Self-organizing maps are claimed to be an approach for dimensionality reduction. However, I am kind of confused about this claim.
Consider the following example, I have a data set with 200 data points and each data point is represented by a feature vector with 1000 dimensions. Assume I would like to train a map with a $1 \times 2$ grid. In other words, I will map these 200 points to two cells. Just for illustration purposes, suppose the first 100 points are mapped onto the first cell and the latter 100 points are mapped onto the second cell. From the viewpoint of dimensionality reduction, we can say we use a 1-dimensional output space to represent the original 1000-dimensional space. But this really confuses me a lot. According to this example, it looks to me that the first 100 points will share the same feature vector, which is just 1 in the one-dimensional space; and the latter 100 points will share the same feature vector, which is 2 in the same one-dimensional space. Is my understanding correct?