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I have a high-dimensional data matrix with K observations and N variables. To predict the label for each observation, I use some dimensionality reduction method (let's say PCA). Now I have K observations and M reduced dims. Observations are then clustered and labeled based on PCs (10 first PCs or so).

I also have a target data matrix with P observations and N variables (same variables as in the source dataset). Is it possible to predict the label of each observation in the target dataset based on PCs from the source dataset?

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  • $\begingroup$ Why do you perform dimensionality reduction? Why don't you cluster the original data? Are those two datasets intrinsically different or did you just randomly split them? What is your original task? $\endgroup$
    – frank
    May 12 at 4:05
  • $\begingroup$ I am applying a new dimensionality reduction method based on non-linear correlation in the biological domain. The results showed that each reduced dimension is biologically meaningful. In other words, observations can be grouped based on reduced dimensions. My test data is different intrinsically. I am trying to think if it is possible to predict observation groups in the test set based on my training set's reduced dimensions. $\endgroup$ May 12 at 12:40

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You can apply the same principal component transformation from the source dataset to the target dataset. This will map your target dataset from the initial N dimensions to the same M dimensions, putting the source and target data in the same PCA space. To label the new points, you can train a classifier on the source data, using any supervised method to identify the discovered classes from PCA features (or the original features, if you prefer). Finally, apply the classifier to the target data to classify each target point as one of the clusters you discovered. Note that traditional classifier metrics such as ROC or accuracy are not terribly meaningful in this case, since there is no independent test set, as all the samples were included in the clustering. A supervised method will basically always do a good job of identifying classes that were found through unsupervised clustering on the same data in the first place.

Alternatively, you could perform a single clustering with both the source and target data combined, although you will likely get somewhat different results than just clustering the source data alone, which may not be what you want to do.

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