ISOMAP is a nonlinear dimension reduction method and a representative of isometric mapping methods. ISOMAP can be regarded as an extension of the metric MDS, where pairwise, the Euclidean distance among data points is replaced by geodesic distances induced by a neighborhood graph.

The description of the ISOMAP algorithm is shown in four steps. First, determine the neighbor of each point. Secondly, construct a neighborhood graph. Thirdly, compute the shortest distance path between two nodes. Finally, find a low dimension embedding of the data by performing MDS.

In this recipe, we demonstrate how to perform a nonlinear dimension reduction using ISOMAP. First, we load the digits data from RnavGraphImageData. Then, after we select one digit and plot its rotated image, we can see an image of the handwritten digit (the numeral 3, in the figure in step 3).

Next, we randomly sample 300 digits as our input data to ISOMAP. We then transpose the dataset to calculate the distance between each image object. Once the data is ready, we calculate the distance between each object and perform a dimension reduction. Here, we use vegdist to calculate the dissimilarities between each object using a Euclidean measure. We then use ISOMAP to perform a nonlinear dimension reduction on the digits data with the dimension set as 6 and the number of shortest dissimilarities retained for a point as 8, and ensure that you analyze the largest connected group by specifying fragmentedOK as TRUE.

Finally, we can use the generated ISOMAP object to make a two-dimension scatter plot (figure in step 6), and also overlay the minimum spanning tree with lines in red on the scatter plot (figure in step 7).