Digital Signal Processing Reference
In-Depth Information
z
i
(k)
•
=
output of the
i
th neuron of layer 1 at the
k
th time step
=
x
i
(k)
,
w
12
•
ij
=
weight connecting the
i
th neuron of layer 1 and the
j
th neuron of layer 2,
•
c
22
weight connecting the
j
th neuron of context units and the
j
th hidden layer
neuron of layer 2,
jj
=
z
j
(k
•
−
1
)
=
output of the
j
th neuron of layer 2, delayed by one time step,
b
j
=
•
bias associated with the
j
th neuron of layer 2,
•
N
=
number of inputs,
•
P
=
number of hidden layer neurons.
Hence the output of the Elman's RNN can be given as:
P
z
3
(k)
z
j
(k)w
23
=
f
2
(12.10)
j
j
=
1
where
z
3
(k)
•
=
output of the only neuron in output layer, at time step
k
,
w
2
j
=
•
weight connecting the
j
th neuron of layer 2 to the only neuron in layer 3,
•
f
1
(
)
represents a nonlinear function, usually chosen as tansigmoidal or logsig-
moidal function,
•
•
f
2
(
•
)
can be either a linear or a nonlinear mapping.
A generalized Elman's RNN can employ multiple neurons in the output layer also.
In the training phase, for a multiclass problem, the output, for each exemplar input
to an ERNN, is chosen for the system as
y
.Here
C
is the total
number of classes in which each RNN is designated to classify its inputs. In the
implementation phase, the output of the ERNN is classified as:
∈{
1
,
2
,...,c,...,C
}
y
class
=
−
≤
+
c
if
(c
0
.
5
)<y
(c
0
.
5
)
(12.11)
except for the two terminal classes where
y
class
=
1if
y<
1
.
5 and
y
class
=
C
if
y>(C
−
0
.
5
)
.
12.5 Time Domain Cross-Correlation Based Scheme for Gait
Signal Classification
For the classification of gait signals using time-domain features, benchmark sig-
nals available from the physionet database [
35
] have been utilized. As mentioned
earlier, the database contains real-life gait signals of 16 healthy subjects, as well
as 15, 19, and 13 pathological subjects having neurological disorders due to PD,
HD, and ALS, respectively. The procedure for obtaining the cross-correlograms has
already been explained. From the cross-correlation sequences, three quantitative de-
scriptors [
13
], namely, the centroid
(cent)
, the mean-square abscissa
(msa)
, and the
variance of abscissa
(va)
, are evaluated for several subjects with known neurolog-
ical states of health and these values are subsequently used to train ERNNs. Once
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