https://doi.org/10.31449/inf.v48i7.5775                                             Informatica 48 (2024) 113–122   113 
                                                         
 
 
Interpolation Analysis of Industrial Big Data Based on KDR Knowledge 
Recognition Algorithm Considering Singular Value Decomposition 
Theory 
 
Cenglin Yao
1,2
, Yongzhou Li
1* 
1
Evergrande School of Management, Wuhan University of Science and Technology, Wuhan, Hubei,430081, China 
2
College of Mechanical and Electrical Engineering, Wuhan Business University, Wuhan, Hubei 430056, China 
E-mail: yl200808@126.com, 20150511@wbu.edu.cn 
*
Corresponding author 
 
Keywords: singular value decomposition, KDR algorithm, industrial big data, interpolation analysis 
 
Recieved: Februry 27, 2024  
Although various algorithms have made some progress in the current research of industrial big data 
interpolation, most of them are only suitable for static KDR operation methods. Most of the data is not 
achieved overnight but in an incremental manner. For example, the data will increase with time. In the 
process of data collection, to ensure the consistency of KDR calculation results under dynamic conditions, 
the same and different information in the old and new data must be merged, to disperse the dynamic data. 
According to the increasing properties of data in Industrial big data analysis, a dynamic KDR operation 
model is established by considering singular value decomposition (SVD) theory. To ensure consistency 
before and after static separation, a rough set method based on Manilkara is used. Under the influence of 
Yalo' s singular value decomposition (SVD) theory, the conventional interval is divided into two parts: the 
core and the blank to express the unstable interval. This method uses the method based on the middle interval. 
By dividing the middle interval again, the interval between the old and the new data is combined. 
Povzetek: V raziskave industrijskih velikih podatkov so vpeljali dinamični model KDR, ki uporablja teorijo 
singularne razčlenitve (SVD) in grobo množico Manilkara za zagotavljanje konsistentnosti med dinamičnimi 
in statičnimi podatki. 
 
 
1  Introduction 
In 1987, KDR was first formally introduced. To solve the 
problem of incomplete numerical properties, Wang and 
Chiu2 gave EFKDR algorithm with equal frequency 
respectively, and the EWKDR algorithm with equal width 
was introduced in the same year. Then, the KDR operation 
method has many directions according to the development 
of the problem. For example, in 1991, Huang and Chiu3' 
proposed the KDR computation of the basic maximum 
direct coefficient, so that the corresponding interval number 
can be automatically obtained according to the 
characteristics of the data in the KDR computation 
processing. In 2018, “Hacibeyoglu and Ibrahim" proposed 
a KDR algorithm for Euonymus according to the EF 
method.  
In maximum likelihood estimation, the distribution of 
boundaries is used to estimate an uncertain parameter, 
usually using the expected maximum (EM).EM method 
requires a large amount of data in theory to ensure the 
asymptotic and normality of the estimation. However, the 
EM algorithm's local optimal solution can be found quickly, 
its convergence is sluggish, and its operation is quite 
intricate. 
The study assumed that the missing data also existed and 
that the missing data were the most valuable, rather than 
simply missing data, so the data were analyzed in a non-
processing manner. For example, if a user uses the attribute 
"obesity," the item "weight" will not be added, but will 
appear directly on the "empty number". The method 
analyzes the original data directly, without any 
preprocessing. The most typical ones are Bayesian 
networks and neural networks. Bayesian network is used to 

