# On the Classification of ECG and EEG Signals with Various Degrees of Dimensionality Reduction

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- Techniques that preserve the local arrangement: locally linear embedding (LLE), Laplacian eigenmaps (LE), manifold charting (MC), Hessian locally linear embedding (HLLE), and
- (b)
- Techniques that conserve global structure: isometric mapping (ISOMAP), diffusion map.

- a nearest-neighbor search,
- defining of distances or affinities between elements,
- resolving a generalized eigenproblem to obtain the embedding of the initial space into a lower dimensional one.

## 2. Materials and Methods

#### 2.1. Laplacian Eigenmaps—LE

- (i.)
- Nearest-neighbor search and adjacency graph construction

- (ii.)
- Weighted adjacency matrix (Choosing the weights)

_{ij}of the symmetric (n × n) vicinity matrix are computed as:

- (iii.)
- Eigenmaps

**D**= (d

_{ij}) is an (n × n) diagonal matrix with

_{0}suitable to the 0 eigenvalue is discarded. The next m eigenvectors related to the next m eigenvalues in increasing gamut are utilized for embedding in a m-dimensional Euclidean space:

_{i}→ (f

_{1}(i), …, f

_{m}(i)),

_{0}, …, f

_{k−}

_{1}are the solutions of (1).

#### 2.2. Locality Preserving Projections—LPP

**X**is the training data matrix and L, D have the same meaning as before.

_{0}, …, a

_{l−1}the column vectors related to the solutions of (2), ordering increasingly λ

_{0}< … < λ

_{l-1}, the mapping is defined as:

_{i}is l-dimensional, and

**A**is a (nxl) matrix.

#### 2.3. Compressed Sensing—CS

**∅**x,

#### 2.4. Classifier Types

#### 2.4.1. Decision Trees

#### 2.4.2. Discriminant Analysis

#### 2.4.3. Naive Bayes

#### 2.4.4. Support Vector Machine—SVM

#### 2.4.5. Nearest Neighbor

#### 2.4.6. Ensembles of Classifiers

## 3. Experimental Results and Discussions

#### 3.1. ECG Signals

^{®}medium (MathWorks, Natick, MA, USA) and we used the next classifiers, each with different versions for tuning their key settings: Decision Trees (with fine, medium and coarse type classifier), Linear Discriminant and Quadratic Discriminant, Naive and Kernel Naive Bayes, Support Vector Machine (Linear, Quadratic, Cubic and Gaussian), k-nearest neighbors (fine, medium, coarse, Cosine, Cubic and Weighted KNN), besides different kinds of the ensemble of classifiers (Boosted and Bagged trees, discriminant and KNN Subspace and RUSBoosted Trees).

