readme

本程序针对一维的数据分析,并对其建立合适的马尔可夫模型

Notes for 1-D HMT code
----------------------

Files: (see file headers, or type help file in MATLAB, for more info)
README - this file

trainEM_tree.m - function that takes a wavelet transform, a number of
states, and a maximum number of iterations and returns HMT
parameters.  No convergence criteria is specified right now (easily
fixed), it just runs a specified number of iterations (default 30).

indmixmod.m - fits and indenpendent mixture model to the data (used to
specify starting points for the EM algorithm).

updown_tree.m - upward-downward algorithm.  Returns hidden state pmfs
and other likelihoods needed for training.

viterbi_tree.m - returns most likely state sequence of the data given
the model parameters.

denoise_tree.m - finds conditional mean estimate given noisy wavelet
coefficients (AWGN) and model.  Need to give it the noise variance,
but you can easily change this.

make_tree_data.m - generated synthetic data given a model


All the code operates on the wavelet transform of the 1-D data.  The
wavelet transform array needs to have the "Tree" ordering described
below ( mdwt() in the Rice Wavelet Toolbox returns it in this order).

All of the routines assume that there is only one observation (full
wavelet decomposition), and the model parameters are tied within
scale.  

General variable names: 
N - number of data points
L - number of levels in the tree (log2(N))
M - number of hidden states
ES - state transistion matrices at each level, dimension MxMxL
ES(a,b,c) is the probability a node at level c is in state b given its
parent is in state a.
POS - hidden state pmf of the root node, dimension Mx1
SI - mixture variances for each level, dimension MxL
MU - mixture means for each level, dimension MxL


"Tree" array order
----------------------
If you are not using Rice Wavelet Toolbox, this is the order the
wavelet coefficients need to be in.

Let W be the array of wavelet coefficients (full decomposition).
W(1) is the scaling coefficient
W(2) is the mother wavelet coefficient
W(2*i-1) is the left child of W(i)
W(2*i) is the right child of W(i)

          W(1)
           |
          W(2)
         /   \
        /     \
    W(3)       W(4)
    /  \      /   \
   /    \    /     \
W(5)  W(6)  W(7)  W(8)

etc.