Visualization for Data Science using Python.

Explore exploratory data analysis with the iris dataset using Matplotlib and Seaborn, identifying features and the label, and understanding data types, datasets, and basic statistics for a classification problem.

Learn to set up python data tools, import pandas and plotting libraries, load the iris dataset from Kaggle, and note its balanced 150x5 structure with setosa, versicolor, virginica.

Explore 2d scatter plots with iris sepal length and width using matplotlib. Learn to create single and multi-plot figures with subplots, labels, and correct scatter syntax.

Explore two dimensional scatter plots in Python with matplotlib and seaborn, color-coding iris species to reveal separations between Setosa, Versicolor, and Virginica.

Explore three-dimensional scatter plots and how adding a third feature improves data separability in visualizations. Understand that machine learning often handles many dimensions beyond what we can visualize.

Explore pair plots to view all feature-pair relationships for four features, revealing six plots with diagonal distributions and showing that petal length and petal width best separate setosa, versicolor, virginica.

Explore code snippets illustrating histogram, pdf, and cdf while transforming scatter plots into a 1d view by plotting petal length on the x axis with zero y, using color to separate species.

Learn how histograms reveal one-dimensional data distributions and how PDFs and CDFs express and accumulate probability through area under the curve.

Explore histograms, pdfs, and cdfs as tools for understanding 1d features, then compare distribution plots and hist plots with cd plots (kernel density estimation) to distinguish species by petal length.

Explore how bin width shapes histograms and distribution plots, showing how smaller bins reveal more detail while larger bins smooth the curve, using sepal width as an example.

Explore histograms and probability density functions, including the normal distribution, and learn how the area under the PDF curve equals one and represents probability between intervals.

Demonstrate drawing a cumulative distribution function from code, using a kde-based pdf plot, and compare petal and sepal lengths and widths.

Explore Python code snippets to compute mean, variance, standard deviation, and median-based measures with numpy, including percentiles, quantiles, interquartile range, and median absolute deviation, using iris data as examples.

Learn how box plots summarize univariate data: median and 25th/75th percentiles, interquartile range, and 1.5 times IQR whiskers with outliers, compared to other plots.

Explore violin plot as a fusion of box plots and probability density functions to reveal univariate data distributions. Learn related plots like histograms and 2D/3D scatter plots.

Explore the Haberman survival dataset through exploratory data analysis using Python libraries like Matplotlib and Seaborn, learning data loading, feature interpretation (age, year of operation, nodes) and survival status.

Explore data overview using describe to view counts, means, medians, and standard deviations, identify missing values, and assess class balance with value_counts for modeling implications.

Explore univariate analysis of age, year, and nodes using histograms and distribution plots; find overlap between survival and non-survival, with nodes below four indicating survival probability, none alone predicts outcomes.

Examine bivariate analysis with age and nodes to predict survival using scatter and pair plots; identify limitations of two-dimensional plots and the need for more complex models.

Recall solving unknowns in a system of linear equations through a bank robbery chase example, and extend to vectors, matrices, and linear models used in data science.

Linear algebra underpins math foundations and pillars such as probability, statistics, and calculus; mastery enables data analysts and engineers to solve optimization, dimensionality reduction (PCA, SVD), and machine learning tasks.

Explore vectors in 1D, 2D, and 3D, and distinguish scalars from vectors by magnitude and direction, using two- and three-dimensional visualization to grasp higher-dimensional data.

Explore how a point is defined by coordinates across dimensions, from 2D to n-dimensional, and apply the pythagorean theorem to compute distances between points or from the origin.

Understand vectors as magnitude and direction that represent points on the x–y plane, and learn to perform operations directly on expanded form x i + y j to simplify results.

Understand row and column vectors, their shapes and dimensions, and how compatible operations like vector multiplication rely on matching rows and columns in data, matrices, and tensors.

Explore the transpose of a matrix, converting rows to columns and reversing the shape, with examples, and preview the special relationship between a matrix and its transpose.

Learn to compute vector magnitude with the L2 norm, or Euclidean distance, and obtain a unit vector by dividing by magnitude, with examples (1,1) -> (1/√2,1/√2) and (3,4) -> (3/5,4/5).

Perform element-wise vector addition and subtraction, ensuring equal length and consistent row or column formats. These operations yield a new vector with magnitude and direction that generalize to n dimensions.

Explore the inverse of a vector, defined as a vector with the same magnitude but opposite direction, demonstrated with (2,3) and (-2,-3), and its role in yielding the zero vector.

Explore the dot product of vectors and its compatibility—columns of the first equal rows of the second—widely used in data analysis and machine learning, unlike the cross product.

Understand how multiplying a vector by a scalar scales its magnitude while preserving its direction, with examples of component-wise scaling and the effect of negative scalars.