114   Informatica 48 (2024) 113–122                                                                    C. Yao et al. 
describe the probability of association between features, 
which is used to reveal the association between data and 
provide a natural expression for it. In a Bayesian network, 
features are represented as features, which correlate with 
attributes represented laterally. The necessity of a Bayesian 
network for data collection, and also is to have the 
understanding of the data collection and the correlation 
between each attribute is clear. Based on this, we must first 
analyze these features, or all of these features are added to 
the model, the cause of the complexity of the Bayesian 
network, but also as the number of properties and geometric 
ratio increase. Although the artificial neural network is also 
a very popular machine learning technique in the present 
situation, it needs more work to interpolate the missing data 
[1-6]. 
In the traditional KDR operation method, the solution of 
interval cut-off is a game method. In the actual KDR 
operation, a point cannot be used to describe the boundary 
point of an interval. In the same period, the boundary of an 
interval will also be different; At the same time, an interval 
can have multiple uncertain tangents. Based on this 
situation, we give an interval that takes into account the 
theory of singular value decomposition. Using the idea of a 
boundary interval in three intervals, the uncertain region is 
extracted to form a boundary interval. When performing 
dynamic fusion, the intervals in the image need to be re-
segmented to achieve the purpose of image delay, to 
achieve the purpose of KDR operation on the image. The 
three intervals can not only express the uncertainty of the 
intervals but also delay the boundary intervals in the 
dynamic KDR operation [10-14]. 
 
2  Related work  
In machine learning, clustering is one of the main methods 
used to analyze non-monitored data, but it still has many 
problems to be solved. When clustering, objects close to the 
edge of the cluster cannot be efficiently classified. Yul3l 
gave three clustering classification methods under the 
influence of singular value decomposition theory.  
Compared with the traditional cluster represented by a 
single set, the 3D group is a new representation of clusters. 
In three subgroups, the objects of a cluster are divided into 
two groups, and the universe of a cluster is divided into core 
domain, edge domain, and irrelevant domain.  
Taking into account the singular value decomposition 
theory, the central and boundary objects of different 
categories can be compared respectively. Based on 
considering the singular value decomposition theory, this 
topic has been deeply discussed and some results have been 
obtained. Given the uncertainty of objects and clusters in 
multi-view clustering, Yu et al. L6l proposed a low-order 
ternary principal component classification method, which 
can not only reflect the correlation between objects and 
clusters but also effectively raise the multidimensional 
clustering's accuracy. To solve the large-scale clustering 
problem, Yu et al. introduced the fusion architecture of 
three clusters in 2019, which combined the clustering 
method with the clustering method, which could not only 
ensure the quality of the cluster but also reduce the time cost 
of calculation. In 2016, Yu et al. proposed singular value 
decomposition (SVD) theory based on different vertex 
distribution characteristics to achieve different vertex 
representations. Under the influence of the singular value 
decomposition theory, Liu et al. proposed an approach 
based on centroids to address the dynamic problem of 
overlapping communities [7-9]. Table 1 shows the 
summary table of the previous literatures. 
 
Table 1: Summary of the literature review 
Author Objective Findings  
[18] The manuscript explores these 
concepts and provides a case study 
that demonstrates the implementation 
of new intelligent hybrid algorithms 
for Industry 4.0 applications with 
limited data. 
An extremely accurate deterministic 
model that fits the real data was 
generated by applying the suggested 
approach. We also employed the UKF 
technique to strengthen the model's 
resistance to uncertainty. 
 
[19] Big data analytics and related 
applications in smart grids are 
The result focuses on the complex 
applications of different data analytics in 

Interpolation Analysis of Industrial Big Data Based on KDR…                         Informatica 48 (2024) 113–122   115 
 
introduced in this study. The initial 
section covers the features of big data, 
smart grids, and huge data collection 
to illustrate the goal and potential 
advantages of incorporating advanced 
data analytics in smart grids. 
 
smart grids. The current power system 
may gain a lot from handling massive 
amounts of data from geographical 
information systems, meteorological 
information systems, and energy 
networks, among other sources. In the 
big data era, this will also enhance 
customer service and societal welfare. 
[20] 
The work presented a novel method 
known as the interpretable kernel DR 
algorithm (I-KDR), which converts 
Information from the characteristics 
space into a lower-dimensional space 
where classes are closer together and 
there is less overlap. 
 
 
Furthermore, the dimensions are created 
by the algorithm based on the local 
contributions of the data samples, which 
facilitates their interpretation by class 
labels. Furthermore, we effectively 
combine the feature selection task with 
the DR to identify the original space's 
most pertinent characteristics for the 
discriminative purpose. 
[21] 
This paper presents a new technique 
that transfers The feature space 
corresponds to data to a lower 
dimensional space where classes are 
closer together and there is less 
overlap: the interpretable kernel DR 
algorithm (I-KDR).  
 
