Abstract
Classification of time series signals can be crucial for many practical applications. While the existing classifiers may accurately classify pure signals, the existence of noise can significantly disturb the classification accuracy of these classifiers. We propose a novel classification approach that uses multiple wavelets together with an ensemble of classifiers to return high classification accuracy even for noisy signals.
The proposed technique has two main steps. In Step 1, We convert raw signals into a useful dataset by applying multiple wavelet transforms, each from a different wavelet family or all from the same family with differing filter lengths. In Step 2, We apply the dataset processed in Step 1 to an ensemble of classifiers. We test on 500 noisy signals from five different classes. Our experimental results demonstrate the effectiveness of the proposed technique, on noisy signals, compared to the approaches that use either raw signals or a single wavelet transform.
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Notes
- 1.
The DWT in principle provides more information than the time series raw data points in classification because the DWT locates where the signal energies are concentrated in the frequency domain [3].
- 2.
In this new vector many data points are almost zero, a sparse representation.
- 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.
If we decompose \(X_t\) to level \(I \le J\) then \( \mathbf V _I\) has \(n/2^{I}\) elements.
- 5.
Initially we applied the MDWT data to a single Decision tree classifier as a baseline and then to ensemble classifiers, which are outlined in Sect. 4.1.
- 6.
With these generated signals we attached class labels and such labels were used as the attribute for Class within the classification methods.
- 7.
Here Accuracy is defined as the number of correctly Classified Instances (with respect to our initial Class labels).
- 8.
Result tables not shown for this exercise.
- 9.
We maintain 500 noise enhanced signals at each step.
- 10.
For evaluation here, we use 80% data to form the training set and 20% of data for testing with 100 trees used for each classifier.
- 11.
The MDWT comprising of four wavelets from different families, we have labelled as “MDWT Diff”, similarly for the MDWT with four wavelets from the same family, as “MDWT Same”.
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Grant, P., Islam, M.Z. (2019). A Novel Approach for Noisy Signal Classification Through the Use of Multiple Wavelets and Ensembles of Classifiers. In: Li, J., Wang, S., Qin, S., Li, X., Wang, S. (eds) Advanced Data Mining and Applications. ADMA 2019. Lecture Notes in Computer Science(), vol 11888. Springer, Cham. https://doi.org/10.1007/978-3-030-35231-8_14
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