What is isomap?

Isomap, short for Isometric Mapping, is a popular nonlinear dimensionality reduction technique used in machine learning and data analysis. It is a method for constructing a low-dimensional embedding of data points in a high-dimensional space based on their pairwise distances.

Isomap works by first constructing a neighborhood graph using the k-nearest neighbors algorithm, where each data point is connected to its closest neighbors. Then, the algorithm computes the geodesic distances on this graph, which represent the shortest path between two points along the edges of the graph.

Finally, Isomap uses classical multidimensional scaling (MDS) to project the data points into a lower-dimensional space while preserving the geodesic distances as much as possible. This allows for identifying the underlying structure of the data and uncovering meaningful relationships between data points.

Isomap is particularly useful for handling high-dimensional data that exhibit nonlinear relationships and complex structures. It can be applied in various domains, such as image processing, speech recognition, bioinformatics, and computer vision, to help with visualization, pattern recognition, and feature extraction tasks.

Overall, Isomap is a powerful tool for exploring and understanding complex datasets by reducing their dimensionality while preserving the intrinsic geometrical properties of the data.