<s>
The	O
Itakura	B-Algorithm
–	I-Algorithm
Saito	I-Algorithm
distance	I-Algorithm
(	O
or	O
Itakura	O
–	O
Saito	O
divergence	O
)	O
is	O
a	O
measure	O
of	O
the	O
difference	O
between	O
an	O
original	O
spectrum	O
and	O
an	O
approximation	O
of	O
that	O
spectrum	O
.	O
</s>
<s>
The	O
Itakura	B-Algorithm
–	I-Algorithm
Saito	I-Algorithm
distance	I-Algorithm
is	O
a	O
Bregman	B-Algorithm
divergence	I-Algorithm
generated	O
by	O
minus	O
the	O
logarithmic	O
function	O
,	O
but	O
is	O
not	O
a	O
true	O
metric	O
since	O
it	O
is	O
not	O
symmetric	O
and	O
it	O
does	O
not	O
fulfil	O
triangle	O
inequality	O
.	O
</s>
<s>
In	O
Non-negative	O
matrix	O
factorization	O
,	O
the	O
Itakura-Saito	O
divergence	O
can	O
be	O
used	O
as	O
a	O
measure	O
of	O
the	O
quality	O
of	O
the	O
factorization	O
:	O
this	O
implies	O
a	O
meaningful	O
statistical	O
model	O
of	O
the	O
components	O
and	O
can	O
be	O
solved	O
through	O
an	O
iterative	B-Algorithm
method	I-Algorithm
.	O
</s>
<s>
The	O
Itakura-Saito	B-Algorithm
distance	I-Algorithm
is	O
the	O
Bregman	B-Algorithm
divergence	I-Algorithm
associated	O
with	O
the	O
Gamma	O
exponential	O
family	O
where	O
the	O
information	O
divergence	O
of	O
one	O
distribution	O
in	O
the	O
family	O
from	O
another	O
element	O
in	O
the	O
family	O
is	O
given	O
by	O
the	O
Itakura-Saito	O
divergence	O
of	O
the	O
mean	O
value	O
of	O
the	O
first	O
distribution	O
from	O
the	O
mean	O
value	O
of	O
the	O
second	O
distribution	O
.	O
</s>
