DS-for-LA/bibliography.md

Bibliography

Mathematics

• Gene H. Golub and Charles F. Van Loan, Matrix Computations. John Hopkins University Press, 2013.
• Mark H. Holmes, Introduction to scientific computing and data analysis. Vol. 13. Springer Nature, 2023.
• David C. Lay, Steven R. Lay, and Judith J. McDonald, Linear Algebra and Its Applications, Pearson, 2021. ISBN 013588280X.
• https://ubcmath.github.io/MATH307/index.html
• https://eecs16b.org/notes/fa23/note16.pdf
• https://en.wikipedia.org/wiki/Low-rank_approximation
• https://www-labs.iro.umontreal.ca/~grabus/courses/ift6760_W20_files/lecture-5.pdf
• https://www.statology.org/polynomial-regression-python/
• https://en.wikipedia.org/wiki/Mean_squared_error
• https://en.wikipedia.org/wiki/Peak_signal-to-noise_ratio

Modelling

• https://www.geeksforgeeks.org/machine-learning/what-is-ridge-regression/
• https://www.geeksforgeeks.org/machine-learning/what-is-lasso-regression/
• https://www.geeksforgeeks.org/machine-learning/principal-component-regression-pcr/
• https://www.geeksforgeeks.org/machine-learning/gradient-descent-algorithm-and-its-variants/
• https://www.geeksforgeeks.org/machine-learning/decision-tree/
• https://www.geeksforgeeks.org/machine-learning/random-forest-algorithm-in-machine-learning/

Python

Numpy (https://numpy.org/doc/stable/index.html)

• numpy basics: https://numpy.org/doc/stable/user/absolute_beginners.html
• numpy.array: https://numpy.org/doc/stable/reference/generated/numpy.array.html
• numpy.hstack: https://numpy.org/doc/stable/reference/generated/numpy.hstack.html (Stack arrays in sequence horizontally (column wise).)
• numpy.column_stack: https://numpy.org/doc/stable/reference/generated/numpy.column_stack.html (Stack 1-D arrays as columns into a 2-D array.)
• numpy.shape: https://numpy.org/doc/stable/reference/generated/numpy.shape.html (Return the shape of an array.)
• numpy.polyfit: https://numpy.org/doc/stable/reference/generated/numpy.polyfit.html (Least squares polynomial fit.)
• numpy.mean: https://numpy.org/doc/stable/reference/generated/numpy.mean.html (Compute the arithmetic mean along the specified axis.)
• numpy.poly1d: https://numpy.org/doc/stable/reference/generated/numpy.poly1d.html (A one-dimensional polynomial class.)
• numpy.set_printoptions: https://numpy.org/doc/stable/reference/generated/numpy.set_printoptions.html (These options determine the way floating point numbers, arrays and other NumPy objects are displayed.)
• numpy.finfo: https://numpy.org/doc/stable/reference/generated/numpy.finfo.html (Machine limits for floating point types.)
• numpy.logspace: https://numpy.org/doc/stable/reference/generated/numpy.logspace.html (Return numbers spaced evenly on a log scale.)
• numpy.sum: https://numpy.org/doc/stable/reference/generated/numpy.sum.html (Sum of array elements over a given axis.)
• numpy.abs: https://numpy.org/doc/stable/reference/generated/numpy.absolute.html (Calculate the absolute value element-wise.)
• numpy.ndarray.T: https://numpy.org/doc/stable/reference/generated/numpy.ndarray.T.html (View of the transposed array.)
• numpy.ones: https://numpy.org/doc/stable/reference/generated/numpy.ones.html (Return a new array of given shape and type, filled with ones.)
• numpy.zeros: https://numpy.org/doc/stable/reference/generated/numpy.zeros.html (Return a new array of given shape and type, filled with zeros.)
• numpy.diag: https://numpy.org/doc/stable/reference/generated/numpy.diag.html (Extract a diagonal or construct a diagonal array.)
• numpy.cumsum: https://numpy.org/doc/stable/reference/generated/numpy.cumsum.html (Return the cumulative sum of the elements along a given axis.)
• numpy.meshgrid: https://numpy.org/doc/stable/reference/generated/numpy.meshgrid.html (Return a tuple of coordinate matrices from coordinate vectors.)
• numpy.linspace: https://numpy.org/doc/stable/reference/generated/numpy.linspace.html (Return evenly spaced numbers over a specified interval.)
• numpy.ravel: https://numpy.org/doc/stable/reference/generated/numpy.ravel.html (Return a contiguous flattened array.)
• numpy.vstack: https://numpy.org/doc/stable/reference/generated/numpy.vstack.html (Stack arrays in sequence vertically (row wise).)

numpy.random (https://numpy.org/doc/stable/reference/random/index.html)

