# Cluster method with binary variable

I need to do a cluster analysis for the following variables:

Trickquestion answer: Good/Wrong
count variable : range 0-9
time in minutes
count variable
Number of observations: 3300


Since I am new to cluster algorithms I'm struggling with choosing the best cluster algorithm. I have read about the following methods:

• k prototypes
• k means with Gower's distance
• PAM algorithm.

For the cluster analysis I need to use R.

Can someone give advice about which methods suits the data best. Since I'm studying mathematics I need to give a full mathematical explanation, so a blackbox algorithm is not an option. Tips were I can find Mathematical information about the algorithms are also welcome.

• That sounds more like a regression task to me than clustering. What do you expect the result to mean? – Has QUIT--Anony-Mousse May 6 '19 at 18:12
• I need to get different types of respondents who responded to my survey. For example serious and not serious respondents or fast/slow respondents. – Ann May 7 '19 at 6:30
• Well, I would then suggest that you define "fast" and "slow", or some quality criterion relevant for your task for the computer to find. Because otherwise you may well get random clusters... – Has QUIT--Anony-Mousse May 7 '19 at 18:05
• So you suggets that I should make the numerical variable time measured in minutes categorical and mark the times as fast, "normal" and slow? – Ann May 8 '19 at 6:24
• No. I suggest you first formalize your problem. Define "fast". – Has QUIT--Anony-Mousse May 8 '19 at 18:26