#### 3.2. EEG Signals

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

- Mordohai, P.; Medioni, G. Dimensionality Estimation, Manifold Learning and Function Approximation using Tensor Voting. J. Mach. Learn. Res.
**2010**, 11, 411–450. [Google Scholar] - Boehmke, B.; Greenwell, B.M. Dimension Reduction. In Hands-On Machine Learning with R; Chapman & Hall, CRC Press: Boca Raton, FL, USA, 2019; pp. 343–396. [Google Scholar]
- Bingham, E.; Mannila, H. Random projection in dimensionality reduction: Applications to image and text data. In Proceedings of the 7-th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, CA, USA, 26–29 August 2001; pp. 245–250. [Google Scholar]
- Lee, J.A.; Verleysen, M. Nonlinear Dimensionality Reduction; Springer: Berlin/Heidelberg, Germany, 2007. [Google Scholar]
- Bengio, Y.; Paiement, J.; Vincent, P.; Delalleau, O.; Le Roux, N.; Ouimet, M. Out-of-sample extensions for LLE, Isomap, MDS, eigenmaps, and spectral clustering. Adv. Neural Inf. Process. Syst.
**2004**, 16, 177–186. [Google Scholar] - Fodor, I. A Survey of Dimension Reduction Techniques; Technical Report; Center for Applied Scientific Computing, Lawrence Livermore National: Livermore, CA, USA, 2002.
- Belkin, M.; Niyogi, P. Laplacian Eigenmaps and Spectral Techniques for Embedding and Clustering. Adv. Neural Inf. Process. Syst.
**2001**, 14, 586–691. [Google Scholar] - Belkin, M. Problems of Learning on Manifolds. Ph.D. Thesis, Department of Mathematics, The University of Chicago, Chicago, IL, USA, August 2003. [Google Scholar]
- Belkin, M.; Niyogi, P. Laplacian eigenmaps for dimensionality reduction and data representation. Neural Comput.
**2003**, 15, 1373–1396. [Google Scholar] [CrossRef] [Green Version] - He, X.; Niyogi, P. Locality preserving projections. In Proceedings of the Conference on Advances in Neural Information Processing Systems, Vancouver, BC, Canada, 8–13 December 2003. [Google Scholar]
- Donoho, D.L. Compressed sensing. IEEE Trans. Inf. Theory
**2006**, 52, 1289–1306. [Google Scholar] [CrossRef] - Candès, E.J.; Wakin, M.B. An Introduction to Compressive Sampling. IEEE Signal Process. Mag.
**2008**, 25, 21–30. [Google Scholar] [CrossRef] - Duda, R.; Hart, P. Pattern Recognition and Scene Analysis; Wiley Interscience: Hoboken, NJ, USA, 1973. [Google Scholar]
- Bishop, C.M. Pattern Recognition and Machine Learning; Springer: Berlin/Heidelberg, Germany, 2006. [Google Scholar]
- Alpaydin, E. Introduction to Machine Learning, 4th ed.; MIT Press: Cambridge, MA, USA, 2020. [Google Scholar]
- MIT-BIH. Arrhythmia Database. Available online: http://www.physionet.org/physiobank/database/mitdb/ (accessed on 8 January 2021).
- Fira, M.; Goraș, L.; Cleju, N.; Barabașa, C. On the classification of compressed sensed signals. In Proceedings of the International Symposium on Signals, Circuits and Systems (ISSCS) 2011, Iasi, Romania, 30 June 2011. [Google Scholar]
- Fira, M.; Goraș, L. On Some Methods for Dimensionality Reduction of ECG Signals. Int. J. Adv. Comput. Sci. Appl.
**2019**, 10, 326–607. [Google Scholar] [CrossRef] - EPFL. Available online: http://mmspg.epfl.ch/cms/page-58322.html (accessed on 22 May 2017).
- Hoffmann, U.; Vesin, J.M.; Ebrahimi, T.; Diserens, K. An efficient P300-based brain-computer interface for disabled subjects. J. Neurosci. Methods
**2008**, 167, 115–125. [Google Scholar] [CrossRef] [PubMed] [Green Version] - Hoffmann, U.; Garcia, G.; Vesin, J.-M.; Diserens, K.; Ebrahimi, T. A Boosting Approach to P300 Detection with Application to Brain-Computer Interfaces. In Proceedings of the IEEE EMBS Conference on Neural Engineering, Arlington, VA, USA, 16–20 March 2005. [Google Scholar]
- Farwell, L.A.; Donchin, E. Talking off the top of your head: A mental prosthesis utilizing event-related brain potentials. Electroencephalogr. Clin. Neurophysiol.
**1988**, 70, 510–523. [Google Scholar] [CrossRef] - Martišius, I.; Šidlauskas, K.; Damaševičius, R. Real-Time Training of Voted Perceptron for Classification of EEG Data. Int. J. Artif. Intell.
**2013**, 10, 207–217. [Google Scholar]

**Figure 10.**Classification results with original EEG signals for configurations with 4, 8 and 23 channels.

**Figure 11.**Results for the dimensionality reduction with CS algorithm for configurations with 8 channels.

**Figure 12.**Results for the dimensionality reduction with LE algorithm for configurations with 8 channels.

**Figure 13.**Results for dimensionality reduction with LPP algorithm for configurations with 8 channels.

**Table 1.**Classification accuracies with CS, LE, LPP algorithms for 2, 3 and 25 dimensions respectively.

ECG Original Centered | Compressed Sensed (CS) | Laplacian Eigenmaps (LE) | Locality Preserving Projections (LPP) | |||||||
---|---|---|---|---|---|---|---|---|---|---|

ECG Original | CS 2 | CS 3 | CS 25 | LE 2 | LE 3 | LE 25 | LPP 2 | LPP 3 | LPP 25 | |

Fine Trees | 83.44 | 49.41 | 55.34 | 79.81 | 76.25 | 77.32 | 86.73 | 54.00 | 66.65 | 81.15 |

Medium Trees | 71.32 | 45.35 | 48.00 | 69.23 | 71.53 | 68.85 | 79.62 | 52.34 | 60.43 | 67.91 |

Coarse Trees | 42.83 | 32.21 | 34.41 | 40.32 | 45.64 | 45.64 | 50.67 | 40.85 | 41.54 | 49.75 |

