# How to deal with with rows with zero in every feature while clustering?

I am working on a clustering problem which has 13000 observations and 15 features. Around 3000 observations in the dataset has zero in every features ( i.e all values zero in 3000 rows). I am trying to do clustering on top of it. What is a better way to deal with it ? I have few things in my mind but would like to get clarity on :

1. Check for number of rows with all zero and remove them ?
2. Include the rows with zero value in every feature and let the clustering algorithm handle the same?

Also,please suggest if there are any better way to handle the same.

Note : I am using k-means clustering.

1. If you expect that all zeros is a result of error in the measuring of the features (i.e. the observations should not be all 0s but they are), then I would say: Keep all the data, but increase k (from k-means) by 1. This extra one will hopefully become the class of all these wrong observations.
Note: If you keep using K-Means having all these extra observations should be fine. However, if you switch to another algorithm which takes densities into account (e.g. Mean Shift) then having all these extra observations might influence your model in ways that you do not expect. For example, the observations [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0.1] might end up being far from the all 0s cluster.