Additionally, the approach produces the 
dimensions based on the data samples' 
local contributions, which make it easier 
to comprehend the data by class labels.  
 
[22] For an improved intrusion detection 
system, the suggested system uses a 
Hybrid Deep Learning (HDL) 
network made up of Long Short-Term 
Memory (LSTM) and Convolutional 
Neural Network (CNN). 
PySpark, which offers Python support 
for the study made use of the Apache 
Spark technology in the Google Colab 
environment. The CIDDS-001 data set 
was used to evaluate the model in 
multiclass mode, and the UNS-NB15 
data set was used to evaluate the model 
in binary mode. 

116   Informatica 48 (2024) 113–122                                                                    C. Yao et al. 
[23] The fusion of conventional machine 
learning algorithms with big data 
technology has created novel and 
captivating obstacles in domains such 
as social media and social networks. 
Data processing, data storage, data 
representation, and the use of data for 
pattern mining, user behavior analysis, 
data visualization, and data tracking 
are among the primary issues 
addressed by these new challenges. 
Big data has emerged as a significant 
topic for several study fields, including 
social networks, data mining, machine 
learning, computational intelligence, 
information fusion, and the Semantic 
Web. The development of several big 
data frameworks for huge data 
processing based on the Map Reduce 
paradigm, like Apache Hadoop and, 
more recently, Spark, has made it 
possible to use data mining techniques 
and machine learning algorithms 
effectively across a variety of domains. 
3  Research methods 
In general, statistical principles and machine learning 
techniques are used to interpolate the defaults to obtain a 
complete data set. At present, the following interpolation 
methods are usually used in data processing:  
 
3.1 Manual interpolation 
This method is done manually based on human experience. 
That is, over the years, they have relied on their years of 
experience and interpolating this type of data, so the manual 
interpolation method is usually more accurate. However, 
with a large number of missing values, this algorithm can 
take a lot of time and effort. 
 
𝑅 ⃐ 
( 𝑋 )= ⋃ {𝑌 𝑖 ∣ 𝑌 𝑖 ∈ 𝑈 /𝐼𝑁𝐷 ( 𝑅 )∧ 𝑌 𝑖 ∩ 𝑋 ≠ ∅}
𝑅 ( 𝑋 )= ⋃ {𝑌 𝑖 ∣ 𝑌 𝑖 ∈ 𝑈 /𝐼𝑁𝐷 ( 𝑅 )∧ 𝑌 𝑖 ⊆ 𝑋 }
      (1) 
 
Where, represents the partition of ambiguous relation on. 
U/IND( R)= {X ∣ ( X ⊆ U ∧ ∀
x∈X,y∈X,∈∈R
( a( x)=
a( y) ) ) }RUY
i
 Represents a set of objects, which can be 
regarded as an equivalence class.Y
i
U/IND( R) Y
i
When the 
intersection with the objective function is not an empty set, 
the upper approximation set requirement is satisfied.Y
i
XY
i
 
According to the theory of singular value decomposition 
(SVD), two classes are divided into three classes. In the 
case of ambiguity, the ambiguous  
information is expressed, and the processing of the 
ambiguous information is realized. This strategy is based 
on human experience and is frequently regarded as correct. 
But, especially when dealing with big datasets, it can be 
labor-time-intensive. The volume of the data may make 
manual interpolation impractical in an industrial big data 
scenario where efficiency and accuracy are critical. 
 
3.2 Specific value imputation 
This algorithm uses a special value to interpolate the 
missing data, which is independent of other eigenvalues. If 
the missing data were all labeled "empty," a completely 
different set of data would be produced, but this would be 
highly biased and generally not beneficial. 
Although the sequential clustering method is used to obtain 
the boundary of the original adjacent interval, there is still 
some uncertainty. There are two types of merging and 
disjunction between two adjacent regions. If the center 
distance between the two spaced groups is small, and the 
sample groups in the interval have high similarity, if the 
stable value between the two intervals is still high, then the 
combination operation is performed. On the contrary, a new 
segment can be formed by splitting the intersecting part of 
the two intervals. 
 