Linear Discriminant | 76.32 | 24.23 | 33.72 | 73.94 | 34.77 | 38.81 | 77.44 | 30.42 | 35.41 | 73.64 |

Quadratic Discriminant | 70.00 | 34.00 | 47.53 | 89.77 | 47.34 | 54.54 | 84.22 | 44.41 | 56.24 | 91.51 |

Naive Bayes | 47.63 | 33.43 | 38.93 | 52.22 | 37.64 | 38.34 | 74.36 | 42.51 | 49.37 | 77.21 |

Kernel Naive Bayes | 62.53 | 45.94 | 48.8 | 71.85 | 70.34 | 69.95 | 81.74 | 52.54 | 62.26 | 82.64 |

Linear SVM | 87.34 | 29.52 | 38.9 | 85.14 | 49.08 | 61.37 | 85.62 | 37.52 | 47.72 | 85.92 |

Quadratic SVM | 95.11 | 44.54 | 54.3 | 94.54 | 43.95 | 59.92 | 90.54 | 44.52 | 64.64 | 94.24 |

Cubic SVM | 95.24 | 42.72 | 53.00 | 94.50 | 26.10 | 33.00 | 91.20 | 27.10 | 47.92 | 94.24 |

Fine Gaussian SVM | 87.47 | 51.80 | 62.90 | 87.91 | 75.36 | 78.75 | 90.69 | 54.40 | 70.10 | 61.14 |

Medium Gaussian SVM | 92.91 | 49.84 | 58.74 | 93.00 | 67.92 | 69.88 | 87.12 | 53.44 | 67.84 | 94.14 |

Coarse Gaussian SVM | 79.47 | 32.85 | 43.65 | 80.97 | 54.36 | 55.41 | 80.92 | 44.45 | 57.82 | 83.82 |

Fine KNN | 93.42 | 39.14 | 55.14 | 93.71 | 79.92 | 83.36 | 89.84 | 45.11 | 63.90 | 93.74 |

Medium KNN | 90.27 | 48.72 | 60.82 | 90.82 | 80.76 | 83.92 | 89.65 | 52.42 | 68.00 | 91.32 |

Coarse KNN | 77.62 | 50.47 | 57.71 | 77.44 | 74.00 | 75.35 | 80.12 | 53.63 | 65.74 | 78.34 |

Cosine KNN | 90.54 | 29.64 | 47.15 | 90.74 | 61.25 | 81.42 | 89.55 | 32.80 | 54.62 | 92.76 |

Cubic KNN | 90.22 | 48.81 | 60.81 | 90.81 | 80.88 | 83.95 | 89.72 | 52.38 | 68.34 | 90.77 |

Weighted KNN | 91.47 | 43.60 | 59.44 | 92.34 | 81.52 | 84.82 | 90.32 | 48.51 | 67.42 | 92.35 |

Ensemble Boosted Trees | 78.34 | 45.97 | 49.45 | 76.81 | 72.65 | 70.19 | 82.49 | 53.55 | 61.36 | 77.67 |

Ensemble Bagged Trees | 91.81 | 43.94 | 59.45 | 90.4 | 80.00 | 83.91 | 90.91 | 48.86 | 68.31 | 91.84 |

Ensemble Subspace Discriminant | 76.24 | 24.31 | 29.14 | 70.3 | 35 | 38.95 | 76.93 | 30.22 | 34.32 | 73.05 |

Ensemble Subspace KNN | 94.71 | 23.34 | 44.00 | 94.04 | 51.24 | 80.82 | 89.98 | 24.14 | 56.10 | 95.34 |

Ensemble RUS Boosted Trees | 71.54 | 45.34 | 47.94 | 69.31 | 71.54 | 68.84 | 79.64 | 52.84 | 60.67 | 67.97 |

ECG Original Centered | CS 2 | CS 3 | CS 4 | CS 5 | CS 7 | CS 9 | CS 10 | CS 15 | CS 20 | CS 25 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Fine Tree | 83.4 | 49.4 | 55.3 | 58.1 | 68.6 | 72.3 | 71.5 | 72.4 | 75.7 | 77.3 | 79.8 |

Medium Tree | 71.3 | 45.3 | 48.0 | 49.3 | 54 | 52.8 | 51.6 | 52.3 | 52.7 | 60.6 | 69.2 |

Coarse Tree | 42.8 | 32.2 | 34.4 | 34.2 | 36.5 | 35.2 | 36.2 | 36.7 | 35.9 | 38.0 | 40.3 |

