I'm implementing color quantization based on k-means clustering method on some RGB images. Then, I will determine the performance the algorithm. I found some information about training and testing. As I understand, I should divide the samples of images for training and testing.
But I am confused about the terms training and testing. What does these mean ? And how to implement with a rank value ?
Training and testing are two common concepts in machine learning. Training and testing are more easily explained in the framework of supervised learning; where you have a training dataset for which you know both input data as well as additional attributes that you want to predict. Training consists in learning a relation between data and attributes from a fraction of the training dataset, and testing consists in testing predictions of this relation on another part of the dataset (since you know the prediction, you can compare the output of the relation and the real attributes). A good introductory tutorial using these concepts can be found on http://scikit-learn.org/stable/tutorial/basic/tutorial.html
However, clustering is a class of unsupervised learning, that is, you just have some input data (here, the RGB values of pixels, if I understand well), without any corresponding target values. Therefore, you can run a k-means clustering algorithm in order to find classes of pixels with similar colors, without the need to train and test the algorithm.
In image processing, training and testing is for example used for classifying pixels in order to segment different objects. A common example is to use a random forest classifier: the user selects pixels belonging to the different objects of interest (eg background and object), the classifier is trained on this set of pixels, and then the remainder of the pixels are attributed to one of the classes by the classifier. ilastik (http://ilastik.org/) is an example of software that performs interactive image classification and segmentation.
I don't know which programming language you're using, but k-means is already implemented in various libraries. For Python, both SciPy (http://docs.scipy.org/doc/scipy/reference/generated/scipy.cluster.vq.kmeans2.html#scipy.cluster.vq.kmeans2) and scikit-learn (http://scikit-learn.org/stable/modules/generated/sklearn.cluster.KMeans.html) have an implementation of K-means. Also note that, depending on your application, you may be interested in clustering pixels together using not only pixels values, but also spatial proximity of pixels. See for example the scikit-image gallery example http://scikit-image.org/docs/dev/auto_examples/plot_rag_mean_color.html