  𝜆 𝑎 =
|𝑉 𝑎 |
𝐹 𝑎                                                                            (2) 
 
It represents a stable region, and the higher its value, the 
less stable it will be. A parameter represents a range. The 
total number of samples in the data represents the width of 
the total sample value of the individual number. Since the 
distribution density of each data is different, a parameter is 
adopted to balance the relationship between the sampling 
frequency and the width of the interval between each 
attribute. The relationship is as follows: 
 
  φ
a
( d
i
)= λ
a
F
d
1
F
+ ( 1 − λ
a
)
W
d
1
W
, λ
a
∈ [0,1]           (3) 
 
The stability of the ordered cluster can be found by using 
this equation. The stability increases with the decrease of 

Interpolation Analysis of Industrial Big Data Based on KDR…                         Informatica 48 (2024) 113–122   117 
 
the stable value. The formula method is used to describe the 
attribute KDR operation degree of numerical values. The 
closer the value is to 1, the smaller the attribute KDR 
operation is, and the higher the attribute KDR operation is. 
Regardless of other eigenvalues, this technique gives 
missing data a unique value. Even if it can be simple, if the 
assigned value is not indicative of the missing data, bias 
might be introduced. Furthermore, it might not fully 
represent the intricacy of industrial data, where missing 
values could have a big influence on studies performed later 
on. 
  
3.3 Average imputation 
In the data set, the eigenvalues are divided into continuous 
and discontinuous values, and the average interpolation is 
carried out according to the size of their eigenvalues. If the 
omission is of continuous type, the missing data are 
interpolated according to the average value of the 
eigenvalue. If the blank is of continuous type, the most (that 
is, the most frequent value) in the eigenvalue of the missing 
data is interpolated according to the method of the statistical 
method. A similar idea is used in the imputation algorithm 
of the conditional mean, that is, the average of the missing 
data is carried out by this algorithm, but it is not selected 
from all the objects in the data set, but obtained from the 
target which is consistent with the target's judged 
eigenvalue. In contrast, the basic idea of both algorithms is 
to use the maximum possible value to insert the missing 
data, but the specific implementation will be different 
depending on the difference in the specific data. Using the 
average eigenvalue as a guide, this method interpolates 
missing data. It is easy to use and straightforward, however, 
it assumes that the dataset is homogeneous, which may not 
be the case in industrial settings where data can be varied 
and heterogeneous. 
 
3.4 Hot card insertion 
Hot card interpolation is looking for and missing from the 
original data collection value closest to the object, the 
object's characteristics and use of interpolation, and through 
the study of the interpolation of the different characteristics 
of the object, and through the data between the 
interconnected to estimate the missing data, its deficiency 
is unable to define similarity and there is much subjective 
influence. 
In this way, a single numerical feature can be assigned to 
the evaluation object. The maximum deviation value 
represents a numerical value as an attribute, and the 
magnitude of the value determines the importance of the 
element. Represents the number of data samples. Is for the 
number characteristic in a pair. This is a special ability. 
Compared with the principal component analysis (PCA) 
method, the variance-based maximum shift method is more 
convenient, but it is not universal and does not involve the 
interaction between attributes. 
MIC, the maximum information, is used to determine the 
correlation of each attribute and is the largest parameter less 
information-based inquiry can not only detect different 
attributes but also find different attributes, to reflect their 
importance. Conventional MIC only studies a single data 
type, 
 
IMIC( a, A)= ∑  
b∈A−a
MIC( a, b)                (4) 
 
Based on MIC, an IMIC algorithm for determining the 
importance of attributes based on MIC is proposed. The 
MIC of each attribute is superimposed with the MIC of 
other attributes to reflect the correlation between each 
attribute, to determine the importance of each attribute 
without supervision. 
In the practical case, we have assumed a normal prosperous 
present value. On this basis, the data sampling values of 
each interval meet the normal allocation, and it is regarded 
as the center point of the interval. Based on the sample size 
represented by the characteristic values of statistical data, 
the interval with the largest sample size in a certain region 
is regarded as the center of the cluster. 
 
