Method of extracting features using singular spectrum analysis

Singular Spectrum Analysis (SSA) is a signal analysis technology based on linear algebra. It can be applied to signal denoising, prediction and feature extraction and other fields. Compared with other methods, SSA is a non-parametric method and therefore does not require any assumptions about the signal. This makes it universal and flexible. The advantage of SSA is that it can extract features in a signal by decomposing it into its components. These components can represent information such as trend, periodicity, and noise of the signal. By analyzing these components, signals can be better understood and processed. In addition, SSA can also be used for signal prediction by predicting future signal changes based on past signal data. In short, SSA is a powerful signal analysis technology

The basic idea of ​​SSA is to decompose the original signal into several components (sub-sequences), each component is composed of several Obtained by linear combination of basis functions. These basis functions are local basis functions constructed from a portion (window) of the original signal. By performing singular value decomposition (SVD) on these basis functions, a set of singular values ​​and singular vectors can be obtained. Singular values ​​represent the energy of the basis function, while singular vectors represent the shape of the basis function.

In SSA, the feature extraction process is to select the most representative components. Generally speaking, we decompose the signal and then select the components that best represent the signal characteristics for analysis. These components typically include trend, cycle, and stochastic components. The trend component reflects the overall trend, the periodic component reflects cyclical changes, and the stochastic component represents noise and random changes.

The feature extraction method of SSA mainly includes the following steps:

Signal decomposition is to split the original signal into multiple components. Obtained by linear combination of basis functions. To ensure accurate and reliable decomposition results, appropriate window size and number of components need to be selected.

Component selection: Based on the energy and shape of the components, select components that can represent the signal characteristics for analysis. Typically, trend components, periodic components, and random components are selected.

Feature extraction: Extract features from the selected components, such as calculating the mean, variance, peak, valley and other statistics of the component, or calculating the period, frequency, amplitude and other characteristics of the component. .

Feature analysis: Analyze the extracted features, such as calculating the correlation between features, statistical distribution, etc. Through the analysis of features, some important features of the signal can be revealed, such as the cycle and trend of the signal.

The SSA feature extraction method has the following advantages:

1.SSA is a non-parametric method that does not require any assumptions about the signal. , so it has strong universality and flexibility.

2.SSA can decompose the signal into several components, each component has a clear physical meaning, which facilitates feature extraction and analysis.

3.SSA can effectively remove noise and interference in the signal and extract the true characteristics of the signal.

4.SSA has a relatively fast calculation speed and can process large-scale data.

In short, the feature extraction method based on singular spectrum analysis is an effective signal analysis method and can be used in fields such as signal denoising, prediction, and feature extraction. In practical applications, it is necessary to select the appropriate window size and number of components according to specific problems, and combine them with other algorithms for analysis and processing.

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