Linear Discriminant | 76.3 | 24.2 | 33.7 | 35.2 | 41.4 | 47.3 | 55.3 | 60.0 | 69.2 | 71.6 | 73.9 |

Quadratic Discriminant | 70.0 | 34.0 | 47.5 | 50.3 | 63.2 | 74.1 | 77.8 | 82.0 | 87.6 | 89.1 | 89.7 |

Naive Bayes | 47.6 | 33.4 | 38.9 | 40.8 | 47.2 | 48.6 | 47.8 | 49.1 | 50.3 | 50.9 | 52.2 |

Kernel Naive Bayes | 62.5 | 45.9 | 48.8 | 51.7 | 62.4 | 66.1 | 68.0 | 68.1 | 70.5 | 70.5 | 71.8 |

Linear SVM | 87.3 | 29.5 | 38.9 | 41.6 | 54.2 | 63.2 | 71.3 | 75.9 | 82.8 | 84.4 | 85.1 |

Quadratic SVM | 95.1 | 44.5 | 54.3 | 61.7 | 74.7 | 85.2 | 88.9 | 90.8 | 93.3 | 94.2 | 94.5 |

Cubic SVM | 95.2 | 42.7 | 53.0 | 62.2 | 75.9 | 86.6 | 90.1 | 91.7 | 93.4 | 94.7 | 94.5 |

Fine Gaussian SVM | 87.4 | 51.8 | 62.9 | 69.5 | 82.0 | 86.4 | 87.8 | 88.5 | 88.0 | 87.6 | 87.9 |

Medium Gaussian SVM | 92.9 | 49.8 | 58.7 | 65.4 | 78.0 | 85.4 | 87.3 | 88.6 | 91.2 | 92.0 | 93.0 |

Coarse Gaussian SVM | 79.4 | 32.8 | 43.6 | 45.2 | 62.1 | 67.2 | 69.5 | 71.8 | 77.5 | 79.5 | 80.9 |

Fine KNN | 93.4 | 39.1 | 55.1 | 64.4 | 80.7 | 87.6 | 89.4 | 91.0 | 92.4 | 93.5 | 93.7 |

Medium KNN | 90.2 | 48.7 | 60.8 | 67.5 | 80.6 | 86.5 | 87.8 | 88.4 | 89.6 | 90.3 | 90.8 |

Coarse KNN | 77.6 | 50.4 | 57.7 | 61.5 | 69.2 | 73.8 | 74.9 | 75.5 | 76.3 | 76.6 | 77.4 |

Cosine KNN | 90.5 | 29.6 | 47.1 | 58.2 | 73.8 | 83.2 | 85.9 | 86.7 | 88.3 | 89.7 | 90.7 |

Cubic KNN | 90.2 | 48.8 | 60.8 | 67.7 | 80.3 | 86.4 | 87.7 | 88.5 | 89.8 | 90.5 | 90.8 |

Weighted KNN | 91.4 | 43.6 | 59.4 | 68.2 | 81.9 | 88.1 | 89.3 | 90.1 | 91.5 | 92.1 | 92.3 |

Ensemble Boosted Trees | 78.3 | 45.9 | 49.4 | 52.2 | 61.8 | 66.1 | 67.5 | 70.6 | 69.5 | 73.8 | 76.8 |

Ensemble Bagged Trees | 91.8 | 43.9 | 59.4 | 65.6 | 80.3 | 85.2 | 87.1 | 88.2 | 89.7 | 90.2 | 90.4 |

Ensemble Subspace Discriminant | 76.2 | 24.3 | 29.1 | 31.5 | 40.0 | 43.9 | 45.6 | 47.0 | 61.1 | 64.4 | 70.3 |

Ensemble Subspace KNN | 94.7 | 23.3 | 44.0 | 49.5 | 74.2 | 86.0 | 89.0 | 90.3 | 92.4 | 93.6 | 94.0 |

Ensemble RUSBoosted Trees | 71.5 | 45.3 | 47.9 | 49.4 | 53.9 | 53.8 | 52.0 | 52.5 | 52.8 | 60.6 | 69.3 |

ECG Original Centred | LE 2 | LE 3 | LE 4 | LE 5 | LE 7 | LE 9 | LE 10 | LE 15 | LE 20 | LE 25 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Fine Tree | 83.4 | 76.2 | 77.3 | 80.4 | 80.4 | 82.9 | 83.7 | 82.8 | 85.8 | 86.5 | 86.7 |

