Machine Learning & Signals Learning
Part IV Appendix
A Notation
Numbers and indexing
| \(a\) | Scalar | |
| \(\ba \) | Vector | |
| \(a_i\) | Element \(i\) of a vector \(a\), indexing starting at 1 | |
| \(\mathbf {A}\) | Matrix | |
| \(a_{ij}\) | Element \(i,j\) of a matrix \(\mathbf {A}\), indexing starting at 1 | |
| \(\real \) | Real numbers domain | |
| \(\real ^D\) | \(D\)-dimensional vector | |
| \(\real ^{D_1\times D_2}\) | matrix of a dimension \(D_1\times D_2\) | |
| \(\bI \) | Identity matrix | |
| \(\bOne \) | Vector/matrix of ones | |
| \(\bZero \) | Vector/matrix of zeros |
Datasets
| \(L\) | Model complexity | |
| \(N\) | Number of features | |
| \(M\) | Number of entries in the dataset | |
| \(K\) | Number of classes | |
| \(\bw \) or \(w_i\) | Model parameters (vector form) | |
| \(f(\cdot ;\bw )\) | Model | |
| \(h(\bx )\) or \(h(x)\) | True unknown function | |
| \(x_{ij}\) | Single data value | |
| \(\bx _i\) | Single data vector (sample \(i\)); \(\bx _i^T\) is the \(i\)-th row of \(\bX \) | |
| \(\btx _j\) | \(j\)-th column (feature) of \(\bX \) | |
| \(\bX \) | Data matrix | |
| \(\by \) | Target vector for the data in \(\bX \) | |
| \(\hat {\by }\) | Prediction vector of \(\by \) | |
| \(y_i\) | Target value | |
| \(\hat {y}_i\) | Predicted target value | |
| \(\loss (\by ,\hat {\by })\) or \(\mathcal {L}(y_i,\hat {y}_i)\) | Loss function | |
| \(\lambda \) | Regularization parameter | |
| \(\ba ^{[k]}\) | Activation of layer \(k\) | |
| \(\bz ^{[k]}\) | Output of layer \(k\) | |
| \(g_k(\cdot )\) | Activation function of layer \(k\) | |
| \(\bth \) or \(\theta _i\) | Model parameters (general form) | |
| \(\balpha \) | Kernel/dual coefficients vector | |
| \(\be \) | Error/residual vector | |
| \(\bepsilon \) or \(\epsilon _i\) | Noise vector/term | |
| \(\bn \) | Noise vector (signal processing) | |
| \(\bh \) | Impulse response / filter coefficients | |
| \(\bP \) | Projection matrix | |
| \(\bK \) | Kernel matrix | |
| \(\bR \) | Autocorrelation matrix | |
| \(\phi (\cdot )\) | Feature mapping / basis function | |
| \(\alpha \) | Learning rate (gradient descent step size) |
Statistics
| \(x\) | Sample set | |
| \(\bar x\) | Sample mean | |
| \(s_x^2\) | Sample variance (biased or unbiased) | |
| \(s_x\) | Sample std (biased or unbiased) | |
| \(s_{xy}\) | Sample covariance (biased or unbiased) | |
| \(r_{xy}\) | Sample correlation coefficient | |
| \(\mu \) | Population mean | |
| \(\sigma ^2\) | Population variance | |
| \(\sigma \) | Population standard deviation | |
| \(\E [\cdot ]\) | Expectation operator | |
| \(\Var [\cdot ]\) | Variance operator | |
| \(\Cov [\cdot ]\) | Covariance operator |
Signals
| \(\omega \) | Angular frequency (discrete) | |
| \(\theta \) | Phase angle | |
| \(A\) | Amplitude | |
| \(F\) | Frequency [Hz] | |
| \(F_s\) | Sampling frequency | |
| \(T\) | Period [sec] |
Bibliography
-
[1] Tomas Andersson. Selected topics in frequency estimation. PhD thesis, KTH Royal Institute of Technology, 2003.
-
[2] Peter J Bickel and Kjell A Doksum. An analysis of transformations revisited. Journal of the American Statistical Association, 76(374):296–311, 1981.
