🧷Intro to Scientific Computing Unit 12 – Data Analysis & Visualization

What's This Unit About?

• Introduces fundamental concepts and techniques for analyzing and visualizing data using computational tools
• Covers the entire data analysis pipeline from data acquisition and cleaning to visualization and interpretation
• Emphasizes hands-on practice with real-world datasets to develop practical skills
• Explores various types of data including numerical, categorical, time series, and geospatial data
• Introduces essential libraries in Python for data manipulation (NumPy, Pandas), visualization (Matplotlib, Seaborn), and statistical analysis (SciPy, Statsmodels)
  • NumPy provides efficient array operations and mathematical functions
  • Pandas simplifies data loading, cleaning, and transformation
  • Matplotlib allows creating a wide range of static, animated, and interactive visualizations
• Discusses the importance of data visualization in communicating insights and telling compelling stories with data
• Highlights the role of statistical analysis in quantifying relationships, testing hypotheses, and making data-driven decisions

Key Concepts to Grasp

• Data types and structures (arrays, dataframes, series)
  • Understanding the differences and use cases for each
• Data preprocessing techniques (cleaning, filtering, transforming)
  • Handling missing values, outliers, and inconsistencies
  • Reshaping data (melting, pivoting, grouping)
• Exploratory data analysis (EDA)
  • Summarizing and visualizing key characteristics of the data
  • Identifying patterns, trends, and relationships
• Visual encoding principles (position, size, color, shape)
  • Choosing appropriate visual encodings based on data types and goals
• Chart types and their use cases (scatter plots, line charts, bar charts, heatmaps)
• Customizing and styling visualizations
  • Adjusting colors, labels, titles, and legends
  • Creating subplots and multi-panel figures
• Statistical concepts (distributions, correlation, regression, hypothesis testing)
  • Understanding when and how to apply different statistical techniques

Essential Tools and Libraries

• Jupyter Notebook/Lab
  • Interactive environment for writing and executing code, visualizing results, and documenting analysis
• NumPy
  • Fundamental package for scientific computing in Python
  • Provides efficient array operations and mathematical functions
• Pandas
  • Powerful library for data manipulation and analysis
  • Offers data structures like DataFrames and Series for handling structured data
• Matplotlib
  • Versatile plotting library for creating static, animated, and interactive visualizations
  • Provides low-level control over every aspect of the figure
• Seaborn
  • Statistical data visualization library based on Matplotlib
  • Offers high-level interface for creating informative and attractive plots
• SciPy
  • Library for scientific and technical computing
  • Includes modules for optimization, linear algebra, integration, and statistics
• Statsmodels
  • Package that provides tools for statistical modeling and econometrics
  • Allows estimating various statistical models and performing statistical tests

Data Wrangling Techniques

• Loading data from various sources (CSV, Excel, SQL databases, APIs)
• Cleaning and preprocessing data
  • Handling missing values (dropna, fillna)
  • Dealing with outliers and anomalies
  • Converting data types (astype)
• Filtering and selecting data (boolean indexing, loc, iloc)
• Transforming data
  • Applying functions to columns or rows (apply, applymap)
  • Creating new columns based on existing ones
• Reshaping data
  • Melting and pivoting dataframes for different analysis perspectives
  • Grouping and aggregating data (groupby, agg)
• Merging and concatenating datasets (merge, concat)
• Handling time series data
  • Resampling and rolling window operations
  • Time-based indexing and slicing

Visualization Basics

• Importing Matplotlib and Seaborn
• Creating basic plots (line, scatter, bar, histogram)
  • Using Pandas plotting methods for quick exploration
• Customizing plot elements
  • Setting titles, labels, and legends
  • Adjusting colors, markers, and linestyles
• Saving plots to files (png, pdf, svg)
• Plotting with Seaborn
  • Using built-in themes and color palettes
  • Creating statistical plots (distribution plots, regression plots)
• Faceting and conditioning plots
  • Creating subplots based on categorical variables (FacetGrid)
• Customizing Seaborn plot aesthetics
  • Controlling figure size, aspect ratio, and style

Advanced Plotting Methods

• Visualizing multidimensional data
  • Scatter plot matrices (pairplot)
  • Parallel coordinates plots
• Plotting geospatial data
  • Using Matplotlib Basemap toolkit
  • Creating choropleth maps
• Creating interactive visualizations
  • Linking plots with widgets (ipywidgets)
  • Using Plotly for interactive web-based plots
• Animating plots
  • Creating dynamic visualizations with Matplotlib animation
• Customizing colormaps and color scales
  • Choosing appropriate colormaps based on data and purpose
  • Defining custom colormaps
• Creating complex layouts
  • Arranging multiple subplots using GridSpec
  • Adding insets, annotations, and custom shapes

Statistical Analysis Crash Course

• Descriptive statistics
  • Measures of central tendency (mean, median, mode)
  • Measures of dispersion (variance, standard deviation)
• Probability distributions
  • Understanding common distributions (normal, binomial, Poisson)
  • Plotting and fitting distributions to data
• Correlation and covariance
  • Measuring the relationship between variables
  • Visualizing correlations using heatmaps
• Linear regression
  • Fitting linear models to data
  • Interpreting coefficients and assessing model performance
• Hypothesis testing
  • Formulating null and alternative hypotheses
  • Conducting common tests (t-test, ANOVA, chi-square)
• Handling outliers and anomalies
  • Detecting outliers using statistical methods (z-score, IQR)
  • Strategies for dealing with outliers (removal, transformation, robust methods)

Real-World Applications

• Exploratory data analysis of real-world datasets
  • Analyzing trends and patterns in sales data
  • Identifying factors influencing customer churn
• Data-driven decision making
  • Using data to inform business strategies and product development
  • A/B testing and experimentation
• Data visualization in different domains
  • Creating dashboards for monitoring key performance indicators (KPIs)
  • Visualizing scientific data (medical imaging, climate data)
• Machine learning applications
  • Preprocessing and visualizing data for machine learning tasks
  • Evaluating and interpreting machine learning models
• Communicating results and insights
  • Creating effective data visualizations for presentations and reports
  • Telling compelling stories with data

Common Pitfalls and How to Avoid Them

• Overplotting and clutter
  • Using transparency, jittering, or sampling to handle large datasets
  • Faceting plots to reduce overplotting
• Misusing color
  • Avoiding rainbow colormaps and using perceptually uniform colormaps
  • Considering color blindness and accessibility
• Misleading visualizations
  • Avoiding truncated axes and distorted scales
  • Using appropriate baselines and references
• Overlooking data quality issues
  • Checking for missing values, outliers, and inconsistencies
  • Validating data integrity and consistency
• Failing to consider the audience
  • Tailoring visualizations to the target audience's background and goals
  • Providing clear context and explanations
• Overcomplicating plots
  • Focusing on clarity and simplicity
  • Removing unnecessary chart junk and decorations
• Not exploring alternative visualizations
  • Trying different chart types and encodings
  • Iterating and refining visualizations based on feedback