Mapping estimation apparatus
A mapping estimation apparatus includes a mapping adjuster. The mapping adjuster estimates mappings which correlate a plurality of subset data items with respective parts of universal set data including union of the plurality of subset data items based on the plurality of subset data items and the universal set data. The mapping adjuster estimates a mode of selecting a plurality of codomain data items from the universal set data and modes of mappings applied to the plurality of subset data items so as to have a maximum probability that data items obtained by selecting a plurality of codomain data items of which a subset of union is the universal set data from the universal set data and applying the mappings to the plurality of subset data items as domains will be respectively the plurality of codomain data items.
1. An apparatus, comprising:
a storage configured to store score data indicating a musical score of a musical performance, the stored score data including full score data and N part score data items stored separately from the full score data, the full score data being a union of the N part score data items that lacks information that separates the N part score data items from each other, wherein N is a natural number greater than 1, and an N-th part score data item among the N part score data items includes a first note having a length of time that differs from the length of time of the first note in the full score data and a second note having a generation time that differs from the generation time of the second note in the full score data,
a display device configured to display an image of a full score indicated by the full score data; and
computer-executable instructions including instructions, that when executed by a computer, cause the apparatus to:
select codomain data items of the N part score data items included in the full score data; and
estimate mappings, which correlate time positions of the data in the full score data with time positions of the data in part score data items among the N part score data items, having a maximum probability that data items, obtained by applying the mappings to the N part score data items as domains, will be codomain data items of N parts, thereby identifying the N part score data items in the full score data such that when the second note in the full score data is indicated in a state that the image of the full score is being displayed by the display device, the apparatus is caused to transmit, to an external apparatus, information indicating the second note of the N-th part score data item corresponding to the second note in the full score data.
2. The apparatus of claim 1 , wherein the computer-executable instructions include instructions, that when executed by the computer, cause the apparatus to estimate the mappings by using the following expressions (3) and (5):
< Z i ( n,p )>∝ p ( S ( n,p )|( A i ( P i ))( n,p )) (3)
〈
Z
i
(
n
,
p
)
〉
∝
p
(
S
(
n
,
p
)
|
(
A
i
(
P
i
)
)
(
n
,
p
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)
(
3
)
A
i
=
arg
max
A
i
′
∑
n
,
p
[
<
Z
i
(
n
,
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>
S
(
n
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)
]
(
A
i
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(
P
i
)
)
(
n
,
p
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(
5
)
wherein Z(n,p) are masks for grids (n, p) of an n-axis and p-axis coordinate system in which the full score data S (n, p) exists, A is the mappings from the full score data, P is the part score data items, and i is an index having a value from 1 to N.
3. The apparatus of claim 2 , wherein the computer-executable instructions include instructions, that when executed by the computer, cause the apparatus to repeatedly execute expressions 3 and 5 for each of the N part score data items a predetermined number of times.
4. The apparatus of claim 1 , wherein the computer-executable instructions include instructions, that when executed by the computer, cause the apparatus to estimate the mappings by using the following expression (10):
A
i
=
arg
max
A
i
′
∑
n
,
p
[
S
(
n
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)
[
1
-
1
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⋃
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≠
i
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A
j
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A
i
′
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P
i
)
(
n
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(
10
)
wherein (n, p) represents grids (n, p) of an n-axis and p-axis coordinate system in which the full score data S (n, p) exists, A is the mappings from the full score data, P is the part score data items, i is an index having a value from 1 to N, and j is an index having a value from 1 to N where j≠i.