Medium Tree | 71.3 | 71.5 | 68.8 | 72.7 | 72.4 | 74.9 | 75 | 75.1 | 78.9 | 80.1 | 79.6 |

Coarse Tree | 42.8 | 45.6 | 45.6 | 52.5 | 52.5 | 50.9 | 51.2 | 51.3 | 51.8 | 51.6 | 50.6 |

Linear Discriminant | 76.3 | 34.7 | 38.8 | 34.7 | 40.3 | 57.8 | 61.1 | 60.3 | 72.1 | 76.2 | 77.4 |

Quadratic Discriminant | 70 | 47.3 | 54.5 | 58.3 | 60.1 | 69 | 72.2 | 73 | 78.1 | 82.1 | 84.2 |

Naive Bayes | 47.6 | 37.6 | 38.3 | 39.8 | 39.5 | 57 | 57.1 | 60.9 | 71.4 | 73.7 | 74.3 |

Kernel Naive Bayes | 62.5 | 70.3 | 69.9 | 70.8 | 71.5 | 74.9 | 73.6 | 74 | 77.3 | 79.5 | 81.7 |

Linear SVM | 87.3 | 49 | 61.3 | 67.3 | 70.2 | 75.3 | 76.9 | 77.5 | 79.1 | 83.7 | 85.6 |

Quadratic SVM | 95.1 | 43.9 | 59.9 | 76.2 | 79 | 86.1 | 87.6 | 87.3 | 87.7 | 89 | 90.5 |

Cubic SVM | 95.2 | 26.1 | 33 | 52.5 | 64.2 | 87.9 | 90.1 | 89.7 | 89.6 | 90.4 | 91.2 |

Fine Gaussian SVM | 87.4 | 75.3 | 78.7 | 81.1 | 82 | 85.2 | 85.9 | 86.5 | 88.6 | 90.4 | 90.6 |

Medium Gaussian SVM | 92.9 | 67.9 | 69.8 | 73.4 | 75.4 | 78.3 | 78.6 | 79.5 | 82.8 | 86.6 | 87.1 |

Coarse Gaussian SVM | 79.4 | 54.3 | 55.4 | 61.2 | 66.2 | 69.2 | 72.1 | 72.5 | 76.6 | 80.1 | 80.9 |

Fine KNN | 93.4 | 79.9 | 83.3 | 85.7 | 86.2 | 86.2 | 87.2 | 87.1 | 88.1 | 88.9 | 89.8 |

Medium KNN | 90.2 | 80.7 | 83.9 | 85 | 85.5 | 86.8 | 87 | 86.3 | 87.4 | 88.9 | 89.6 |

Coarse KNN | 77.6 | 74 | 75.3 | 75.3 | 77.1 | 79 | 78.6 | 78.5 | 78.3 | 80.6 | 80.1 |

Cosine KNN | 90.5 | 61.2 | 81.4 | 83.8 | 85.9 | 86.9 | 86.7 | 86.9 | 87.6 | 88.9 | 89.5 |

Cubic KNN | 90.2 | 80.8 | 83.9 | 84.7 | 85.5 | 86.8 | 86.8 | 86.1 | 87.4 | 89 | 89.7 |

Weighted KNN | 91.4 | 81.5 | 84.8 | 86.6 | 86.9 | 87.4 | 88.1 | 87.8 | 89.1 | 89.9 | 90.3 |

Ensemble Boosted Trees | 78.3 | 72.6 | 70.1 | 75.5 | 76 | 78.3 | 79.2 | 79.9 | 81.4 | 82.2 | 82.4 |

Ensemble Bagged Trees | 91.8 | 80 | 83.9 | 86.2 | 86.6 | 88.2 | 88.6 | 88.7 | 89.9 | 90.9 | 90.9 |

Ensemble Subspace Discriminant | 76.2 | 35 | 38.9 | 34.7 | 40.2 | 59.2 | 61.9 | 60.5 | 72.2 | 75.9 | 76.9 |

Ensemble Subspace KNN | 94.7 | 51.2 | 80.8 | 83.2 | 86.1 | 86.9 | 87.6 | 87.8 | 88.7 | 89.6 | 89.9 |

Ensemble RUSBoosted Trees | 71.5 | 71.5 | 68.8 | 72.7 | 72.4 | 74.9 | 75 | 75.1 | 79 | 80.1 | 79.6 |

ECG Original Centered | LPP 2 | LPP 3 | LPP 4 | LPP 5 | LPP 7 | LPP 9 | LPP 10 | LPP 15 | LPP 20 | LPP 25 | |
---|---|---|---|---|---|---|---|---|---|---|---|