KL
i
= ( f( d
i
)− f( d
i−1
) ) /( d
i
− d
i−1
)
KR
i
= ( f( d
i
)− f( d
i+1
) ) /( d
i
− d
i+1
)
K
i
= KL
i
× KR
i
                (5) 
 
This technique uses the properties of neighboring values in 
the dataset to approximate missing data. However, defining 
similarity and figuring out which values are closest might 
be subjective, which could produce biased findings, 
particularly in intricate industrial datasets with a variety of 
features. 
 
3.5 K-adjacent interpolation 
This algorithm is based on the nearest K sampling values of 
the object to the missing data and uses the weighted average 
of the K sampling values to estimate [3]. K-nearest 
neighbor interpolation uses the hierarchical clustering 

118   Informatica 48 (2024) 113–122                                                                    C. Yao et al. 
pattern to estimate the missing data class and interpolates 
the average of this class. 
The idea is to insert all the values in the missing data and 
see if the inserted values achieve the best interpolation 
result. As you can imagine, such an algorithm is indeed a 
good solution in the case of a small amount of data, but if 
the number of data is too large, the data is lost too much, 
and a lot of data is needed, so a lot of data is needed to test. 
To prove that the data has the characteristics of regularity, 
that is data clustering. By the degree of concentration of 
these data, we can find the average value in these data. In 
this paper, the statistics and analysis of Sat image in UCI 
are presented. 
On this basis, the maximum shift method is used to solve 
the attribute importance. The larger the value of variance is, 
the existence of the item is indicated. 
The higher the uncertainty, the higher the importance. The 
specific algorithm is as follows: 
 
Y
a
i
= ∑  
n
j=1
∑  
n
k=1
√(
v
j
−v
i
k
W
a
i
)
2
, i = 1,2, … , k                   (6) 
 
Using the closest K sampling values, this technique predicts 
missing data. Despite providing a mathematical 
methodology and its efficacy may differ based on the 
distribution and features of industrial big data. 
 
 
3.6 A comprehensive approach 
This method also allows for a test on the missing data, with 
the difference that the inserted data is the best of the final 
attribute reductions to be used as an interpolation for the 
missing data. This algorithm can improve the accuracy of 
the algorithm on the premise of increasing the complexity 
of the operation. Obviously, in the case of big data, there 
will be a lot of loss of these data, so this algorithm can 
obtain good interpolation accuracy, but it costs a lot of time. 
Most of the commonly used methods for missing 
information interpolation are regression-based methods. 
However, all regression methods are built based on 
complete data, so the data should be pre-processed. In the 
case of missing data, the known feature quantities are used 
to predict, and the method is used to predict the missing 
data. This paper also focuses on the interpolation method of 
the missing data. The solution of MIC value is the largest 
way of parameter-less search based on data. According to 
the experimental results of reference [66], the larger the 
MIC value, the greater the correlation between the two 
properties. If the MIC of both personalities is 1, it indicates 
that there is a linear relationship between the two 
personalities’ divides the two-dimensional data into grids, 
and accumulates the mutual information in the grids to 
obtain the initial mutual information system. Finally, the 
cumulative value obtained from the different grid 
assignments is the MIC value, square formula (2.7).MIC 
can be used to find out the direct relationship of each 
attribute, as well as their internal relationship, to reflect the 
importance of each attribute. 
 
MIC( a, b)=
max
n×m<𝐵  (
∑  
x∈X,y∈Y
 P( x,y)log
P( x,y)
∑  
x∈X
 P( x,y)∑  
y∈Y
 P( x,y)
)
log m {n,m}
)             (7) 
 
Each interval in the core interval is represented by the 
traditional interval representation, and the cut points in each 
interval are obtained by the static singular value 
decomposition (SVD) algorithm based on the data samples. 
These cut points are supported by the data, and the 
corresponding attribute values can be found in the original 
data samples [15-17]. 
 
