Unit 6: Advanced topics

• Basic analysis of algorithms: The Big O
• Visualizations for Data Science:
• Picking the "right" visualization
• Tooling primer: matplotlib, pandas
• (Library support):
• High-level libraries: pandas (cont'd)
• Low-level libraries: numpy, scipy
• Plotting (cont'd): seaborn, bokeh
• Parsing

Readings:

• Grus, J. (2015) Data Science from Scratch, O'Reilley, Chapter 3 (available via the WU library, EBSCO)

Analysis of algorithms (1)

• We encountered many different computational procedures (algorithms) for different purposes in data processing throughout Units 1 to 5, e.g.:
• Data filtering
• Data sorting
• Data sampling
• Deduplication (blocking, windowing)
• Why do we want to describe the complexity of these procedures (or, the underlying algorithms)?
• How can we describe the their complexity: space vs. time complexity?

Analysis of algorithms (2)

• Studying the complexity of a computation (procedure, algorithm) involves quantifying and describing ...
• ... the difficulty of solving a computational problem (e.g., sorting)
• ... in terms of the required computational resources:
• running time of a computation
• memory ("space") consumed by a computation
• Note: There can be a fundamental trade-off between running time
and memory consumption.
• Our take: Time complexity of basic opterations in (Python) data processing.

Analysis of algorithms (3)

• How fast does the (running/ execution) time required by an operation grow as the size of the problem increases in the worst case?
• "Size of a problem" (\( n \)), eg.: number of elements in a list or array, number of rows in a table or DataFrame.
• "time required" (\( f \)): a function of N, i.e., \( f(n) \)
• When this function \( f(n) \) grows rapidly, an operation (algorithm) will become unusable the larger \( n \).
• When this function \( f(n) \) grows "slowly, an operation (algorithm) will remain usable even at larger \( n \).

Analysis of algorithms (4): Types of growth

Commonly found types of time growth for some input n:

• \( f(n) = 1 \): Time required is constant, independent of \( n \) (e.g., hash searching).
• \( f(n) = log(n) \): increasing n by a factor \( c \), e.g., doubling \( n \)

• \( f(n) = n \): Required time grows linearly with problem size (linear search in \( n \)-element list)
• \( f(n) = n * log(n) \): Doubling \( n \) increases the required time by more than a double (merge sort, Python's timsort).
• \( f(n) = n^2 \), \( f(n) = n^3 \): quadratic, cubic, etc. Doubling \( n \) results in a four-/ eight-fold increase in the required time (simple sorting, matrix multiplication)
• \( f(n) = c^n \): Doubling the problem size squares the time required, a.k.a. exponential growth).

Analysis of algorithms (5): Big O(rder) notation

• Often, when planning data-processing steps, we want to compare two or available operations (e.g., search strategies).
• Objective: Comparison based on their relative time complexities or growth rates: \( f(n) \) vs. \( g(n) \).
• "Strictness" of comparison, e.g., "equal or less than", "same as".
• Big O(rder): \(g \in O(f)\) iff \( |g(x)| \) is smaller than some constant multiple of \( |f(x)| \) (i.e., \( f \) is of smaller or equal order than \( g \)).
• Example: \( n^2 \) vs. \( (n^2 + 2n + 3) \) vs. \( 2n \)

Analysis of algorithms (6): Big O(rder) notation

Analysis of algorithms (7): Urban Audit example

Let's look at the excerpts from the following notebook

haystack = [('BE', 10839905),
 ('BG', 7563710),
 ('CZ', 10532770),
 ('DE', 81802257),
 ('EE', 1365275),
 ('ES', 47021031),
 ('FR', 64611814),
 ('IT', 60340328),
 ('CY', 819100),
 ('HU', 10014324),
 ('NL', 16574989),
 ('PL', 38529866),
 ('PT', 10573479),
 ('RO', 22480599),
 ('SK', 5435273),
 ('FI', 5351427),
 ('SE', 9415570),
 ('NO', 4858199),
 ('CH', 7877571)]
haystack.sort() # by country code
haystack.sort(key=lambda x:x[1]) # by population count

Analysis of algorithms (8): Urban Audit (cont'd)

Note: if you know that a file is sorted, then searching in that file becomes easier/cheaper!

• Answer: \( O(\log{}n) \)
• Why?
• Answer: Binary Search!

Bottomline: (pre-)sorting can be costly, but might speed up other operations... another example: grouping!

