Data Mining situation - data-mining

Question

Suppose I have the data as mentioned below.
11AM user1 Brush
11:05AM user1 Prep Brakfast
11:10AM user1 eat Breakfast
11:15AM user1 Take bath
11:30AM user1 Leave for office
12PM user2 Brush
12:05PM user2 Prep Brakfast
12:10PM user2 eat Breakfast
12:15PM user2 Take bath
12:30PM user2 Leave for office
11AM user3 Take bath
11:05AM user3 Prep Brakfast
11:10AM user3 Brush
11:15AM user3 eat Breakfast
11:30AM user3 Leave for office
12PM user4 Take bath
12:05PM user4 Prep Brakfast
12:10PM user4 Brush
12:15PM user4 eat Breakfast
12:30PM user4 Leave for office
This data tell me about the daily routine of different people. From this data it seems user1 and user2 behave similarly (though there is a difference in time they perform the activity but they are following the same sequence). With the same reason, User3 and User4 behave similarly.
Now I have to group such users into different groups. In this example, group1- user1 and USer2 ... followed by group2 including user3 and user4
How should I approach this kind of situation. I am trying to learn data mining and this is an example I thought of as a data mining problem. I am trying to find an approach for the solution, but I can not think of one. I believe this data has the pattern in it. but I am not able to think of the approach which can reveal it.
Also, I have to map this approach on the dataset I have, which is pretty huge but similar to this :) The data is about logs stating occurrence of events at a time. And I want to find the groups representing similar sequence of events.
Any pointers would be appreciated.

Answer 1

It looks like clustering on top of associating mining, more precisely Apriori algorithm. Something like this:
Mine all possible associations between actions, i.e. sequences Bush -> Prep Breakfast, Prep Breakfast -> Eat Breakfast, ..., Bush -> Prep Breakfast -> Eat Breakfast, etc. Every pair, triplet, quadruple, etc. you can find in your data.
Make separate attribute from each such sequence. For better performance add boost of 2 for pair attributes, 3 for triplets and so on.
At this moment you must have an attribute vector with corresponding boost vector. You can calculate feature vector for each user: set 1 * boost at each position in the vector if this sequence exists in user actions and 0 otherwise). You will get vector representation of each user.
On this vectors use clustering algorithm that fits your needs better. Each found class is the group you use.
Example:
Let's mark all actions as letters:
a - Brush
b - Prep Breakfast
c - East Breakfast
d - Take Bath
...
Your attributes will look like
a1: a->b
a2: a->c
a3: a->d
...
a10: b->a
a11: b->c
a12: b->d
...
a30: a->b->c->d
a31: a->b->d->c
...
User feature vectors in this case will be:
attributes = a1, a2, a3, a4, ..., a10, a11, a12, ..., a30, a31, ...
user1 = 1, 0, 0, 0, ..., 0, 1, 0, ..., 4, 0, ...
user2 = 1, 0, 0, 0, ..., 0, 1, 0, ..., 4, 0, ...
user3 = 0, 0, 0, 0, ..., 0, 0, 0, ..., 0, 0, ...
To compare 2 users some distance measure is needed. The simplest one is cosine distance, that is just value of cosine between 2 feature vectors. If 2 users have exactly the same sequence of actions, their similarity will equal 1. If they have nothing common - their similarity will be 0.
With distance measure use clustering algorithm (say, k-means) to make groups of users.

Answer 2

Using an itemset mining algorithm like Apriori as proposed in the other answer is not the best solution because Apriori does not consider time or the sequential ordering. Thus, it requires to do an additional pre-processing step to consider ordering.
A better solution is to use a sequential pattern mining algorithm like PrefixSpan, SPADE, or CM-SPADE directly. A sequential pattern mining algorithm will directly find subsequences that appears often in a set of sequences.
Then you can still apply clustering on the sequential patterns found!