Performance considerations
by Patrick R. Nicolas, Arun Manivannan, Pascal Bugnion
Scala: Guide for Data Science Professionals
- Scala: Guide for Data Science Professionals
- Table of Contents
- Scala: Guide for Data Science Professionals
- Scala: Guide for Data Science Professionals
- Credits
- Preface
- 1. Module 1
- 1. Scala and Data Science
- 2. Manipulating Data with Breeze
- Code examples
- Installing Breeze
- Getting help on Breeze
- Basic Breeze data types
- Vectors
- Dense and sparse vectors and the vector trait
- Matrices
- Building vectors and matrices
- Advanced indexing and slicing
- Mutating vectors and matrices
- Matrix multiplication, transposition, and the orientation of vectors
- Data preprocessing and feature engineering
- Breeze – function optimization
- Numerical derivatives
- Regularization
- An example – logistic regression
- Towards re-usable code
- Alternatives to Breeze
- Summary
- References
- 3. Plotting with breeze-viz
- 4. Parallel Collections and Futures
- 5. Scala and SQL through JDBC
- Interacting with JDBC
- First steps with JDBC
- JDBC summary
- Functional wrappers for JDBC
- Safer JDBC connections with the loan pattern
- Enriching JDBC statements with the "pimp my library" pattern
- Wrapping result sets in a stream
- Looser coupling with type classes
- Creating a data access layer
- Summary
- References
- 6. Slick – A Functional Interface for SQL
- 7. Web APIs
- 8. Scala and MongoDB
- 9. Concurrency with Akka
- GitHub follower graph
- Actors as people
- Hello world with Akka
- Case classes as messages
- Actor construction
- Anatomy of an actor
- Follower network crawler
- Fetcher actors
- Routing
- Message passing between actors
- Queue control and the pull pattern
- Accessing the sender of a message
- Stateful actors
- Follower network crawler
- Fault tolerance
- Custom supervisor strategies
- Life-cycle hooks
- What we have not talked about
- Summary
- References
- 10. Distributed Batch Processing with Spark
- 11. Spark SQL and DataFrames
- DataFrames – a whirlwind introduction
- Aggregation operations
- Joining DataFrames together
- Custom functions on DataFrames
- DataFrame immutability and persistence
- SQL statements on DataFrames
- Complex data types – arrays, maps, and structs
- Interacting with data sources
- Standalone programs
- Summary
- References
- 12. Distributed Machine Learning with MLlib
- 13. Web APIs with Play
- Client-server applications
- Introduction to web frameworks
- Model-View-Controller architecture
- Single page applications
- Building an application
- The Play framework
- Dynamic routing
- Actions
- Interacting with JSON
- Querying external APIs and consuming JSON
- Creating APIs with Play: a summary
- Rest APIs: best practice
- Summary
- References
- 14. Visualization with D3 and the Play Framework
- A. Pattern Matching and Extractors
- II. Module 2
- 1. Getting Started with Breeze
- Introduction
- Getting Breeze – the linear algebra library
- Working with vectors
- Getting ready
- How to do it...
- Creating vectors
- Constructing a vector from values
- Creating a vector out of a function
- Creating a vector of linearly spaced values
- Creating a vector with values in a specific range
- Creating an entire vector with a single value
- Slicing a sub-vector from a bigger vector
- Creating a Breeze Vector from a Scala Vector
- Vector arithmetic
- Scalar operations
- Calculating the dot product of two vectors
- Creating a new vector by adding two vectors together
- Appending vectors and converting a vector of one type to another
- Concatenating two vectors
- Standard deviation
- Find the largest value in a vector
- Finding the sum, square root and log of all the values in the vector
- Working with matrices
- Vectors and matrices with randomly distributed values
- How it works...
- Creating vectors with uniformly distributed random values
- Creating vectors with normally distributed random values
- Creating vectors with random values that have a Poisson distribution
- Creating a matrix with uniformly random values
- Creating a matrix with normally distributed random values
- Creating a matrix with random values that has a Poisson distribution
- How it works...
