🍃Isomap
Both PCA and LDA are linear methods, meaning they look for a hyperplane (line or plane) to separate the data. In contrast, Isomap is a non-linear method that does not rely on such a hyperplane. Instead, it uses non-linear techniques like KNN (K-Nearest Neighbors).
Let's dive deeper into how Isomap works:
It uses KNN to find the K nearest neighbors for each data point.
It then constructs a neighborhood graph, connecting only neighboring points while leaving non-neighbors unconnected.
Finally, it applies MDS (Multidimensional Scaling) to compute the shortest geodesic distances between all data pairs on the graph and projects the data into a lower-dimensional space while preserving these between-point distances.
As we can see, Isomap is a non-linear dimensional reduction method aiming at preserve the local structure.
To reduce our campaign data into 3 dimensions using Isomap, the code looks like:
and the data plot looks like:
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