Abstract
Classification of time series signals has become an important construct and has many practical applications. With existing classifiers, we may be able to classify signals accurately; however, that accuracy may decline if using a reduced number of attributes. Transforming the data and then undertaking a dimensionality reduction may improve the quality of the data analysis, decrease the time required for classification and simplify models. We propose an approach, which chooses suitable wavelets to transform the data, then combines the output from these transformations to construct a dataset by applying ensemble classifiers. We demonstrate this on different data sets across different classifiers and use different evaluation methods. Our experimental results demonstrate the effectiveness of the proposed technique, compared to the approaches that use either raw signal data or a single wavelet transform.
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Notes
- 1.
Noise here includes missing or misclassification of values as well as other induced random fluctuations in the data.
- 2.
We designate these signals as raw or unmodified Data.
- 3.
note: \(\sum ^J_{j=1} \frac{n}{2^j} = \frac{n}{2} + \frac{n}{4} + \dots + 2 + 1 = 2^J -1 = n-1\).
- 4.
Decomposing \(X_t: n=2^J\), to level \(J_0 : 1 \le J_0 \le J\) then \({\textbf {V}}_{J_0}\) has \(n/2^{J_0}\) elements.
- 5.
Which permits construction of a plot of cumulative energy% in the signal (or representation of), against the number of data points, see Fig. 2.
- 6.
As the DWT is an orthonormal transform, the energy in the transform (consisting of all \(J + 1\) subvectors) equates to the energy in the signal.
- 7.
We also applied single Decision tree classifiers to the MDWT data as a baseline to compare with ensemble classifiers.
- 8.
Smoothness defined here as: standard deviation of the of first differences of a time series elements. i.e. standard deviation of (\(X_S\)) : \(X_S = x_1 - x_2, x_2 - x_3, \ldots , x_{n-1} - x_n \).
- 9.
For the Ensemble Classifiers* throughout our experiment we set number of trees used to 100, no fine tuning of parameters was undertaken.
- 10.
In this instance we also include the Extra coefficients as they represent considerable signal energy.
- 11.
Using Accuracy % here is a suitable metric, as the dataset is reasonably balanced i.e. Class 1 has 81 records, Class 2 and 3 have 65 records each.
- 12.
As indicated by the NPES, Fig. 2.
- 13.
The average energy/information provided by the Extra coefficients at level \(\mathcal {S}_3\), per transformed signal is only 0.5% hence little if at all any gain in accuracy is achieved by including the Extra coefficients at this level.
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Grant, P., Islam, M.Z. (2022). Signal Classification Using Smooth Coefficients of Multiple Wavelets to Achieve High Accuracy from Compressed Representation of Signal. In: Chen, W., Yao, L., Cai, T., Pan, S., Shen, T., Li, X. (eds) Advanced Data Mining and Applications. ADMA 2022. Lecture Notes in Computer Science(), vol 13726. Springer, Cham. https://doi.org/10.1007/978-3-031-22137-8_13
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