![hat in time palette swaps hat in time palette swaps](http://3.bp.blogspot.com/-FaKNFoyYaPY/UYzHUHQLPRI/AAAAAAABZsc/pYvOcxo8hCA/s1600/natg__day_24___robin___hooves_by_xain_russell-d5cix1p.png)
Also, the exact location where the prototype is relocated is not important, as long as it is in the immediate neighborhood where the prototype is needed. An important observation is that it is not even necessary to swap one of the redundant prototypes but simply removing any prototype in their immediate neighborhood is enough since k-means can fine-tune their exact location locally. 2, only one swap is needed to fix the solution. On the other hand, the correct locations of the prototypes can be solved by a sequence of prototype swaps, and leaving the fine-tuning of their exact location to k-means. If the ground truth is not available, the result can be compared with the global minimum (if available), or with the best available solution used as gold standard. Sometimes we normalize CI by the number of clusters, and report the relative CI-value (CI/ k). Specifically, if CI = 0, the result is correct clustering. This value provides a clear intuition about the result. 1 where four real clusters are missing a prototype. The CI-value is the higher of these two numbers. It counts how many real clusters are missing a prototype, and how many have too many prototypes. We use the centroid index (CI) as our primary measure of success. After the pre-processing steps, the main challenge is to optimize the clustering so that the objective function would be minimized. Outlier removal can also be integrated in the clustering directly by modifying the objective function. Another approach is to perform the clustering first, and then label points that did not fit into any cluster as outliers. Detection of outliers is typically considered as a separate pre-processing step. Noise and outliers can also bias the clustering especially with the SSE objective function. Otherwise some data imputation technique should be used to predict the missing values for some alternatives see. If the number of missing attributes is small, we can simply exclude these data vectors from the process. The next step is to deal with missing attributes and noisy data. They have the biggest influence on the clustering result, and their choice is the most important challenge for practitioners. The first step is to choose the attributes and the objective function according to the data. Quality of clustering depends on several factors. In case of categorical data, several alternatives were compared including k- medoids, k- modes, and k- entropies.
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It is not trivial how to do it, but if properly solved, then k-means can be applied.
![hat in time palette swaps hat in time palette swaps](https://64.media.tumblr.com/a92fc1f58f3e3093bfaeb09ca0cd11d3/tumblr_pjrf3ldEi31y1bqr8o1_1280.jpg)
The key is to define the distance or similarity between the data vectors, and to be able to define the prototype (center). Since then, it has also been applied to other types of data. K-means was originally defined for numerical data only. The aim of clustering is to group a set of N data vectors.