• numpy.random.seed: https://numpy.org/doc/stable/reference/random/generated/numpy.random.seed.html (Reseed the singleton RandomState instance.)
• numpy.random.normal: https://numpy.org/doc/stable/reference/random/generated/numpy.random.normal.html (Draw random samples from a normal (Gaussian) distribution.)
• numpy.random.default_rng: https://numpy.org/doc/stable/reference/random/generator.html (Construct a new Generator with the default BitGenerator (PCG64).)
• numpy.random.uniform: https://numpy.org/doc/stable/reference/random/generated/numpy.random.uniform.html (Draw samples from a uniform distribution.)

numpy.linalg (https://numpy.org/doc/stable/reference/routines.linalg.html)

• numpy.linalg.qr: https://numpy.org/doc/stable/reference/generated/numpy.linalg.qr.html (Compute the qr factorization of a matrix.)
• numpy.linalg.svd: https://numpy.org/doc/stable/reference/generated/numpy.linalg.svd.html (Singular Value Decomposition.)
• numpy.linalg.solve: https://numpy.org/doc/stable/reference/generated/numpy.linalg.solve.html (Solve a linear matrix equation, or system of linear scalar equations.)
• numpy.linalg.lstsq: https://numpy.org/doc/stable/reference/generated/numpy.linalg.lstsq.html (Return the least-squares solution to a linear matrix equation.)
• numpy.linalg.norm: https://numpy.org/doc/stable/reference/generated/numpy.linalg.norm.html (Matrix or vector norm.)
• numpy.linalg.pinv: https://numpy.org/doc/stable/reference/generated/numpy.linalg.pinv.html (Compute the (Moore-Penrose) pseudo-inverse of a matrix.)
• numpy.linalg.cond: https://numpy.org/doc/stable/reference/generated/numpy.linalg.cond.html (Compute the condition number of a matrix.)

Matplotlib (https://matplotlib.org/stable/users/getting_started/)

• matplotlib.pyplot: https://matplotlib.org/stable/api/pyplot_summary.html
• matplotlib.figure: https://matplotlib.org/stable/api/figure_api.html (Implements the following classes: Figure and SubFigure)
• mpl_toolkits.mplot3d.axes3d.Axes3D.plot_surface: https://matplotlib.org/stable/api/_as_gen/mpl_toolkits.mplot3d.axes3d.Axes3D.plot_surface.html#mpl_toolkits.mplot3d.axes3d.Axes3D.plot_surface (Create a surface plot.)
• colormaps: https://matplotlib.org/stable/users/explain/colors/colormaps.html

matplotlib.pyplot

• matplotlib.pyplot.plot: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.plot.html (Plot y versus x as lines and/or markers.)
• matplotlib.pyplot.quiver: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.quiver.html (Plot a 2D field of arrows.)
• matplotlib.pyplot.tight_layout: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.tight_layout.html (Adjust the padding between and around subplots.)
• matplotlib.pyplot.legend: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.legend.html (Place a legend on the Axes.)
• matplotlib.pyplot.show: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.show.html (Display all open figures.)
• matplotlib.pyplot.xlabel: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.xlabel.html (Set the label for the x-axis.)
• matplotlib.pyplot.ylabel: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.ylabel.html (Set the label for the y-axis.)
• matplotlib.pyplot.title: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.title.html (Set a title for the Axes.)
• matplotlib.pyplot.scatter: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.scatter.html (A scatter plot of y vs. x with varying marker size and/or color.)
• matplotlib.pyplot.imshow: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.imshow.html (Display data as an image, i.e., on a 2D regular raster.)
• matplotlib.pyplot.axis: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axis.html (Convenience method to get or set some axis properties.)
• matplotlib.pyplot.semilogy: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.semilogy.html (Make a plot with log scaling on the y-axis.)
• matplotlib.pyplot.subplots: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.subplots.html (Create a figure and a set of subplots.)
• matplotlib.pyplot.contour: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contour.html (Plot contour lines.)
• matplotlib.pyplot.contourf: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.contourf.html (Plot filled contours.)
• matplotlib.pyplot.axhline: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axhline.html (Add a horizontal line spanning the whole or fraction of the Axes.)
• matplotlib.pyplot.axvline: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.axvline.html (Add a vertical line spanning the whole or fraction of the Axes.)
• matplotlib.pyplot.gca: https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.gca.html (Get the current Axes.)

matplotlib.figure

• matplotlib.figure.Figure.add_subplot : https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.add_subplot.html (Add an Axes to the figure as part of a subplot arrangement.)]

