Description: Spectral embedding is a dimensionality reduction method based on the spectrum of the Laplacian matrix of a graph. This approach allows representing high-dimensional data in a lower-dimensional space while preserving the structural relationships between data points. The technique is grounded in graph theory and spectral analysis, where a graph is constructed from the data, and the Laplacian matrix is used to capture the connectivity and structure of the graph. By calculating the eigenvalues and eigenvectors of this matrix, one can identify the directions in which the data varies the most, facilitating visualization and analysis. Spectral embedding is particularly useful in contexts where data exhibit complex relationships, as it allows discovering patterns and groupings that would not be evident in a high-dimensional space. Furthermore, this technique can be applied in various fields, such as biology, sociology, and image processing, where understanding the relationships between data is crucial for decision-making and developing predictive models.
