Hidden markov model next state only depends on pre

问题:

I am working on a prototype framework.

Basically I need to generate a model or profile for each individual's lifestyle based on some sensor data about him/her, such as GPS, motions, heart rate, surrounding environment readings, temperature etc.

The proposed model or profile is a knowledge representation of an individual's lifestyle pattern. Maybe a graph with probabilities.

I am thinking to use Hidden Markov Model to implement this. As the states in HMM can be Working, Sleeping, Leisure, Sport and etc. Observations can be a set of various sensor data.

My understanding of HMM is that next state S(t) is only depends on previous one state S(t-1). However in reality, a person's activity might depends on previous n states. Is it still a good idea to use HMM? Or should I use some other more appropriate models? I have seen some work on second order and multiple order of Markov Chains, does it also apply HMM?

I really appreciate if you can give me a detailed explanation.

Thanks!!

回答1:

What you are talking about is a First Order HMM in which your model would only have knowledge of the previous history State. In case of an Order-n Markov Model, the next state would be dependent on the previous 'n' States and may be this is what you are looking for right?

You are right that as far as simple HMMs are considered, the next state is dependent only upon the current state. However, it is also possible to achieve a mth Order HMM by defining the transition probabilities as shown in this link. However, as the order increases, so does the overall complexity of your matrices and hence your model, so it's really upto you if your up for the challenge and willing to put the requisite effort.