matplotlib.axes

• matplotlib.axes.Axes.set_title: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_title.html (Set a title for the Axes.)
• matplotlib.axes.Axes.imshow: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.imshow.html (Display data as an image, i.e., on a 2D regular raster.)
• matplotlib.axes.Axes.axis: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.axis.html (Convenience method to get or set some axis properties.)
• matplotlib.axes.Axes.text: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.text.html (Add text to the Axes.)
• matplotlib.axes.Axes.set_xlabel: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_xlabel.html (Set the label for the x-axis.)
• matplotlib.axes.Axes.set_ylabel: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_ylabel.html (Set the label for the y-axis.)
• matplotlib.axes.Axes.set_xlim: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_xlim.html (Set the x-axis view limits.)
• matplotlib.axes.Axes.set_aspect: https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.set_aspect.html (Set the aspect ratio of the Axes scaling, i.e. y/x-scale.)

Scatter plots with line of best fit

• https://stackoverflow.com/questions/37234163/how-to-add-a-line-of-best-fit-to-scatter-plot
• https://www.statology.org/line-of-best-fit-python/
• https://stackoverflow.com/questions/6148207/linear-regression-with-matplotlib-numpy

Pandas

• pandas basics: https://pandas.pydata.org/docs/user_guide/index.html
• pandas.DataFrame: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.html (Two-dimensional, size-mutable, potentially heterogeneous tabular data.)

pandas.DataFrame

• pandas.DataFrame.describe: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.describe.html (Generate descriptive statistics.)
• pandas.DataFrame.corr: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.corr.html (Compute pairwise correlation of columns, excluding NA/null values.)
• pandas.DataFrame.to_numpy: https://pandas.pydata.org/docs/reference/api/pandas.DataFrame.to_numpy.html (Convert the DataFrame to a NumPy array.)
• pandas.DataFrame.plot: https://pandas.pydata.org/pandas-docs/stable/reference/api/pandas.DataFrame.plot.html (Make plots of Series or DataFrame.)

scikit-learn

• sklearn basis: https://scikit-learn.org/stable/getting_started.html#fitting-and-predicting-estimator-basics
• sklearn.datasets.fetch_california_housing: https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_california_housing.html (Load the California housing dataset (regression).)
• sklearn.tree.DecisionTreeRegressor: https://scikit-learn.org/stable/modules/generated/sklearn.tree.DecisionTreeRegressor.html (A decision tree regressor.)
• sklearn.ensemble.RandomForestRegressor: https://scikit-learn.org/stable/modules/generated/sklearn.ensemble.RandomForestRegressor.html (A random forest regressor.)
• sklearn.pipeline.make_pipeline: https://scikit-learn.org/stable/modules/generated/sklearn.pipeline.make_pipeline.html (Construct a Pipeline from the given estimators.)
• sklearn.decomposition.PCA: https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html (Principal component analysis (PCA).)

sklearn.preprocessing

• sklearn.preprocessing.PolynomialFeatures: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.PolynomialFeatures.html (Generate polynomial and interaction features.)
• sklearn.preprocessing: https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.StandardScaler.html (Standardize features by removing the mean and scaling to unit variance.)

sklearn.linear_model

• sklearn.linear_model.LinearRegression: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html (Ordinary least squares Linear Regression.)
• sklearn.linear_model.Ridge: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Ridge.html (Linear least squares with l2 regularization.)
• sklearn.linear_model.Lasso: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.Lasso.html (Linear Model trained with L1 prior as regularizer (aka the Lasso).)
• sklearn.linear_model.LassoCV: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LassoCV.html (Lasso linear model with iterative fitting along a regularization path.)
• sklearn.linear_model.SGDRegressor: https://scikit-learn.org/stable/modules/generated/sklearn.linear_model.SGDRegressor.html (Linear model fitted by minimizing a regularized empirical loss with SGD.)

sklearn.model_selection

• sklearn.model_selection.train_test_split: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.train_test_split.html (Split arrays or matrices into random train and test subsets.)
• sklearn.model_selection.cross_val_score: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.cross_val_score.html (Evaluate a score by cross-validation.)
• sklearn.model_selection.KFold: https://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html (K-Fold cross-validator.)

sklearn.metrics

• sklearn.metrics.mean_squared_error: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.mean_squared_error.html (Mean squared error regression loss.)
• sklearn.metrics.r2_score: https://scikit-learn.org/stable/modules/generated/sklearn.metrics.r2_score.html (R^2 (coefficient of determination) regression score function.)

Pillow

• PIL basics: https://pillow.readthedocs.io/en/stable/
• PIL.Image: https://pillow.readthedocs.io/en/stable/reference/Image.html

Math

• Math basics: https://docs.python.org/3/library/math.html
• math.ceil: https://docs.python.org/3/library/math.html#math.ceil (Return the ceiling of x, the smallest integer greater than or equal to x)