Analysis of algorithms (9): Urban Audit example

# Search for first entry bigger than number in a sorted
# list of lists of length 2:
def binary_search(number, array, lo, hi):

    if hi < lo: return array[lo]       # no more numbers
    mid = (lo + hi) // 2               # midpoint in array
    if number == array[mid][0]:
        return array[mid]              # number found here
    elif number < array[mid][0]:
        # try left of here
        return binary_search(number, array, lo, mid - 1)
    else:
        # try above here
        return binary_search(number, array, mid + 1, hi)

# Sample call: Find me a country with a pop. > 5m people?
binary_search(5000000, haystack, 0, len(haystack))

Analysis of algorithms (10): Outlook

• Python's sort applies Timsort: \( O(n\log{}n) \) (worst case).
• Custom algorithmic recipes for Python 3 (incl. sorting algorithms): http://python3.codes/.
• Sampling: probability-based sampling (pandas)
• Deduplication: total complexity of naive algorithm: \( O(n^2) \) (pairwise comparison). Possible improvements:
• Blocking: \( O(n(n/b + \log{}n)) \) with block size \( b < n \)
• Windowing: \( O(n(w + \log{}n)) \) with window size \( w < n \)
• Sorting+Scan: \( O(n * \log{}n + n) \)

Visualization (1)

• Visualizations
• can support a number of data-processing activities (before analysis!);
• can be used to deliver analysis results;
• See Chapter 3 of "Data Science from Scratch":
• matplotlib
• pandas wrapper around matplotlib
• Notebook
• Corresponding code examples:
• matplotlib: GitHub.
• pandas: "Visualization tutorial":""
• Advanced use of visualizations, such as graphical inference, beyond the scope of this course.

Visualization (2)

• Tasks supported by visualisations:
• Anomaly detection: data outliers;
• Grouping: Forming and characterising aggregates of similar data points;
• Finding association (correlation) between pairs of variables;
• Computing derivatives (e.g., sums) of data points;
• Finding extremes, ranges, and orders (rankings) in data points;
• Filtering data points (e.g., for ranges);
• Retrieval of selected data points;
• (Describing data distributions;)

Visualization (3)

• Which visualization type is most effective for a given task?
• Accuracy
• Performance time
• Personal preferences
• No One Size Fits All!

Visualization (4a): Scatterplot

Visualization (4b): Scatterplot

Visualization (5a): Lineplot

Visualization (5b): Lineplot

Visualization (6a): Barplot

Visualization (6b): Barplot

Visualization (7): Boxplot

Visualization (8): Task-based effectiveness

Visualization (9)

• Dos:
• Finding groups: Use bar charts (preference bias towards pie charts!)
• Finding associations and trends: Use line plots and scatterplots (preference bias towards line plots!)
• Finding anomalies: Use scatterplots
• Donts:
• Finding groups: Avoid line charts;
• Compute derivatives: Avoid line charts;
• Finding associations and trends: Avoid tables and pie charts;

High-level libraries

• Agate: agate is a Python data analysis library that is optimized for humans instead of machines. It is an alternative to numpy and pandas that solves real-world problems with readable code.
• Pandas: pandas is an open source, BSD-licensed library providing high-performance, easy-to-use data structures and data analysis tools for the Python programming language.

Pandas

import pandas as pd

contains high-level data structures and tools designed to make data analysis fast and easy. Pandas are built on top of NumPy, and makes it easy to use in NumPy-centric applications.

Pandas is well suited for many different kinds of data:

• Tabular data with heterogeneously-typed columns
• Ordered and unordered (not necessarily fixed-frequency) time series data.
• Arbitrary matrix data (homogeneously typed or heterogeneous) with row and column labels
• Any other form of observational / statistical data sets. The data actually need not be labeled at all to be placed into a pandas data structure

Pandas features (1/2)

Here are just a few of the things that pandas does well:

• Handling of missing data
• Adding and deleting columns_ on the fly
• data alignment: objects can be explicitly aligned to a set of labels/columns
• Group by functionality and apply split-apply-combine operations on data sets to aggregate and transform data
• label-based slicing, no need for indices
• Merging and joining

Pandas features (2/2)