Fine Tree | 83.4 | 54 | 66.6 | 73 | 75.6 | 77.2 | 77.8 | 77.5 | 81.5 | 81.3 | 81.1 |

Medium Tree | 71.3 | 52.3 | 60.4 | 65.9 | 66.5 | 66.8 | 66.9 | 67 | 68 | 68.1 | 67.9 |

Coarse Tree | 42.8 | 40.8 | 41.5 | 46.7 | 46.6 | 46.9 | 49.7 | 49.9 | 49.7 | 49.7 | 49.7 |

Linear Discriminant | 76.3 | 30.4 | 35.4 | 35.5 | 37.8 | 47.5 | 63.2 | 65.3 | 71.2 | 72.6 | 73.6 |

Quadratic Discriminant | 70 | 44.4 | 56.2 | 65.1 | 67.6 | 76.2 | 82.3 | 83.4 | 89.1 | 90.5 | 91.5 |

Naive Bayes | 47.6 | 42.5 | 49.3 | 58.3 | 58.1 | 63.5 | 71.5 | 72.5 | 76.5 | 77.5 | 77.2 |

Kernel Naive Bayes | 62.5 | 52.5 | 62.2 | 65.6 | 70.6 | 73.6 | 77 | 77.7 | 81.3 | 82.6 | 82.6 |

Linear SVM | 87.3 | 37.5 | 47.7 | 53.6 | 58.9 | 70.4 | 76.9 | 78.1 | 83.5 | 84.8 | 85.9 |

Quadratic SVM | 95.1 | 44.5 | 64.6 | 73.5 | 77.6 | 86.4 | 90.2 | 90.9 | 93.7 | 94.1 | 94.2 |

Cubic SVM | 95.2 | 27.1 | 47.9 | 74.3 | 81.2 | 88.1 | 91.2 | 91.8 | 94.3 | 94.5 | 94.2 |

Fine Gaussian SVM | 87.4 | 54.4 | 70.1 | 77.3 | 81.2 | 84.8 | 84.4 | 82.9 | 75.8 | 65.2 | 61.1 |

Medium Gaussian SVM | 92.9 | 53.4 | 67.8 | 75.4 | 79.2 | 86.7 | 90.2 | 90.4 | 93.5 | 93.8 | 94.1 |

Coarse Gaussian SVM | 79.4 | 44.4 | 57.8 | 65.8 | 68.9 | 73.4 | 77.4 | 78 | 82.1 | 83 | 83.8 |

Fine KNN | 93.4 | 45.1 | 63.9 | 73.9 | 80 | 87.3 | 91.4 | 91.5 | 93.3 | 93.8 | 93.7 |

Medium KNN | 90.2 | 52.4 | 68 | 77 | 80.8 | 87 | 89.9 | 89.9 | 91.9 | 92.1 | 91.3 |

Coarse KNN | 77.6 | 53.6 | 65.7 | 70.6 | 72.2 | 77.3 | 80 | 80.3 | 81 | 79.3 | 78.3 |

Cosine KNN | 90.5 | 32.8 | 54.6 | 70.7 | 76.4 | 84.1 | 88.4 | 88.9 | 92.2 | 92.7 | 92.7 |

Cubic KNN | 90.2 | 52.3 | 68.3 | 76.8 | 80.6 | 86.8 | 89.2 | 89.3 | 91.6 | 91.1 | 90.7 |

Weighted KNN | 91.4 | 48.5 | 67.4 | 77.3 | 82.3 | 87.9 | 91 | 91.1 | 93 | 92.9 | 92.3 |

Ensemble Boosted Trees | 78.3 | 53.5 | 61.3 | 68.1 | 70 | 72 | 75.8 | 76.5 | 77.6 | 77.3 | 77.6 |

Ensemble Bagged Trees | 91.8 | 48.8 | 68.3 | 77.2 | 81.9 | 87.3 | 89.1 | 89.9 | 91.2 | 90.8 | 91.8 |

Ensemble Subspace Discriminant | 76.2 | 30.2 | 34.3 | 37 | 37.7 | 46.3 | 62 | 63.2 | 70.3 | 70.9 | 73 |

Ensemble Subspace KNN | 94.7 | 24.1 | 56.1 | 62.6 | 76.3 | 86.4 | 91.2 | 91.6 | 94.5 | 95.4 | 95.3 |

