Simulated breathing stop was successfully detected by this algorithm. Prior works have suggested that a general algorithm to detect anomaly motion would be difficult. This paper tried to overcome the difficulty using singular spectrum analysis. A snapshot of real-time anomaly detection. Depth data blue curve and Anomaly score red curve are shown. Window length dependencies of anomaly score in the case of breathing stop.

The window length w is a main parameter of the analysis. The result depends on the parameter. However, there has been no universal selection rule. Therefore, we analyzed a respiratory curve with different length and compared them by visual inspection. Figure 6 shows anomaly scores with different time window w for a sudden stop of breathing event. As shown in Figure 6 , smaller window length tends to increase time resolution of anomaly detection, while the score itself tends to be noisy.

We did the same way to the cough events and obtained the Figure 7. We found the same tendency in the figure and determined the window length to be 8 sec. The optimum window length, however, depends on a patient. There has a limitation, however, in this algorithm. One of the demerit in our method is the difficulty of the simple and explicit interpretation of the anomaly model.

There has no clear-cut threshold to alarm an error.

Singular spectrum analysis : a new tool in time series analysis in SearchWorks catalog

Users should be aware of these difficulties. The merit of this approach is the fact that no a priori modeling of anomaly motion is required. Because anomaly motion is defined as a deviation from the normal motion, an explicit pre-implementation of anomaly mode is considered to be difficult. Using this algorithm, an unexpected anomaly motion could be detected. Hence, this algorithm will be a good supporting tool for medical staffs.

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We have demonstrated that automatic anomaly detection of respiratory motion using singular spectrum analysis was successful in the cough and sudden stop of breathing. The clinical use of this algorithm will be very hopeful. Window length dependencies of anomaly score in the case of cough. Physics in Medicine and Biology, 54, Physics in Medicine and Biology, 52, Physics in Medicine and Biology, 59, Physics in Medicine and Biology, 60, Communications in Statistics-Simulation and Computation, 32, Open Journal of Medical Imaging. A Language and Environment for Statistical Computing.

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R Foundation for Statistical Computing, Vienna. The paper is not in the journal. ABSTRACT The realization of automatic anomaly detection of respiratory motion could be very useful to prevent accidental damage during radiation therapy. In this paper, we proposed an automatic anomaly detection method using singular value decomposition analysis.

Singular spectrum analysis :

Before applying this method, the investigator needs a normal respiratory motion data of a patient. From these data, a trajectory matrix representing normal time-series feature is created.


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Decomposing the matrix, we obtained the feature of normal time series. Then, we applied the same procedure to real-time data and obtained real-time features. Calculating the similarity of those feature matrixes, an anomaly score was obtained. Patient motion was observed by a depth camera. In our simulation, two types of motion e. Received 2 February ; accepted 26 February ; published 29 February 1.

Introduction Monitoring of a patient has been an important but tedious work for medical staffs. Materials and Methods 2. Measurement In this study, we applied the singular decomposition technique to measured respiratory motion obtained by a depth camera Microsoft Kinect v1. Anomaly Detection Method To detect an anomaly motion, we first extracted the feature of the time-series data with window length w based on singular value spectrum analysis [9] [10].

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We can define a trajectory matrix as 1 The matrix holds the feature of normal time series data at a reference time with look-back time of w. Next, we decomposed the matrix and using singular value decomposition 3 here is an orthogonal matrix and is an orthogonal matrix and W is a diagonal matrix with singular values of and there is a constraint of. From this decomposition of matrix, the matrix can be approximated as 4 This is an example of well-known spectrum decomposition of a matrix. For , in the similar manner, we obtain the following formula Figure 1 shows the singular values of and.