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Register a new userOn the use of Singular Spectrum Analysis
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Added by
Ana Maria Tome
Publication date
2018
fields
Electronic Engineering
and research's language is
English
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Singular Spectrum Analysis (SSA) or Singular Value Decomposition (SVD) are often used to de-noise univariate time series or to study their spectral profile. Both techniques rely on the eigendecomposition of the cor- relation matrix estimated after embedding the signal into its delayed coordi- nates. In this work we show that the eigenvectors can be used to calculate the coefficients of a set of filters which form a filter bank. The properties of these filters are derived. In particular we show that their outputs can be grouped according to their frequency response. Furthermore, the fre- quency at the maximum of each frequency response and the corresponding eigenvalue can provide a power spectrum estimation of the time series. Two different applications illustrate how both characteristics can be applied to analyze wideband signals in order to achieve narrow-band signals or to infer their frequency occupation.
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We present a new approach to solve the exponential retrieval problem. We derive a stable technique, based on the singular value decomposition (SVD) of lag-covariance and crosscovariance matrices consisting of covariance coefficients computed for index translated copies of an initial time series. For these matrices a generalized eigenvalue problem is solved. The initial signal is mapped into the basis of the generalized eigenvectors and phase portraits are consequently analyzed. Pattern recognition techniques could be applied to distinguish phase portraits related to the exponentials and noise. Each frequency is evaluated by unwrapping phases of the corresponding portrait, detecting potential wrapping events and estimation of the phase slope. Efficiency of the proposed and existing methods is compared on the set of examples, including the white Gaussian and auto-regressive model noise.
EEG is a non-invasive technique for recording brain bioelectric activity, which has potential applications in various fields such as human-computer interaction and neuroscience. However, there are many difficulties in analyzing EEG data, including its complex composition, low amplitude as well as low signal-to-noise ratio. Some of the existing methods of analysis are based on feature extraction and machine learning to differentiate the phase of schizophrenia that samples belong to. However, medical research requires the use of machine learning not only to give more accurate classification results, but also to give the results that can be applied to pathological studies. The main purpose of this study is to obtain the weight values as the representation of influence of each frequency band on the classification of schizophrenia phases on the basis of a more effective classification method using the LES feature extraction, and then the weight values are processed and applied to improve the accuracy of machine learning classification. We propose a method called weight-voting to obtain the weights of sub-bands features by using results of classification for voting to fit the actual categories of EEG data, and using weights for reclassification. Through this method, we can first obtain the influence of each band in distinguishing three schizophrenia phases, and analyze the effect of band features on the risk of schizophrenia contributing to the study of psychopathology. Our results show that there is a high correlation between the change of weight of low gamma band and the difference between HC, CHR and FES. If the features revised according to weights are used for reclassification, the accuracy of result will be improved compared with the original classifier, which confirms the role of the band weight distribution.
N-body simulations provide most of our insight into the structure and evolution of galaxies, but our analyses of these are often heuristic and from simple statistics. We propose a method that discovers the dynamics in space and time together by finding the most correlated temporal signals in multiple time series of basis function expansion coefficients and any other data fields of interest. The method extracts the dominant trends in the spatial variation of the gravitational field along with any additional data fields through time. The mathematics of this method is known as multichannel singular spectrum analysis (M-SSA). In essence, M-SSA is a principal component analysis of the covariance of time series replicates, each lagged successively by some interval. The dominant principal component represents the trend that contains the largest fraction of the correlated signal. The next principal component is orthogonal to the first and contains the next largest fraction, and so on. Using a suite of previously analysed simulations, we find that M-SSA describes bar formation and evolution, including mode coupling and pattern-speed decay. We also analyse a new simulation tailored to study vertical oscillations of the bar using kinematic data. Additionally, and to our surprise, M-SSA uncovered some new dynamics in previously analysed simulations, underscoring the power of this new approach.
Using multi-scale ideas from wavelet analysis, we extend singular-spectrum analysis (SSA) to the study of nonstationary time series of length $N$ whose intermittency can give rise to the divergence of their variance. SSA relies on the construction of the lag-covariance matrix C on M lagged copies of the time series over a fixed window width W to detect the regular part of the variability in that window in terms of the minimal number of oscillatory components; here W = M Dt, with Dt the time step. The proposed multi-scale SSA is a local SSA analysis within a moving window of width M <= W <= N. Multi-scale SSA varies W, while keeping a fixed W/M ratio, and uses the eigenvectors of the corresponding lag-covariance matrix C_M as a data-adaptive wavelets; successive eigenvectors of C_M correspond approximately to successive derivatives of the first mother wavelet in standard wavelet analysis. Multi-scale SSA thus solves objectively the delicate problem of optimizing the analyzing wavelet in the time-frequency domain, by a suitable localization of the signals covariance matrix. We present several examples of application to synthetic signals with fractal or power-law behavior which mimic selected features of certain climatic and geophysical time series. A real application is to the Southern Oscillation index (SOI) monthly values for 1933-1996. Our methodology highlights an abrupt periodicity shift in the SOI near 1960. This abrupt shift between 4 and 3 years supports the Devils staircase scenario for the El Nino/Southern Oscillation phenomenon.
One-bit radar, performing signal sampling and quantization by a one-bit ADC, is a promising technology for many civilian applications due to its low-cost and low-power consumptions. In this paper, problems encountered by one-bit LFMCW radar are studied and a two-stage target detection method termed as the dimension-reduced generalized approximate message passing (DR-GAMP) approach is proposed. Firstly, the spectrum of one-bit quantized signals in a scenario with multiple targets is analyzed. It is indicated that high-order harmonics may result in false alarms (FAs) and cannot be neglected. Secondly, based on the spectrum analysis, the DR-GAMP approach is proposed to carry out target detection. Specifically, linear preprocessing methods and target predetection are firstly adopted to perform the dimension reduction, and then, the GAMP algorithm is utilized to suppress high-order harmonics and recover true targets. Finally, numerical simulations are conducted to evaluate the performance of one-bit LFMCW radar under typical parameters. It is shown that compared to the conventional radar applying linear processing methods, one-bit LFMCW radar has about $1.3$ dB performance gain when the input signal-to-noise ratios (SNRs) of targets are low. In the presence of a strong target, it has about $1.0$ dB performance loss.
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