Live briefing
Everything about Isomap
Nonlinear dimensionality reduction method
Isomap is a nonlinear dimensionality reduction method. It is one of several widely used low-dimensional embedding methods. Isomap is used for computing a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points. The algorithm provides a simple method for estimating the intrinsic geometry of a data manifold based on a rough estimate of each data point’s neighbors on the manifold. Isomap is highly efficient and generally applicable to a broad range of data sources and dimensionalities. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: IsomapA 5-minute orientation
- Skim a recent paper: Robust Image Hashing With Isomap and Saliency Map for Copy DetectionInfluential work since 2022
- Pick up a classic book: Neural Information ProcessingThe most-reprinted book on the subject
- Read the landmark paper: Conceptual and empirical comparison of dimensionality reduction algorithms (PCA, KPCA, LDA, MDS, SVD, LLE, ISOMAP, LE, ICA, t-SNE)Cited 800 times
- Go sideways: Nonlinear dimensionality reductionA closely related topic
- Go sideways: Dimensionality reductionA closely related topic
📖 Definitions
Noun (The use of) a nonlinear dimensionality-reduction method for generating a quasi-isometric, low-dimensional embedding of a set of high-dimensional data points, allowing for visualization etc.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Conceptual and empirical comparison of dimensionality reduction algorithms (PCA, KPCA, LDA, MDS, SVD, LLE, ISOMAP, LE, ICA, t-SNE)
The Isomap Algorithm and Topological Stability
Robust kernel Isomap
Nonlinear projection with curvilinear distances: Isomap versus curvilinear distance analysis
Selection of the optimal parameter value for the Isomap algorithm
Semi-supervised local multi-manifold Isomap by linear embedding for feature extraction
Facial Expression Recognition Based on Local Binary Patterns and Kernel Discriminant Isomap
Geographic assignment with stable isotopes in IsoMAP
🆕 Influential since 2022
Robust Image Hashing With Isomap and Saliency Map for Copy Detection
Multi-class data augmentation and fault diagnosis of wind turbine blades based on ISOMAP-CGAN under high-dimensional imbalanced samples
Mid- to Long-Term Electric Load Forecasting Based on the EMD–Isomap–Adaboost Model
Research on transformer fault diagnosis based on ISOMAP and IChOA‐LSSVM
Neural networks based linear (PCA) and nonlinear (ISOMAP) feature extraction for soil swelling pressure prediction (North East Algeria)
📚 Books worth reading
Neural Information ProcessingTingwen Huang · 2012
Evolutionary Computation, Machine Learning and Data Mining in BioinformaticsLeonardo Vanneschi · 2012
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Nonlinear dimensionality reduction Nonlinear dimensionality reduction (NLDR), also known as manifold learning, is any of various related techniques that aim to project high-dimensional data…
- Dimensionality reduction Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the…
- Semidefinite embedding Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to…
- Diffusion map Diffusion maps is a dimensionality reduction or feature extraction algorithm introduced by Coifman and Lafon which computes a family of embeddings of a…
- Multidimensional scaling Multidimensional scaling (MDS) is a means of visualizing the level of similarity of individual cases of a data set. MDS is used to translate distances…
- Spectral clustering In multivariate statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality…
- Kernel principal component analysis In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques…
- K-nearest neighbors algorithm In statistics and machine learning, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method that assigns weightage only…