ISOMAP is one of the approaches for manifold learning, which generalizes linear framework to nonlinear data structures. Similar to MDS, ISOMAP creates a visual presentation of similarities or dissimilarities (distance) of a number of objects. However, as the data is structured in a nonlinear format, the Euclidian distance measure of MDS is replaced by the geodesic distance of a data manifold in ISOMAP. In this recipe, we will illustrate how to perform a nonlinear dimension reduction with ISOMAP.
Performing nonlinear dimension reduction with ISOMAP
by Chiu Yu-Wei, AshishSingh Bhatia
Machine Learning with R Cookbook - Second Edition
- Preface
- Practical Machine Learning with R
- Introduction
- Downloading and installing R
- Downloading and installing RStudio
- Installing and loading packages
- Understanding of basic data structures
- Basic commands for subsetting
- Reading and writing data
- Manipulating data
- Applying basic statistics
- Visualizing data
- Getting a dataset for machine learning
- Data Exploration with Air Quality Datasets
- Analyzing Time Series Data
- R and Statistics
- Introduction
- Understanding data sampling in R
- Operating a probability distribution in R
- Working with univariate descriptive statistics in R
- Performing correlations and multivariate analysis
- Conducting an exact binomial test
- Performing a student's t-test
- Performing the Kolmogorov-Smirnov test
- Understanding the Wilcoxon Rank Sum and Signed Rank test
- Working with Pearson's Chi-squared test
- Conducting a one-way ANOVA
- Performing a two-way ANOVA
- Understanding Regression Analysis
- Introduction
- Different types of regression
- Fitting a linear regression model with lm
- Summarizing linear model fits
- Using linear regression to predict unknown values
- Generating a diagnostic plot of a fitted model
- Fitting multiple regression
- Summarizing multiple regression
- Using multiple regression to predict unknown values
- Fitting a polynomial regression model with lm
- Fitting a robust linear regression model with rlm
- Studying a case of linear regression on SLID data
- Applying the Gaussian model for generalized linear regression
- Applying the Poisson model for generalized linear regression
- Applying the Binomial model for generalized linear regression
- Fitting a generalized additive model to data
- Visualizing a generalized additive model
- Diagnosing a generalized additive model
- Survival Analysis
- Classification 1 - Tree, Lazy, and Probabilistic
- Introduction
- Preparing the training and testing datasets
- Building a classification model with recursive partitioning trees
- Visualizing a recursive partitioning tree
- Measuring the prediction performance of a recursive partitioning tree
- Pruning a recursive partitioning tree
- Handling missing data and split and surrogate variables
- Building a classification model with a conditional inference tree
- Control parameters in conditional inference trees
- Visualizing a conditional inference tree
- Measuring the prediction performance of a conditional inference tree
- Classifying data with the k-nearest neighbor classifier
- Classifying data with logistic regression
- Classifying data with the Naïve Bayes classifier
- Classification 2 - Neural Network and SVM
- Introduction
- Classifying data with a support vector machine
- Choosing the cost of a support vector machine
- Visualizing an SVM fit
- Predicting labels based on a model trained by a support vector machine
- Tuning a support vector machine
- The basics of neural network
- Training a neural network with neuralnet
- Visualizing a neural network trained by neuralnet
- Predicting labels based on a model trained by neuralnet
- Training a neural network with nnet
- Predicting labels based on a model trained by nnet
- Model Evaluation
- Introduction
- Estimating model performance with k-fold cross-validation
- Estimating model performance with Leave One Out Cross Validation
- Performing cross-validation with the e1071 package
- Performing cross-validation with the caret package
- Ranking the variable importance with the caret package
- Ranking the variable importance with the rminer package
- Finding highly correlated features with the caret package
- Selecting features using the caret package
- Measuring the performance of the regression model
- Measuring prediction performance with a confusion matrix
- Measuring prediction performance using ROCR
- Comparing an ROC curve using the caret package
- Measuring performance differences between models with the caret package
- Ensemble Learning
- Introduction
- Using the Super Learner algorithm
- Using ensemble to train and test
- Classifying data with the bagging method
- Performing cross-validation with the bagging method
- Classifying data with the boosting method
- Performing cross-validation with the boosting method
- Classifying data with gradient boosting
- Calculating the margins of a classifier
- Calculating the error evolution of the ensemble method
- Classifying data with random forest
- Estimating the prediction errors of different classifiers
- Clustering
- Introduction
- Clustering data with hierarchical clustering
- Cutting trees into clusters
- Clustering data with the k-means method
- Drawing a bivariate cluster plot
- Comparing clustering methods
- Extracting silhouette information from clustering
- Obtaining the optimum number of clusters for k-means
- Clustering data with the density-based method
- Clustering data with the model-based method
- Visualizing a dissimilarity matrix
- Validating clusters externally
- Association Analysis and Sequence Mining
- Introduction
- Transforming data into transactions
- Displaying transactions and associations
- Mining associations with the Apriori rule
- Pruning redundant rules
- Visualizing association rules
- Mining frequent itemsets with Eclat
- Creating transactions with temporal information
- Mining frequent sequential patterns with cSPADE
- Using the TraMineR package for sequence analysis
- Visualizing sequence, Chronogram, and Traversal Statistics
- Dimension Reduction
- Introduction
- Why to reduce the dimension?
- Performing feature selection with FSelector
- Performing dimension reduction with PCA
- Determining the number of principal components using the scree test
- Determining the number of principal components using the Kaiser method
- Visualizing multivariate data using biplot
- Performing dimension reduction with MDS
- Reducing dimensions with SVD
- Compressing images with SVD
- Performing nonlinear dimension reduction with ISOMAP
- Performing nonlinear dimension reduction with Local Linear Embedding
- Big Data Analysis (R and Hadoop)
- Introduction
- Preparing the RHadoop environment
- Installing rmr2
- Installing rhdfs
- Operating HDFS with rhdfs
- Implementing a word count problem with RHadoop
- Comparing the performance between an R MapReduce program and a standard R program
- Testing and debugging the rmr2 program
- Installing plyrmr
- Manipulating data with plyrmr
- Conducting machine learning with RHadoop
- Configuring RHadoop clusters on Amazon EMR
Performing nonlinear dimension reduction with ISOMAP
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