Dear Esakki ponraj Esakkimuthu

There is no perfect method to estimate the number of HMM states. You can choose a minimum number of states (i.e. two states), and also you can use only one state as I use in my face recognition project.

Increasing number of states requires more training iterations.

Select any number of HMM states with one Gaussian Mixture and record the results. Then examine different numbers of states with different numbers of Gaussian Mixtures and make a comparison between these experiments.

Dear Hameed R. Farhan,

Thanks for your answers.

But I have a few questions to be clarified related to HMM since I am not sure I am doing correctly or not. I request you to please take some time and read through the points which I want some clarity and confirmations from experts.

A list contains normalized training data.

Total Elements inside the list = 75

Each element inside the list is an np array.

The data inside the list is Vehicle driving data which is continuous.

'X_train = [[100*4], [100*4], [100*4], [100*4].........................[100*4]]' len(X_train) = 75 X_Train[0] = [100*4] X_Train.columns=['Veh.Speed','Strg Angle', 'Lat_Acceleration', 'Long_Acceleration']

Note:

Every [100*4] data received from vehicle at specific Time intervals. Lets say X_train[0] is 15 to 30 seconds driving study data. X_train[1] may be 15 to 30 seconds driving study data and so on .....

First I will explain the steps I followed and begin my clarification points.

Now I will start my confusion points while I perform training operation

Problem Faced When I print my cost function, Till 200 - 300 iteration my cost function reduces gradually and it becomes NAN around a value of 8950.

What I tried to avoid NAN

I believe that the problem will be in learning rate, so i multiply my learning rate for every 75 iterations with 0.1, so that I update my new learning rate which is smaller. But after it comes to that value of around 8900 to 9000 it becomes NAN once again

My Questions

• Why it becomes NAN after several iterations
• Whether the cost function value will converge to a local/global optima like a gradient descent ?
• Since I want to perform Forward Algorithm after training, with the use of X_test Data, whether I can note down the updated parameters (pi, trans_mat, Gaussianm_mix matrix, mean, Covariance) before NAN occurs and test the probability ?
• Whether it will produce good results or it is wrong to do that ?
• What are the other ways to make my cost function converge ?
• In what ways can i improve the training based on the history of my work ? If I missed something wrong, please let me know.

If you haven't understand any point please let me know .

Kindly reply.

I would like to know if you use an available python toolbox for continuous HMM, or you constructed it?

I used Matlab and BNT toolbox. I examined five states with only one Gaussian mixture and the system converged with less than 10 iterations. After that I examined from 4 states to one state, where the system converges with one iteration in case of using only one state of HMM.

Dear Hameed R. Farhan

I have constructed it. (Since I find an tutorial code though Git hub, i used that and modified based on my data set)

If you would like to get any information I can share you.

I think it is difficult to build such a toolbox.

Can you use Matlab instead of Python?

I can use Matlab, But Since I have done all my project in python, i would be happy if i get some solution in python.

Also, I have been try to implement in python using a HMM library called hmmlearn.

But I haven't understand the documentation, I am struggling to input my data set using that library.

You can't use the HMM toolbox included in Matlab because it is dedicated for discrete HMM.

I suggest you use an external toolbox called BNT for the continuous HMM and Gaussian mixture.

If the obtained results are same as those of Python, this means that the data are incorrectly manipulated. Otherwise, the Python code may be contain some errors.

I would like to confirm before i proceed, I got a recommendation to check from one of the forums

1. To check whether my data should actually looks like an Gaussian ?

2. To check for singularity of my data set (variance = 0) ?

I don't no how to check proceed the above two steps.

Do you have any comment or suggestion ?

In the case of continuous data, it is difficult to process each element in the array individually. So, a set of elements can be taken into a probability density function (PDF), where the Gaussian function is frequently used.

The PDFs of any matrix appear in the form of mean and covariance matrices. Therefore, you can use the Gaussian function for any data.

It is not important whether the data are in the form of Gaussian shape or not. Gaussian means the type of PDF for this case.

@Hameed R. Farhan

I would like to confirm some concepts about HMM.

I would be happy if i get some Information from you.

***** Background******

I have two list contains observation data each of length 100.

Example :

St = [X[0], X[1], ......X[99]]

Rt = [X[0], X[1], ......X[99]]

Each element inside St & Rt is an array (X[i]), of size 100 rows *4 columns

In X[i], each rows is a sequential data (continuous)

Note : I have already mentioned this info in the above question, but just for your understanding i repeated again.

***** Activity : What I have done******

I have trained both the St & Rt as two seperate HMM - GMM Models .

- 2 Hidden States & 2 Gaussians

- Baum Welch Algo/EM Algo / Forward backward Algo

Say St_Model & Rt_model

***** My Question ******

I have 2 Questions in testing the Model with forward Algorithm

Q- No : 1

I took an untrained observation data say, X[j] which is originally from St list into both Model (St_Model & Rt_model) and perform forward algorithm i,.e P(X[j]|St_model) & P(X[j]|Rt_model). Based on the higher probability value I finalized that the data X[j] belongs to which class.

Is this the method what I am doing is right ? (Like a classification problem)

Q- No : 2

Can I slice the testing data and provide as an input into the model ?

Lets say, testing data X[j] is 100 rows * 4 column.

Now I am giving only the first 60 rows into both model (X[j][:60])and calculate the probability between both.

Like in Q-No : 1, Higher the probability, corresponds to the class.

In forward Algorithm, whether we can give arbitary seq of length and predict the probability instead of giving a full sequence length like we trained our model ?

Dear Esakki ponraj Esakkimuthu

If you get best results from using less data, this means that you can reduce your data using different methods such as DWT, DCT, SVD, LBP and others.

The length of the sequence must be unchanged, so you cannot use arbitrary length of sequences. In this case, the length of larger sequence is considered and the empty elements of other sequences may be filled with zeros or a very small value like 0.000001 to avoid dividing by zero.