Ensemble RUSBoosted Trees | 71.5 | 52.8 | 60.6 | 66 | 66.5 | 66.8 | 66.8 | 67.1 | 68 | 68.1 | 67.9 |

ECG Orig. | EEG 8 Channels CS | ||||
---|---|---|---|---|---|

8 Channels | CS 3 | CS 5 | CS 10 | CS 15 | |

Fine Tree | 73.8 | 55.1 | 61.4 | 64.8 | 69.5 |

Medium Tree | 75.5 | 59.8 | 60.8 | 68.4 | 73.1 |

Coarse Tree | 75.8 | 59.6 | 59.4 | 65.7 | 70.5 |

Linear Discriminant | 77.2 | 68.3 | 74 | 79.9 | 84.6 |

Quadratic Discriminant | 63.4 | 66.5 | 68 | 72.6 | 71.2 |

Logistic Regression | 50.5 | 67.8 | 73.2 | 80.6 | 83.7 |

Naive Bayes | 81.7 | 66.3 | 68.5 | 72.4 | 75.8 |

Kernel Naive Bayes | 79.8 | 64.1 | 68.5 | 72 | 74.9 |

Linear SVM | 84.1 | 68.3 | 73.4 | 80.9 | 84 |

Quadratic SVM | 84.4 | 69 | 72.4 | 81.1 | 85.1 |

Cubic SVM | 83.7 | 64.4 | 70.8 | 80.6 | 83.8 |

Fine Gaussian SVM | 50.5 | 50.7 | 50.5 | 50.5 | 50.5 |

Medium Gaussian SVM | 85.4 | 69.3 | 73.6 | 80.8 | 83.9 |

Coarse Gaussian SVM | 82.1 | 68.7 | 72.1 | 76.9 | 79.6 |

Fine KNN | 69.2 | 56.4 | 59.9 | 63.8 | 65.2 |

Medium KNN | 77.8 | 61.8 | 65.4 | 69 | 74.7 |

Coarse KNN | 78.7 | 66.8 | 69.9 | 73.9 | 78 |

Cosine KNN | 78.5 | 63.3 | 67.4 | 70 | 74.1 |

Cubic KNN | 75.9 | 60.8 | 66.3 | 69.9 | 74.3 |

Weighted KNN | 77.9 | 62.6 | 66.8 | 69.4 | 74.2 |

Ensemble Boosted Trees | 82.3 | 64.5 | 68.9 | 74.9 | 80 |

Ensemble Bagged Trees | 77.5 | 65.6 | 67.7 | 70 | 72.8 |

Ensemble Subspace Discriminant | 71.8 | 68.3 | 73.4 | 81 | 85 |

Ensemble Subspace KNN | 71.1 | 62.3 | 64 | 69.1 | 69.7 |

Ensemble RUSBoosted Trees | 77 | 59.1 | 64.1 | 69 | 74.4 |

ECG Originals | EEG 8 Channels LE | ||||
---|---|---|---|---|---|

8 Channels | LE 3 | LE 5 | LE 10 | LE 15 | |

Fine Tree | 73.8 | 71.1 | 72 | 70.3 | 69.6 |

Medium Tree | 75.5 | 75.1 | 75.3 | 71.8 | 72.3 |

Coarse Tree | 75.8 | 75.1 | 74.3 | 74.1 | 75.2 |

Linear Discriminant | 77.2 | 79.1 | 81.6 | 83.2 | 81.1 |

Quadratic Discriminant | 63.4 | 77.8 | 76.9 | 77.9 | 77.2 |

Logistic Regression | 50.5 | 78.7 | 81.4 | 81.6 | 78.8 |

Naive Bayes | 81.7 | 76.5 | 76.6 | 77 | 77.1 |

Kernel Naive Bayes | 79.8 | 75.5 | 77.1 | 76.1 | 76.3 |

Linear SVM | 84.1 | 79.2 | 80.8 | 82.8 | 80.8 |

Quadratic SVM | 84.4 | 78.2 | 79.1 | 81.7 | 81.1 |

Cubic SVM | 83.7 | 72.9 | 77.7 | 79.5 | 80.4 |

Fine Gaussian SVM | 50.5 | 50.7 | 50.5 | 50.5 | 50.5 |

Medium Gaussian SVM | 85.4 | 79.2 | 80.3 | 81.1 | 81 |

Coarse Gaussian SVM | 82.1 | 79.2 | 80 | 81.4 | 79 |

Fine KNN | 69.2 | 66.1 | 69.1 | 67.6 | 68.2 |

Medium KNN | 77.8 | 73.1 | 74.4 | 75.6 | 76.1 |

Coarse KNN | 78.7 | 77.7 | 77.8 | 79.1 | 78.8 |

Cosine KNN | 78.5 | 74.4 | 74.8 | 75.5 | 76.4 |

