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Suppose i have a labelled training set with 1's and 0's already labelled for a binary classification problem. Suppose i wanted to use a clustering algorithm to classify. So i form clusters and then see if 1's and 0's tend to cluster well together. How would i do it?

Could i remove the labels create clusters and then see the proportions of 1's to 0's in each cluster? Then i could use this as a classifier. So if a cluster has a larger proportions of 1's any new item that needs to be classified would be also assigned a 1, otherwise a 0. Is this approach commonly used? What are the potential drawbacks?

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Clustering is not classification. If you have labels that you want to predict, use a classifier. If you have no labels but wish to explore the structure of your data, clustering is fine.

You write "What are the potential drawbacks?". I will answer by example. Suppose that you have some data about all of the people in a country that includes labels as to whether or not they are left handed. You run a clustering algorithm on the data and separate the data into two clusters which perfectly reflect whether or not the person has blue eyes. Is that a success or a failure? From the point of view of clustering, I would say it is a great success. The algorithm found meaningful structure in your data. But if you are looking for a classifier for handedness, it is no good. Now think how many other traits could be used to divide the data into two groups. Male/female. Rh-positive/Rh-Negative blood type. Way too many possibilities. How could any clustering simultaneously identify all of these traits?

In general, when you run a clustering algorithm, you can reasonably hope that it will find structure in your data. But if you have some particular structure in mind, you have no reason to think that it will find that structure.

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