• Reshaping
• Hierarchical labels
• Loading data from flat files (CSV and delimited), Excel files, databases, and saving / loading data from the ultrafast HDF5 format
• Time series-specific functionality: date range generation and frequency conversion, moving window statistics, moving window linear regressions, date shifting and lagging, etc.
• plotting support. e.g. see the official tutorial

Pandas: Some more words

It takes a while to get used to pandas. The documentation is exhaustive and there exists hundreds of tutorials and use cases

• Pandas Cookbooks
• Datacamp tutorial
• Dataquest.io tutorial

Some hands on

Checkout the notebook pandas.ipynb

Low-level libraries

• Chardet: Character encoding auto-detection in Python. As smart as your browser. Open source.
• dateutils: The dateutil module provides powerful extensions to the standard datetime module, available in Python.
• Csvkit: csvkit is a suite of command-line tools for converting to and working with CSV, the king of tabular file formats
• Numpy the fundamental package for scientific computing with Python
• SciPy is open-source software for mathematics, science, and engineering

Numpy

import numpy as np

Numpy the fundamental package for scientific computing with Python. It contains among other things:

• a powerful N-dimensional array object
• sophisticated (broadcasting) functions
• tools for integrating C/C++ and Fortran code
• useful linear algebra, Fourier transform, and random number capabilities

NumPy does not provide high-level data analysis functionality, having an understanding of NumPy arrays and array-oriented computing will help you use tools like Pandas much more effectively.

SciPy

SciPy is open-source software for mathematics, science, and engineering

The SciPy library depends on NumPy, which provides convenient and fast N-dimensional array manipulation. The SciPy library is built to work with NumPy arrays, and provides many user-friendly and efficient numerical routines , such as routines for numerical integration and optimization.

SciPy subpackages (1/2)

• cluster: Clustering algorithms
• constants: Physical and mathematical constants
• fftpack Fast Fourier Transform routines
• integrate Integration and ordinary differential equation solvers
• interpolate Interpolation and smoothing splines
• linalg Linear algebra
• ndimage N-dimensional image processing

SciPy subpackages (2/2)

• odr Orthogonal distance regression
• optimize Optimization and root-finding routines
• signal Signal processing
• sparse Sparse matrices and associated routines
• spatial Spatial data structures and algorithms
• special Special functions
• stats Statistical distributions and functions

from scipy import linalg, optimize

SciPy

Again, check out the official tutorials

Some examples:

• Interpolation
• Solving linear system, Eigenvalues and eigenvectors
• Signal processing
• Statistics, random variables, fitting distributions, ..

Plotting

Plotting

There exists many libraries for plotting:

• matplotlib: Python's most popular and comprehensive plotting library that is especially useful in combination with NumPy/SciPy.
• seaborn: extension for matplotlib with enchanced visual styles and additional plots
• qqplot ( like qqplot2 in R)
• bokeh: Bokeh is a plottling library for interactive plots typically viewed in Web applications
• folium leaflets

Machine learning?

Machine learning

• scikit-learn builds on NumPy and SciPy, including clustering, regression, and classification, well documented, many tutorials and examplesUsed by data-heavy startups, including Evernote, OKCupid, Spotify, and Birchbox.
• Theano Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. Theano features:
• TensorFlow developed by Google, is an open source software library for numerical computation using data flow graphs. It can be used for deep learning scenarios. Check out their Python API
• Keras: Keras is a high-level neural networks API, written in Python and capable of running on top of either TensorFlow or Theano. It was developed with a focus on enabling fast experimentation. Being able to go from idea to result with the least possible delay is key to doing good research.

Data Mining & NLP

Data Mining & NLP

• Scrapy an open source and collaborative framework for extracting the data you need from websites. In a fast, simple, yet extensible way.
• NLTK NLTK is a leading platform for building Python programs to work with human language data. It provides easy-to-use interfaces to over 50 corpora and lexical resources such as WordNet, along with a suite of text processing libraries for classification, tokenization, stemming, tagging, parsing, and semantic reasoning and wrappers for industrial-strength NLP libraries.

References

• Chapter 3, Data Science from Scatch
• Reingold (2014): "Basic Techniques for Design and Analysis of Algorithms", Chapter 4, In: Computing Handbook, CRC Press.
• B. Saket, A. Endert and Ç. Demiralp (2019), "Task-Based Effectiveness of Basic Visualizations," in IEEE Transactions on Visualization and Computer Graphics, vol. 25, no. 7, pp. 2505-2512, DOI: 10.1109/TVCG.2018.2829750