Cubic KNN | 75.9 | 72.7 | 73.5 | 74.5 | 73.8 |

Weighted KNN | 77.9 | 73.5 | 74.3 | 76.5 | 76.8 |

Ensemble Boosted Trees | 82.3 | 77.7 | 78.3 | 78.3 | 78 |

Ensemble Bagged Trees | 77.5 | 76.8 | 74.4 | 72.9 | 76 |

Ensemble Subspace Discriminant | 71.8 | 79 | 80 | 82.5 | 81.7 |

Ensemble Subspace KNN | 71.1 | 73 | 75.2 | 74.8 | 73 |

Ensemble RUSBoosted Trees | 77 | 75.4 | 74.9 | 72.6 | 73.6 |

EEG Orig. | EEG 8 Channels | ||||
---|---|---|---|---|---|

8 Channels | LPP 3 | LPP 5 | LPP 10 | LPP 15 | |

Fine Tree | 73.8 | 53.2 | 50.8 | 50.7 | 49.8 |

Medium Tree | 75.5 | 53.8 | 49.8 | 51.2 | 52.2 |

Coarse Tree | 75.8 | 50.4 | 48.6 | 50.3 | 55.6 |

Linear Discriminant | 77.2 | 56.3 | 51.9 | 54.9 | 56.6 |

Quadratic Discriminant | 63.4 | 55 | 50.7 | 53.1 | 52.1 |

Logistic Regression | 50.5 | 56.3 | 52 | 54.8 | 57.5 |

Naïve Bayes | 81.7 | 53.2 | 54.2 | 51.3 | 57 |

Kernel Naïve Bayes | 79.8 | 53.8 | 51.2 | 50.2 | 55.6 |

Linear SVM | 84.1 | 55.7 | 49.5 | 54 | 59.4 |

Quadratic SVM | 84.4 | 56.2 | 52.5 | 52.7 | 58.8 |

Cubic SVM | 83.7 | 52 | 54 | 52.1 | 54.9 |

Fine Gaussian SVM | 50.5 | 51.8 | 50.5 | 53.5 | 54.5 |

Medium Gaussian SVM | 85.4 | 52.5 | 50 | 51 | 55.1 |

Coarce Gaussian SVM | 82.1 | 52.9 | 49.2 | 52.9 | 58.8 |

Fine KNN | 69.2 | 49.8 | 48.9 | 52.1 | 53.1 |

Medium KNN | 77.8 | 51.3 | 50.3 | 49.7 | 54.2 |

Coarse KNN | 78.7 | 51.7 | 48.9 | 50.8 | 53.7 |

Cosine KNN | 78.5 | 49.6 | 48.5 | 52.7 | 56.4 |

Cubic KNN | 75.9 | 49.4 | 49.7 | 50.6 | 52.7 |

Weighted KNN | 77.9 | 51.3 | 49.9 | 51.8 | 57.3 |

Ensemble Boosted Trees | 82.3 | 51 | 48.3 | 51.7 | 54.9 |

Ensemble Bagged Trees | 77.5 | 51.3 | 47.9 | 50.8 | 52.8 |

Ensemble Subspace Discriminant | 71.8 | 55 | 51 | 53.5 | 58.4 |

Ensemble Subspace KNN | 71.1 | 53 | 48.5 | 51.3 | 53.2 |

Ensemble RUSBoosted Trees | 77 | 54 | 48.8 | 51.9 | 52.1 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Fira, M.; Costin, H.-N.; Goraș, L.
On the Classification of ECG and EEG Signals with Various Degrees of Dimensionality Reduction. *Biosensors* **2021**, *11*, 161.
https://doi.org/10.3390/bios11050161

**AMA Style**

Fira M, Costin H-N, Goraș L.
On the Classification of ECG and EEG Signals with Various Degrees of Dimensionality Reduction. *Biosensors*. 2021; 11(5):161.
https://doi.org/10.3390/bios11050161

**Chicago/Turabian Style**

Fira, Monica, Hariton-Nicolae Costin, and Liviu Goraș.
2021. "On the Classification of ECG and EEG Signals with Various Degrees of Dimensionality Reduction" *Biosensors* 11, no. 5: 161.
https://doi.org/10.3390/bios11050161