What is Applications of Isomap?

In this article, we will learn Applications of Isomap,This free Python tutorial for complete beginners will help you learn Python from scratch.

Applications of Isomap

Geodesic Distance vs. Euclidean Distance: Unveiling the Variance in Measurement

Visualizing Handwritten Digits with Isomap Dimensionality Reduction

Isomap can be used for a variety of tasks, including:

image classification: Use isomap to decrease the dimensionality of picture data before training a classifier. This can increase the classifier’s performance while also shortening the training time.
Video compression: Before reducing video data, isomap can be employed to minimise its dimensionality. This can lower the size of the compressed video file while maintaining quality.
Fraud detection: Isomap has the ability to detect fraudulent transactions. Isomap, for example, may be used to identify transactions that are far apart in the geodesic space.
Natural language processing: Before doing natural language processing activities such as sentiment analysis or topic modelling, Isomap may be used to decrease the dimensionality of text input.

Isomap for Dimensionality Reduction in Python

In the realm of machine learning and data analysis, grappling with high-dimensional datasets has become a ubiquitous challenge. As datasets grow in complexity, traditional methods often fall short of capturing the intrinsic structure, leading to diminished performance and interpretability. In this landscape, Isomap (Isometric Mapping) emerges as a potent technique designed explicitly to navigate the intricacies of complex, non-linear structures inherent in data. Dimensionality reduction is a crucial aspect of machine learning and data analysis, especially when dealing with high-dimensional datasets. One powerful technique for this purpose is Isomap, an algorithm designed to capture the underlying geometry of complex, non-linear structures. Isomap stands for Isometric Mapping, and its primary goal is to unfold intricate patterns in high-dimensional data into a lower-dimensional space while preserving the essential relationships between data points.

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Euclidean Distance Geodesic Distance Definition Euclidean distance is the straight-line distance between two points in Euclidean space.It represents the length of the shortest path between two points in a flat, Cartesian space.Geodesic distance is the shortest path between two points on a curved surface, such as a manifold or graph.It accounts for the curvature or non-linearity of the space, providing a more accurate measure on non-flat surfaces.Measurement Basis Based on the straight-line distance formula derived from the Pythagorean theorem.Assumes a flat, linear space without considering any curvature or obstacles.Based on the shortest path along the curved surface.Reflects the intrinsic structure of the space, considering any bends or twists.Applicability Appropriate for flat, Euclidean spaces.Well-suited for measuring distances in traditional Cartesian coordinate systemsEssential for measuring distances on curved surfaces, manifolds, or graphs.Suitable for capturing distances in spaces with non-linear structures.Calculation Method Computed using the familiar straight-line distance formula in Euclidean space.For two points (x1 ,y1) and (x2 ,y2) the Euclidean distance is given bysquare root ((x2-x1)2+(y2-y1)2)Computed based on the shortest path along the curved surface.Often involves algorithms like Dijkstra’s algorithm on a graph or specialized methods for manifold spaces.Sensitivity to Structure Insensitive to the underlying structure of the space.Treats the space as flat and measures distances without considering bends or twists.Sensitive to the intrinsic structure of the space.Captures the true distances, accounting for the non-linearities present.Example On a flat map, the Euclidean distance between two cities is a straight-line measurement. On the surface of the Earth, the geodesic distance between two cities considers the curvature of the planet, providing a more accurate representation. Representation in Isomap Isomap, when using Euclidean distances, assumes a flat geometry. Isomap, utilizing geodesic distances (shortest paths on the neighborhood graph), captures the non-linear structure of the data. Impact on Dimensionality Reduction May lead to inaccurate representations when dealing with non-linear manifold data. Ensures a more accurate representation of the underlying structure, crucial for preserving relationships in non-linear spaces....