Recognition System
of Japanese Characters
Scaling Computation
Because 
and 
are
probabilities between 0~1 and a large amount of multiplications are computed,
the output probability decrease exponentially to zero when the lenght sequence T
increase. Then, we need to scale the forward and backward variables to avoid a
underflow computation.
Firstly, we defined a new forward and backward variables as:
Also we defined a scale coefficient variable as:
Using this definitions, the scaled forward algorithm is modified as:
1. Initialization
2. Recursion
3. Termination
Because the denominator of the scaled output probability is too small, we will use the probability logarithm.
The scaled backward algorithm is modified as:
1. Initialization
2. Recursion
The scaled Baulm-Welch algorithm is modified as:
Last update 01.15.2004
These pages are maintained by Jorge Solis