-
[3] Alexei Botchkarev. Performance metrics (error measures) in machine learning regression, forecasting and prognostics: Properties and typology. arXiv preprint arXiv:1809.03006, 2018. https://arxiv.org/abs/1809.03006.
-
[4] Dima Bykhovsky. Experimental lognormal modeling of harmonics power of switched-mode power supplies. Energies, 15(2), 2022.
-
[5] Dima Bykhovsky and Asaf Cohen. Electrical network frequency (ENF) maximum-likelihood estimation via a multitone harmonic model. IEEE Transactions on Information Forensics and Security, 8(5):744–753, 2013.
-
[6] Lorenzo Ciampiconi, Adam Elwood, Marco Leonardi, Ashraf Mohamed, and Alessandro Rozza. A survey and taxonomy of loss functions in machine learning. arXiv preprint arXiv:2301.05579, 2023.
-
[7] Angus Dempster, François Petitjean, and Geoffrey I Webb. Rocket: exceptionally fast and accurate time series classification using random convolutional kernels. Data Mining and Knowledge Discovery, 34(5):1454–1495, 2020.
-
[8] Angus Dempster, Daniel F Schmidt, and Geoffrey I Webb. Minirocket: A very fast (almost) deterministic transform for time series classification. In Proceedings of the 27th ACM SIGKDD conference on knowledge discovery & data mining, pages 248–257, 2021.
-
[9] Bo Diao, Kun Wen, Jian Chen, Yueping Liu, Zilin Yuan, Chao Han, Jiahui Chen, Yuxian Pan, Li Chen, Yunjie Dan, Jing Wang, Yongwen Chen, Guohong Deng, Hongwei Zhou, and Yuzhang Wu. Diagnosis of acute respiratory syndrome coronavirus 2 infection by detection of nucleocapsid protein. medRxiv, 2020.
-
[10] Sharon Gannot, Zheng-Hua Tan, Martin Haardt, Nancy F Chen, Hoi-To Wai, Ivan Tashev, Walter Kellermann, and Justin Dauwels. Data science education: The signal processing perspective [sp education]. IEEE Signal Processing Magazine, 40(7):89–93, 2023.
-
[11] Toni Giorgino. Computing and visualizing dynamic time warping alignments in r: the dtw package. Journal of statistical Software, 31:1–24, 2009.
-
[12] Monson H Hayes. Statistical Digital Signal Processing and Modeling. John Wiley & Sons, 1996.
-
[13] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Delving deep into rectifiers: Surpassing human-level performance on imagenet classification. In Proceedings of the IEEE international conference on computer vision, pages 1026–1034, 2015.
-
[14] Steven M. Kay. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory. Prentice Hall, 1993.
-
[15] Nitish Shirish Keskar, Dheevatsa Mudigere, Jorge Nocedal, Mikhail Smelyanskiy, and Ping Tak Peter Tang. On large-batch training for deep learning: Generalization gap and sharp minima. arXiv preprint arXiv:1609.04836, 2017.
-
[16] Jason Lines, Sarah Taylor, and Anthony Bagnall. Hive-cote: The hierarchical vote collective of transformation-based ensembles for time series classification. In 2016 IEEE 16th international conference on data mining (ICDM), pages 1041–1046. IEEE, 2016.
-
[17] Boaz Porat. Digital processing of random signals: theory and methods. Courier Dover Publications, 2008.
-
[18] Pavel Senin and Sergey Malinchik. Sax-vsm: Interpretable time series classification using sax and vector space model. In 2013 IEEE 13th international conference on data mining, pages 1175–1180. IEEE, 2013.
-
[19] Albert Wong, Athena Nguyen, Eugene Li, Yew-Wei Lim, Mike Wu, and Shuk Wai Tsang. Combining classifiers for improved accuracies -voting and linearly weighted algorithms, Feb 2026.
-
[20] Lexiang Ye and Eamonn Keogh. Time series shapelets: a new primitive for data mining. In Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining, pages 947–956, 2009.