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Let's say that I use Dynamic Time Warping (DTW) along with K-Medoids to cluster unlabeled time-series into a number of clusters. In this way, several clustering solutions in $k_i,i=[1,...,m]$ clusters create 'ground truths' for all the instances.
UPDATE: My goal is to create a predictive model of new time-series instances, which a-priori are unlabeled. Initially the data are completely unlabeled. The clustering aims to build a robust cluster labeling, while the classification is intended to predict the cluster membership for new data.

Classification after clustering:
A. - Does it sound correct to split this dataset into training and test set for classification purposes, built several classification models on the training set, and measure the overall accuracy by applying these models on the test set (using the "ground truth" labels)?
- Or, the test set should not be used during the clustering? Besides, can I create its labels for the classification by assigning to the class label of the closest cluster center as these are derived from the clustering of the training set only?
- In other words, is the classification biased by the labels of the test set that are created during a clustering process where the test set participates in shaping all the pairwise distances, and consequently the clustering decision boundaries?

B. - If so, a good classification accuracy is an indicator of an appropriate clustering into $k_j$ clusters?

C. - Is a deep learning approach more appropriate here? The few labeled data could be the cluster centers or some time-series profiles selected and verified by a domain expert.

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    $\begingroup$ It's hard to understand your question, but it sounds like your goal is to train a classifier that will take in a time series and output a class label that corresponds to membership in one of your clusters. If the goal is to map new time series to clusters, why not just assign each new time series to the nearest cluster centroid, as K-Medoids does? $\endgroup$
    – user20160
    May 27, 2016 at 1:04
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    $\begingroup$ The goal is to create a labeling in order to be used as a training test to a predictive model. New data that are coming through the database should be used as the test set. My questions is more about the participation of the test set in the clustering process. $\endgroup$
    – user26872
    May 27, 2016 at 21:17

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If you used k-medoids, you do not need to train a classifier afterwards: every new object should be assigned to the nearest medoid...

Deep learning requires massive labeled training data!

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  • $\begingroup$ I need a classifier because I want to see something like the confusion matrix, interpret the results through, for instance, decisions trees, and because I just want to build the labeling, train/update a model and use it iteratively to data that have just been generated. $\endgroup$
    – user26872
    May 27, 2016 at 21:21
  • $\begingroup$ That is a classifier - but one that you do not need to train. $\endgroup$ May 27, 2016 at 21:24
  • $\begingroup$ It is, but K-Medoids cannot come up with confusion matrix or the advantages of decision trees. And, for sure, I don't want each time to do clustering with an increasing number of data. $\endgroup$
    – user26872
    May 27, 2016 at 21:31
  • $\begingroup$ @user26872 The only thing your classifier will do in this case is try to approximate the output of k-medoids. If you could train the perfect classifier, what it would learn to do is assign points to the nearest medoid. Since you already have the medoids and know the optimal decision rule, there's no reason to train a classifier, and no advantage to decision trees, etc. The confusion matrix is a measure of classifier performance so, as before, there's not much reason for it. $\endgroup$
    – user20160
    May 28, 2016 at 3:51
  • $\begingroup$ Let's assume that I have a limited number of prototype time-series; these could be the medoids and a few more per class. Is it recommended to assign labels to new data based on the DTW similarity instead of trying any learning process through advanced classification approaches? $\endgroup$
    – user26872
    May 28, 2016 at 6:27
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when you do the clustering and then labeling for training purpose, you have to compare the analysis results in a common comparable values. The results of clustering are some classes. Generally, labeling would be based on the characteristics of centers of these classes. For the testing, imagine you do not follow this point and use the data as before clustering, Then in a confusion matrix , you can not compare target class and output class. So, the testing data also should participate in clustering. Let me explain easier, the good question is when do you split the data in to testing and training? you split the data after labeling. there are some labels unused still in testing data. you use only a partial of labeled data for training not all of them. So every thing include splitting the data, training and testing or classification happen after CTL( Cluster-Then-Label).

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