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In-Depth Information
k
×
(
n
−
q
)
amatrix
B
k
×
q
and a
∈ R
∈ R
k
neighboring instance vectors, a matrix
A
∈ R
(
n
−
q
)
×
1
are formed. The
i
th row vector
a
i
vector
w
of the matrix
A
consists
of the
i
th nearest neighbor instances
x
S
i
1
×
n
∈ R
,
≤
≤
k
, with its elements at
the
q
missing locations of MVs of
x
1
excluded. Each column vector of the matrix
B
consists of the values of the
j
th location of the MVs
1
i
of the
k
vectors
x
S
i
.
(
1
≤
j
≤
q
)
The elements of the vector
w
are the
n
q
elements of the instance vector
x
whose
missing items are deleted. After the matrices
A
and
B
and a vector
w
are formed, the
least squares problem is formulated as
−
A
T
z
min
x
||
−
w
||
2
(4.65)
T
of
q
MVs can be estimated as
Then, the vector
u
=
(α
1
,α
2
,...,α
q
)
⎛
⎝
⎞
⎠
=
α
1
.
α
q
B
T
z
B
T
A
T
†
w
u
=
=
(
)
,
(4.66)
A
T
†
is the pseudoinverse of
A
T
.
where
(
)
Table 4.1
Recent and most well-known imputation methods involving ML techniques
Clustering
Kernel methods
MLP hybrid
[
4
]
Mixture-kernel-based iterative estimator
[
105
]
Rough fuzzy subspace clustering
[
89
]
Nearest neighbors
LLS based
[
47
]
ICkNNI
[
40
]
Fuzzy c-means with SVR and Gas
[
3
]
Iterative KNNI
[
101
]
Biclustering based
[
32
] CGImpute
[
22
]
KNN based
[
46
] Boostrap for maximum likelihood
[
72
]
Hierarchical Clustering
[
30
]
kDMI
[
75
]
K2 clustering
[
39
]
Ensembles
Weighted K-means
[
65
] Random Forest
[
42
]
Gaussian mixture clustering
[
63
] Decision forest
[
76
]
ANNs
Group Method of Data Handling (GMDH)
[
104
]
RBFN based
[
90
] Boostrap
[
56
]
Wavelet ANNs
[
64
]
Similarity and correlation
Multi layer perceptron
[
88
]
FIMUS
[
77
]
ANNs framework
[
34
]
Parameter estimation for regression imputation
Self-organizing maps
[
58
]
EAs for covariance matrix estimation
[
31
]
Generative Topographic Mapping
[
95
]
Iterative mutual information imputation
[
102
]
Bayesian networks
CMVE
[
87
]
Dynamic bayesian networks
[
11
] DMI (EM
+
decision trees)
[
74
]
Bayesian networks with weights
[
60
] WLLSI
[
12
]