ED
a
= {[p
min
, p
1,3
) , [p
1,3
, p
2,3
) , … , [p
k−1,3
, p
max
]}    (8) 
 
BD
a
= {( p
1,2
, p
2,1
) , ( p
2,2
, p
3,1
) , … , ( p
k−1,2
, p
k,1
) }      (9) 
 
Each interval in the blank interval is represented by the 
traditional interval representation, and each interval is 
based on the interval segments not included in the 
corresponding core interval set, as shown in Table 2 below: 
 
Table 2: Case table of singular value decomposition 
theory 
u
1
 b c d 
u
2
 0.8 2 1 
u
3
 1 0.5 0 
u
4
 1.3 3 0 
u
5
 1.4 1 1 
u
6
 1.4 2 1 
u
7
 1.6 3 1 
 

Interpolation Analysis of Industrial Big Data Based on KDR…                         Informatica 48 (2024) 113–122   119 
 
Data are assumed to be incremented over time, and the 
nature of numerical data follows a normal assignment. If a 
data set containing numeric characteristic data is entered at 
a certain time, the continuity between all characteristics of 
the data is taken into account, so that the resulting data 
intervals have a certain order, that is, a priority in the case 
of sequence clusters. On this basis, firstly, the feature set of 
numbers is extracted to determine the importance of the 
attributes of the numbers, and then the corresponding 
attribute set is obtained by sorting the numbers in order of 
size. The expected KDR digit feature is regarded as the net 
ranking of each data in the sequence cluster, and the 
sequence clustering method is used to sort the unlabeled 
information to obtain the three interval sets of the initial 
KDR operation. Then, the uncertain regions in the middle 
are re-evaluated and segmented, and then the original data 
is KDR operation. Finally, the data set after the unlabeled 
KDR operation is obtained by successive KDR operations 
on the numeric attribute group. These features include the 
features of the KDR operation and the features of the KDR 
operation, and then these features are introduced into the 
new separated features. In this method, the dynamic KDR 
operation method is adopted, and the combination process 
is carried out to obtain a new KDR operation information 
system. Although it requires more computer power and 
complexity, this method combines several approaches to 
increase interpolation accuracy. In industrial settings where 
precision is crucial, this method might make up for the extra 
computing burden. 
4   Result analysis 
In Table 3 below, statistics of the NB algorithm are 
performed on the data after the KDR operation. In general, 
the NB algorithm has the same good performance as the 
Euonymus algorithm. From a personal point of view, this 
method is better than EF1l, EW9, and EF_Unique7.In 
general, the results of 27 out of 33 trials were better than 
those of the control method, reaching 81.82%. The average 
accuracy of the proposed method was 82.53%, ranking first. 
Compared with 81.07, which ranked second, it increased by 
1.46 percentage points. The statistical analysis of the 
suggested approach combining KDR operation with NB, 
KNN, and C4.5 algorithms will yield encouraging results. 
With a noteworthy gain of 1.46 percentage points over the 
second-ranking approach, the average accuracy of 82.53% 
beats alternative methods. Furthermore, with 81.82% of 
trials producing better outcomes than control approaches, 
the suggested strategy shows a significant improvement 
over other method. The suggested approach specifically 
shows superiority in 78.79% of cases with respect to recall 
rates and precision, indicating its efficacy in classification 
tasks. The advantages of the suggested technique are 
particularly evident when compared to rule-based systems, 
as demonstrated by the C4.5 process's lower production of 
leaf nodes. These results highlight how important it is to 
combine different methods to improve classification 
efficiency and accuracy. Moreover, the technique's 
enhanced performance in comparison to well-known 
algorithms like Euonymus, EF1l, EW9, and EF_Unique7 
highlights its potential for real-world uses. The statistical 
tests validate the importance of these results, indicating the 
robustness and dependability of the suggested approach in 
successfully handling classification problems. 
In this method, KNN and NB methods were used to 
calculate KDR operation data, and C4.5 was used to 
analyze KDR operation data. In a single aspect, this method 
is 6 times better than the EF algorithm, 8 times better than 
the EW method, and 6 times better than the Euonymus 
method. In general, the total number of times was 20, and 
the proportion was 60.61%. As a rule-based method, C4.5 
will produce incomplete rules when the real rules are 
generated, which makes some problems difficult to classify 
accurately when conducting experiments. Therefore, we 
also make a statistic for the average recall rate of each data 
set. Comparison results show that the effect of this method 
is better than that of the control method in 26 cases, 
reaching 78.79%.On this basis, the average precision and 
average recall of the proposed algorithm have reached a 
good level. The number of leaf nodes produced by the C4.5 
process is illustrated. As can be seen in Table 3 and Figure 
1, after adopting the method of the invention, the number 
of leaf nodes produced is less than the others. 
Table 3: Schedule of dynamic Singular value 
Decomposition theory 
Time( ms) 80 60 50 
HTRU2 354743 228578 195755 
A villa 205466 135768 124841 
B an 3950123 1528104 1481980 
Shuttle 2306469 2007489 1477111 
 