- Reading and writing CSV files
- 2. Getting Started with Apache Spark DataFrames
- Introduction
- Getting Apache Spark
- Creating a DataFrame from CSV
- Manipulating DataFrames
- Creating a DataFrame from Scala case classes
- 3. Loading and Preparing Data – DataFrame
- 4. Data Visualization
- 5. Learning from Data
- Introduction
- Supervised and unsupervised learning
- Gradient descent
- Predicting continuous values using linear regression
- Binary classification using LogisticRegression and SVM
- Binary classification using LogisticRegression with Pipeline API
- How to do it...
- Importing and splitting data as test and training sets
- Construct the participants of the Pipeline
- Preparing a pipeline and training a model
- Predicting against test data
- Evaluating a model without cross-validation
- Constructing parameters for cross-validation
- Constructing cross-validator and fit the best model
- Evaluating the model with cross-validation
- How to do it...
- Clustering using K-means
- Feature reduction using principal component analysis
- How to do it...
- Dimensionality reduction of data for supervised learning
- Mean-normalizing the training data
- Extracting the principal components
- Preparing the labeled data
- Preparing the test data
- Classify and evaluate the metrics
- Dimensionality reduction of data for unsupervised learning
- Mean-normalizing the training data
- Extracting the principal components
- Arriving at the number of components
- Evaluating the metrics
- How to do it...
- 6. Scaling Up
- 7. Going Further
- 1. Getting Started with Breeze
- III. Module 3
- 1. Getting Started
- 2. Hello World!
- 3. Data Preprocessing
- 4. Unsupervised Learning
- 5. Naïve Bayes Classifiers
- 6. Regression and Regularization
- 7. Sequential Data Models
- 8. Kernel Models and Support Vector Machines
- 9. Artificial Neural Networks
- Feed-forward neural networks (FFNN)
- The multilayer perceptron (MLP)
- The activation function
- The network architecture
- Software design
- Model definition
- Training cycle/epoch
- Training strategies and classification
- Evaluation
- Benefits and limitations
- Summary
- 10. Genetic Algorithms
- 11. Reinforcement Learning
- 12. Scalable Frameworks
- B. Basic Concepts
- C. Bibliography
- Index
The three unsupervised learning techniques share the same limitation—a high computational complexity.
The K-means has the computational complexity of O(iKnm), where i is the number of iterations, K the number of clusters, n the number of observations, and m the number of features. The algorithm can be improved through the use of other techniques by using the following techniques:
- Reducing the average number of iterations by seeding the centroid using an algorithm such as initialization by ranking the variance of the initial cluster as described at the beginning of this chapter.
- Using a parallel implementation of K-means and leveraging a large-scale framework such as Hadoop or Spark.
- Reducing the number of outliers and possible features by filtering out the noise with a smoothing algorithm such as a discrete Fourier transform or a Kalman filter.
- Decreasing the dimensions of the model by following a two-step process: a first pass with a smaller number of clusters K and/or a loose exit condition regarding the reassignment of data points. The data points close to each centroid are aggregated into a single observation. A second pass is then run on a smaller set of observations.
The computational complexity of the expectation-maximization algorithm for each iteration (E + M steps) is O(m2n), where m is the number of hidden or latent variables and n is the number of observations.
A partial list of suggested performance improvement includes:
- Filtering of raw data to remove noise and outliers
- Using a sparse matrix on a large feature set to reduce the complexity of the covariance matrix, if possible
- Applying the Gaussian mixture model (GMM) wherever possible: the assumption of Gaussian distribution simplifies the computation of the log likelihood
- Using a parallel data processing framework such as Apache Hadoop or Spark as explained in the Apache Spark section in Chapter 12, Scalable Frameworks
- Using a kernel method to reduce the estimate of covariance in the E-step
The computational complexity of the extraction of the principal components is O(m2n + n3), where m is the number of features and n the number of observations. The first term represents the computational complexity for computing the covariance matrix. The last term reflects the computational complexity of the eigenvalue decomposition.
The list of potential performance improvements or alternative solutions for PCA includes:
- Assuming that the variance is Gaussian
- Using a sparse matrix to compute eigenvalues for problems with large feature sets and missing data
- Investigating alternatives to PCA to reduce the dimension of a model such as the discrete Fourier transform (DFT) or singular value decomposition (SVD) [4:16]
- Using the PCA in conjunction with EM (a research)
- Deploying a dataset on a parallel data processing framework such as Apache Spark or Hadoop as explained in the Apache Spark section in Chapter 12, Scalable Frameworks
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