Explore the distributive properties of vectors and scalars and define the angle between two vectors, theta, with x-y axis scenarios and the smallest angle.

Compute the angle between two vectors using the dot product and magnitudes, guided by cos theta = (v1 dot v2)/(||v1|| ||v2||). The example v1=(1,0), v2=(0,1) gives theta=90 degrees.

Explore orthogonal vectors, defined as perpendicular vectors with a 90-degree angle and a zero dot product, illustrated through examples of v1 and v2 in various placements.

Explore orthonormal vectors: orthogonal vectors with unit magnitude, how to convert vectors to unit vectors by dividing by their magnitude, and the role of dot product in measuring angles.

Present the equation of a line as a dot product w^T x + w0 = 0, generalizing from y=mx+c to n dimensions for linear and logistic regression.

Demonstrate how a line is expressed as w^T x + w0 = 0, show when it passes through origin, and connect this to linear algebra in machine learning.

Explain that a line through the origin is perpendicular to its vector w, with w^T x = 0 and a point on the line like (1,1) for x−y=0.

Learn that a line is defined by W^T x = 0, with W perpendicular to every point on the line, and that angle depends only on direction, not magnitude.

Explore the projection of a vector onto axes and arbitrary lines using magnitude, cosine of the angle, and coordinate geometry, with x1 and x2 coordinates.

Learn to compute the perpendicular distance from a point to a line in vector form using dot products and projections, deriving the distance as (W^T P + w0)/||W||.

Determine which side of a line a point lies on using the signed distance from W^T x = 0 and W^T x + w0 = 0 with circles and dimensions.

Explore matrices as rectangular 2d arrays of numbers, distinguish vectors from matrices, and learn matrix size notation (m x n) and indexing like a11, a12.

Explore matrix addition, subtraction, and the Hadamard product, then master matrix multiplication via the dot product with shape compatibility, illustrated through row and column operations and practical linear algebra applications.

Explore core matrix concepts, including transpose, square and diagonal matrices, symmetry with A equals A^T, and the identity matrix, plus how dot products and scalar multiplication work.

Learn that an orthonormal matrix has every row and column as unit vectors, mutually perpendicular, with a^T a = I; illustrated by identity and diagonal examples.

Learn to compute a matrix inverse by using the minor and cofactor of elements, and calculate determinants via expansion and the ad-bc rule.

Compute the inverse of a square matrix by determinant, cofactors, and adjoint, then divide the adjoint by the determinant; for orthogonal matrices, A^T equals A^{-1}.

Explain dimensionality and why reducing it aids visualization, and show how data sit as n points by d features, using column vectors and x versus x transpose.

Learn data normalization and standardization as essential preprocessing, addressing dirty real-world data. Apply min max normalization, featurewise scaling, and compute the mean vector for a data matrix.

Explore data normalization and data standardization: min-max normalization scales data to 0–1, while standardization centers features at zero with unit variance, often applied per column.

Compute variance and covariance between data sets, then construct a d-by-d covariance matrix from a data matrix by subtracting column means and applying matrix multiplication.

Recognize the covariance matrix as square and symmetric, with Sij = Sji, arising from column interactions f_i^T f_j; standardized data with mu = 0 reduces to X^T X over n-1.

Explore the geometric intuition of dimensionality reduction with PCA, derive its formula, and implement it in Python to visualize data using the axis with maximum variance.

Explore how PCA selects a unit direction mu to maximize the variance of standardized data projections, using x_i dot mu, with mu^T mu = 1.

Explore the mathematical formulation of PCA by projecting data onto a unit vector mu and maximizing the squared projection (1/N) sum (x_i · mu)^2, with mu^T mu = 1.

Learn to formulate PCA as a constrained optimization, derive the covariance eigenproblem S mu = lambda mu, and project data onto top eigenvectors for visualization.

Explore failure cases of PCA as a dimensionality reduction tool for visualization, including when variances are similar, projections merge distinct clusters, or sinusoidal data lose structure.

Connect Colab to Google Drive to store and access data for visualization projects, mount drive, and read MNIST train CSV with pandas, numpy, and matplotlib in Colab.

Explore the MNIST dataset of handwritten digits 0–9, represented as 28 by 28 pixel images flattened into 784 features, with labels for digit classification and pixel value ranges 0–255.

Visualize a MNIST digit by reshaping a 784-length row to a 28 by 28 image and displaying it in grayscale with imshow; then outline PCA via covariance, standardization, and eigenvectors.

Standardize MNIST data with mu and sigma, then project to two dimensions using PCA by computing eigenvalues and eigenvectors. Visualize the two-dimensional coordinates by digit labels with Seaborn scatter plots.

Apply Python and Sklearn to perform PCA on standardized data, using decomposition with n_components=2, fit_transform, yielding two principal components for visualization of MNIST data.