I've got an interview for a Ph.D. position and I need to give a ten-minute presentation for my recent research. I have completed two projects and right now I am doing another research which has a close correlation to the advertised position. These three projects have no correlation. I would like to present the last project I am working on, but unfortunately, I have a few results to exhibit. So I do not know how to present an unfinished project. Should I follow the outline like background, purpose, methods, and results? And any tips or advice for the interview?
Ten minutes is like "no time at all". You can do very little. However, it is likely that the hiring committee is much more interested in what you will do in the future, related to their general concerns, than what you have done in the past.
So, I'd suggest you mention, briefly, the past results but stress the work in progress and the possible benefits if it pays off. The committee can explore your past work in publications, of course, but the work in progress and contemplated, needs to come from you. Look to the future, not the past.
"What you're thinking you're becoming." Be confident and honest.
Present the current project you are working on and be upfront, transparent, and honest; mention how you just started on the current project and present it in a way that shows your planning and execution plan: how you start it, how you research for it, how you implement it, and how you execute it. Use this as an opportunity to paint a good picture for them to see how your work flow is. Showing them insight to how you set goals will help.