120   Informatica 48 (2024) 113–122                                                                    C. Yao et al. 
 
Figure 1: Scheduling performance of dynamic SVD theory 
 
The performance of several algorithms, including KNN, 
KDR, PLS, and SVD-KDR, over various time intervals is 
shown in the Table 4 and Figure 2. KNN reaches 0.1 
accuracy at 5%-time allocation, while KDR reaches the 
highest at 0.8. With 0.7 accuracy, KDR holds its lead when 
time rises to 10%. Fascinatingly, PLS and SVD-KDR both 
exhibit robustness and efficiency in time-sensitive tasks, 
consistently obtaining 0.9 accuracy or above across all time 
intervals. 
 
Table 4: Outcomes of interpolation method  
 
Missing 
percentage  
Interpolation method 
KNN KDR PLS SVD-
KDR 
5 0.1 0.8 0.9 1.0 
10 0 0.7 0.8 0.9 
15 0.1 0.3 0.9 1.0 
20 0.0 0.1 0.9 1.0 
25 0 0.1 0.9 1.0 
  
 
Figure 2: Comparison of interpolation method 
 
Three algorithms, KNN, NB, and C45 are used in the 
experiments. The above studies show that the algorithm is 
effective for unsupervised data processing. In the NB and 
C4.5 methods, better results are obtained. 
In the industrial big data environment, based on the 
characteristics of industrial data, this paper proposed a 
decentralized problem method based on industrial big data. 
In this paper, the definition of KDR computation and the 
research status at home and abroad are described in detail. 
This paper focuses on the basic principle of bidirectional 
selection and related theories at home and abroad. At 
present, most of the KDR calculation methods are only used 
to deal with static data and do not pay attention to the 
dynamic change of data. Therefore, this paper will further 
discuss the kinetic characteristics of KDR and Industrial big 
data analysis from the perspective of kinetics. There are 
three main aspects of this study: 
 
4.1 A dynamic model of KDR operation is 
established by using a three-branch decision 
In the case of Industrial imputation data, due to the dynamic 
nature of the original data, the relationship between the 
original data and the new time data cannot be guaranteed 
when KDR operation is carried out. When there is a big 
difference between the new and old-time data, it will cause 
an unsatisfactory separation. However, most of the current 
KDR computational theories ignore the dynamic properties 
of the data. To solve this problem, a dynamic data analysis 
method based on KDR operation is established by taking 
into account the singular value decomposition theory. This 
model can be divided into two categories: static and 
dynamic. Firstly, the static KDR operation method is used 
to perform the initial KDR operational processing at each 

Interpolation Analysis of Industrial Big Data Based on KDR…                         Informatica 48 (2024) 113–122   121 
 
time point. On this basis, the interval method is used to fuse 
the KDR operation information at each time point. In 
consideration of singular value decomposition (SVD) 
theory, the delay decision method considering SVD theory 
is introduced, and the original interval is replaced by the 
form of a three-branch interval. In dynamic fusion, only the 
core region is fused, the existing blank region is discarded, 
and the delay method is used to segment the blank region. 
Lastly, the accuracy of the suggested analysis algorithm is 
confirmed using the UCI test results. The technique has a 
promising future for KDR computational processing of 
dynamic data, according to the experimental results. 
 
