Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences

Osipov, Vladimir Al.

doi:10.1007/s10955-016-1537-5

Cited by 2 publications

(4 citation statements)

References 46 publications

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“…The max-min normalization method [12]: this kind of wavelet is similar to the RBF network, but the scale parameter and displacement parameter of the wavelet network can be set according to the time-frequency localization characteristics of the wavelet [13,14].…”

Section: Wavelet Analysismentioning

confidence: 99%

Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

Liu

Yan

2021

Journal of Sensors

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In recent years, people are more and more interested in time series modeling and its application in prediction. This paper mainly discusses a financial time series image algorithm based on wavelet analysis and data fusion. In this research, we conducted an in-depth study on the scale decomposition sequence and wavelet transform sequence in different scale domains of wavelet transform according to the scale change rule based on wavelet transform. We use wavelet neural network with different input neurons and hidden neurons to predict, respectively. Finally, the prediction results are integrated into the final prediction results based on the original time series by using wavelet reconstruction technology. Using RBF algorithm in neural network and SPSS Clementine, the wavelet transform sequences on five scales are modeled. Each network model has three layers: one input layer, one hidden layer, and one output layer, and each output layer has only one output element. In order to compare the prediction effect of the model proposed in this study, the ordinary RBF network is used to model and predict the log yield itself. When the input sample is 5, the minimum mean square error is obtained when the hidden layer is 6, and the mean square error is 1.6349. The mean square error of the training phase is 0.0209, and the validation error is 1.6141. The results show that the prediction results of the wavelet prediction method combined with the RBF network prediction method are better than those of wavelet prediction or RBF network prediction.

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Section: Wavelet Analysismentioning

confidence: 99%

Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

Liu

Yan

2021

Journal of Sensors

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“…2.3. Very recently, in 2016, Osipov [15] introduced the problem of counting "p-ary f -fold de Bruijn sequences." However, Osipov only gives a partial solution, which appears to be incorrect; see Sec.…”

Section: Multi De Bruijn Sequencementioning

confidence: 99%

“…Osipov [15] recently defined a "p-ary f -fold de Bruijn sequence"; this is the same as a cyclic multi de Bruijn sequence but in different terminology and notation. The description below is in terms of our notation m, q, k, which respectively correspond to Osipov's f, , p (see Table 2).…”

Section: Generating Multi De Bruijn Sequences By Brute Forcementioning

confidence: 99%

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Multi de Bruijn sequences

Tesler

2017

Journal of Combinatorics

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We generalize the notion of a de Bruijn sequence to a "multi de Bruijn sequence": a cyclic or linear sequence that contains every k-mer over an alphabet of size q exactly m times. For example, over the binary alphabet {0, 1}, the cyclic sequence (00010111) and the linear sequence 000101110 each contain two instances of each 2-mer 00, 01, 10, 11. We derive formulas for the number of such sequences. The formulas and derivation generalize classical de Bruijn sequences (the case m = 1). We also determine the number of multisets of aperiodic cyclic sequences containing every k-mer exactly m times; for example, the pair of cyclic sequences (00011)(011) contains two instances of each 2-mer listed above. This uses an extension of the Burrows-Wheeler Transform due to Mantaci et al, and generalizes a result by Higgins for the case m = 1.LinearLinear, starts with k-mer y L y (m, q, k) W (m, q, k)/q k Linearized, starts with y LC y (m, q, k) W (m, q, k)/q k Cyclic, order d C (d) (m, q, k)

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Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences

Cited by 2 publications

References 46 publications

Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

Financial Time Series Image Algorithm Based on Wavelet Analysis and Data Fusion

Multi de Bruijn sequences

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