If I convert continuous data into ordinal discrete data, but number of the class is 100(1 class per 1 percentile), can I say this is 'continuous'? I have some continuous data, and want to do kmeans clustering with this.
But weirdly when I did kmean clustering with this data, the outcome was very conflicted with my presumption. So I decided to do same thing with ordinal categorial data, but I was reluctant to converting continuous form into discrete form, because as I know it loses information and characteristics of data to a certain degree.
So, I devided data by 100 classes, 1 class for 1 percentile of whole data. But since I coded names of class as 1, 2, 3...from minimum to maximum, I can say it still has 'volume' or 'value'. For example, the class covers 99~100 percentile of whole data is named '100', which is the ordinal category that contains the biggest value. And the result based on this were exactly same as I intended.
But here is my dilema. People say don't do kmeans with discrete data. And with the original form of mine, coninuous form, I don't get good result, but with discrete form, I do. Kmodes, used for discretized data was already turned out to be effectless in my case. That is why I am trying to do like this. I think my method is quite plausible because I devided class by percentile, not the uniform interval. Plus, since the number of class is 100, it is thought to preserve the information of data quite well compare to typical binarization consists less than 10 or something like that.
So if someone asks me 'why did you use discrete data with the algorithm don't recommended with it?', can I insist my data is discretized but it is still has characteristics of continuous data to certain degree?

It is often OK to quantize your data as long as it doesn't lose "too much" information. So in principle, you are right here.
But in your example, it sounds like quantization does lose a lot of information since your results change drastically.
So I would try to figure out, why your results change that much through quantization. First, ensure that your results from k-means are robust and don't just depend on random initialization. Then, you might want to gradually change the degree of quantization to see when your results change; this might give you a clue as to what is going on. Finally, try other clustering algorithms, like e.g. DBSCAN, to see whether your observations are dependent on the algorithm you are using.