4.2 Three-branch interval method taking into 
account singular value decomposition theory 
According to the kinetic characteristics of Industrial 
imputation data, the three-branch interval analysis method 
is given. To solve the problem that the boundary of the 
KDR operation interval is uncertain in dynamic data, this 
paper uses the method of considering singular value 
decomposition (SVD) to redefine it, so that it cannot only 
express the boundary of the region but also update the edge 
of the dynamic region in real time. After describing the 
space interval, the space interval is used to distribute the 
space appropriately, to achieve dynamic adjustment of the 
KDR operation interval for massive information, and to 
solve the attribute KDR operation problem of incremental 
big data. The gap between the three root intervals can not 
only show the change in the region but also dynamically 
adjust the region according to the size of the space. 
 
5  Discussion  
The time measurements in milliseconds (ms) for the various 
tasks completed by HTRU2, A villa, B an, and Shuttle are 
shown in this table. A separate entity is represented by each 
row, and a different time condition 80, 60, and 50 
milliseconds is represented by each column. For example, 
HTRU2 took 354,743 ms to finish its assignment under the 
80 ms condition, while A villa took 205,466 ms, B and took 
3,950,123 ms, and Shuttle took 2,306,469 ms. under a 
similar vein, HTRU2 took 228,578 ms, A villa took 
135,768 ms, B and took 1,528,104 ms, and Shuttle took 
2,007,489 ms under the 60 ms condition. In the end, 
HTRU2 took 195,755 ms, A villa took 124,841 ms, B and 
took 1,481,980 ms, and Shuttle took 1,477,111 ms under 
the 50 ms constraint. Singular value decomposition (SVD) 
theory is incorporated into our study's dynamic KDR 
operating model for industrial big data interpolation, which 
takes into account the incremental nature of data 
accumulation. Notably, our strategy deviates from static 
techniques that are common in the literature and frequently 
ignore the dynamic change of data over time. We guarantee 
the consistency of KDR calculation results under dynamic 
situations by combining SVD theory with a rough set 
approach based on Manilkara. By contrasting our findings 
with previous research, we find that most algorithms are not 
built to take into consideration the incremental nature of 
industrial data because they are intended for static KDR 
processes. By overcoming this gap and offering a thorough 
foundation for dynamic interpolation, our methodology 
makes a novel contribution. Moreover, our methodology 
enables a more precise depiction of changing data trends, 
augmenting the resilience and dependability of industrial 
big data examination. We show the unique qualities and 
benefits of our suggested model through this comparative 
analysis, opening the door for more developments in the 
area. 
 
5.1 Limitations  
There are drawbacks to the suggested dynamic KDR 
operation model that integrates the rough set method with 
SVD theory. Its computational complexity might make it 
difficult to use with very large datasets. Additionally, 
problems with data quality or outliers may make it less 
effective to combine old and new data. Dependence on 
theoretical frameworks such as SVD may restrict the 
application to a variety of commercial datasets, 
necessitating rigorous cross-domain validation.  
 
6  Conclusion  
Although there has been research on the non-monitoring 
nature of interpolation in industrial big data, these problems 
caused by interpolation have not been completely solved. 
In the processing of industrial big data, there is often a lack 
of data. For such incomplete dynamic KDR operational 
methods, there is still a lack of relevant theories and 
methods at home and abroad. The processing of missing 
data often leads to the loss of data and thus affects the 
analysis of data. Therefore, considering the theory of 
singular value analysis, it is a very promising solution to 
explore the KDR operation. The study of industrial big data 
interpolation is still beset with numerous issues. According 
to the statistics of the industrial data, it is found that the data 
is extremely uneven. The root cause of the problem is that 

122   Informatica 48 (2024) 113–122                                                                    C. Yao et al. 
the consistency between the pre-KDR and the interval is 
guaranteed by using a wide range of cell merging. 
Therefore, the correctness of the algorithm can be tested by 
using UCI data. Experiments show that the algorithm can 
not only solve the non-monitored static data effectively but 
also separate the non-monitored dynamic data effectively, 
which provides a useful reference for the subsequent KDR 
computation of dynamic data. 
 
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