Isomap Isometric Mapping and Dimensionality Reduction

Isomap (a nonlinear dimensionality reduction method) along with other isometric mapping techniques, feature extraction approaches, and their applications in machine learning represent cutting-edge research topics. The Isomap algorithm operates by constructing a neighborhood graph from high-dimensional data, computing geodesic distances using shortest-path algorithms like Dijkstra's, and then performing multidimensional scaling (MDS) to embed data into lower-dimensional space while preserving intrinsic geometric relationships. Feature extraction serves as a fundamental data preprocessing technique that employs methods like PCA (Principal Component Analysis) or autoencoders to distill the most representative features from raw data, facilitating subsequent machine learning tasks. Machine learning constitutes a field focused on enabling computers to learn patterns from data, where algorithms such as neural networks and support vector machines analyze large datasets to discover underlying patterns and solve real-world problems through iterative optimization processes.