Privacy Preservation for Machine Learning in IIoT Data via Manifold

Learning and Elementary Row Operations

E. Fatih Yetkin

and Tu

gc¸e Ballı

Department of Management Information Systems, Kadir Has University, Istanbul, 34083, Turkey

Keywords:

Privacy Preservation, IIoT, Manifold Learning, Machine Learning.

Abstract:

Modern large-scale production sites are highly data-driven and need large computational power due to the

amount of the data collected. Hence, relying only on in-house computing systems for computational work-

ﬂows is not always feasible. Instead, cloud environments are often preferred due to their ability to provide

scalable and on-demand access to extensive computational resources. While cloud-based workﬂows offer nu-

merous advantages, concerns regarding data privacy remain a signiﬁcant obstacle to their widespread adoption,

particularly in scenarios involving sensitive data and operations. This study aims to develop a computation-

ally efﬁcient privacy protection (PP) approach based on manifold learning and the elementary row operations

inspired from the lower-upper (LU) decomposition. This approach seeks to enhance the security of data col-

lected from industrial environments, along with the associated machine learning models, thereby protecting

sensitive information against potential threats posed by both external and internal adversaries within the col-

laborative computing environment.

1 INTRODUCTION

Since the advent of the Industrial Internet of Things

(IIoT), companies have been able to operate more ef-

ﬁciently, enhancing production quality and reducing

costs (Raptis et al., 2019). A well-known example

includes manufacturing companies transferring their

IIoT data to a ML-based third party service or a cloud

system for processing to facilitate predictive mainte-

nance (Hongxia et al., 2016). However, IIoT data of-

ten contains sensitive information related to produc-

tion processes, which poses a risk of information leak-

age for companies (Hindistan and Yetkin, 2023).

Modern large-scale production systems are highly

data-driven and need large computational power due

to the amount of the data collected. Therefore, it is not

always possible to use the in-house computing sys-

tems for the computational workﬂow. Indeed, mostly

the cloud environment is preferred since it can pro-

vide a large amount of computing resources on de-

mand (Soveizi et al., 2023). Although cloud-based

workﬂows offer numerous advantages, security con-

cerns remain a signiﬁcant barrier to their adoption,

particularly in applications involving sensitive data

and operations (Varshney et al., 2019).

Outsourcing workﬂows or parts of them to cloud

https://orcid.org/0000-0003-1115-4454

https://orcid.org/0000-0002-6509-3725

systems result in the losing control over certain tasks

and data, potentially increasing security vulnerabili-

ties and exposing workﬂows to a heightened risk of

malicious attacks (Soveizi et al., 2023).

The security challenges in cloud computing arise

from shared infrastructure and data transmission over

potentially untrusted networks, along with dynamic

operational conditions which can bind to cloud ser-

vices that may later reveal security vulnerabilities.

Additionally, cloud providers, while adhering to pro-

tocols, may still attempt to infer sensitive informa-

tion about users’ data and workﬂow logic. There are

many attempts in the literature to handle these privacy

issues which are particularly important for industrial

data that can possibly impact the daily life of people

both digitally and physically.

To address these issues, this work extends the ex-

isting privacy preservation (PP) approaches by im-

plementing two distinct mechanisms before sharing

the data in collaborative environment: a) The feature

space created within in-house computing systems will

be projected onto a manifold via a nonlinear transfor-

mation to hide its physical properties while preserving

its mathematical properties. However, this approach

alone does not fully secure the data in untrusted en-

vironments, such as cloud platforms and also it is not

a certain prevention mechanism for reconstruction or

model inversion attacks, particularly for in-company

intruders. b) A random reversible permutation will

Yetkin, E. F. and Ballı, T.

Privacy Preservation for Machine Learning in IIoT Data via Manifold Learning and Elementary Row Operations.

DOI: 10.5220/0013275000003899

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 11th International Conference on Information Systems Security and Privacy (ICISSP 2025) - Volume 2, pages 607-614

ISBN: 978-989-758-735-1; ISSN: 2184-4356

607

be applied onto the input and output of the reduced

model to ensure its privacy by using a appropriate

seed. Perturbation mechanism, designed as a one-way

function will hide the relevant information from the

intruders. This mechanism will be easy to solve in

forward direction but infeasible in reverse direction.

The proposed approach can be interpreted as a com-

bination of performing dimensionality reduction and

adding random noise to the reduced subspace.

The rest of this paper organized is as follows. In

the next section, we will discuss about related works.

In methodology section, the proposed approach will

be depicted. Since it is an ongoing work we will

show our preliminary results with a single experimen-

tal dataset collected for predictive maintenance pur-

poses in numerical experiments section. Finally, we

will discuss the future studies in the conclusion sec-

tion.

2 RELATED WORKS

The standard approach for the protection of the data

privacy is called differential privacy. This approach

is based on probability theory for ensuring the pri-

vacy (Dwork et al., 2014a). Even though it has sev-

eral advantages, differentially private algorithms may

exhibit errors that are inﬂuenced by the intrinsic di-

mension n of the input data, therefore Dwork et.al.,

proposed an approach based on PCA to reduce the di-

mensionality of the input data (Dwork et al., 2014b).

There are also many attempts in literature exploring

the randomized projections as a means of implement-

ing privacy mechanisms (Kung, 2017). Those ap-

proaches are mainly based on adding a noise matrix

to the original data before the calculation of the asso-

ciated covariance matrix (Blum et al., 2005). As dis-

cussed in (Hindistan and Yetkin, 2023), noise addition

can still be considered a reliable privacy meachanism

especially when combined with a generative adver-

sarial network (GAN) based syntheticization mecha-

nism. Other common approach involves using cryp-

tographic methods such as Homomorphic Encryp-

tion (Yi et al., 2014), Garbled Circuits (Frederiksen

et al., 2015) and Secret Sharing (Bogdanov et al.,

2018). However, cryptographic approaches are com-

putationally very expensive and they may not be fea-

sible for application especially with large scale data

sets(Al-Rubaie and Chang, 2019).

3 METHODOLOGY

Privacy protection schemes should rely on a speciﬁc

scenario. In our case, we focused on a scenario sim-

ilar to the scenario discussed in (Kung, 2017). Un-

like the traditional communication based scenarios,

we consider four parties in our case. The data owner,

trusted third party, malicious actors from the external

network, and from the collaborative computing sys-

tem (or with traditional namings; Alice, Bob, Eve1,

and Eve2 respectively). Here, we are aiming to con-

vey the sensitive data from Alice to Bob by hiding

its internal statistical dynamics from both Eve1 and

Eve2. Therefore, we designed our experimental setup

as depicted in Fig. 1. The main purpose of our study

is to increase the privacy of the data collected from

industrial environment while preventing the possibil-

ity of extracting additional information from the data

and the model by the malicious actors from outside

or inside the network. Besides, we aim to protect

the model parameters from the intruders. In Fig. 1

we assume there are two possible intrusions from the

perspective of data privacy: a) outside (Eve1) and b)

inside (Eve2) the collaborative network environment.

Overall, this mechanism is based on hiding the raw

data as much as possible from the third parties includ-

ing the trusted ones.

The protection mechanisms offered in this study

has two phases. In the ﬁrst phase, the produced fea-

ture space will be projected onto a manifold via a non-

linear transformation. Since it is an ongoing study

we have only used the Laplacian Eigenmaps (Belkin

and Niyogi, 2003), on the other hand there are more

advanced and ﬂexible supervised mechanisms (met-

ric learning approaches) to improve the overall pri-

vacy attack mitigation schemes, such as Large Mar-

gin Nearest Neighbours (LMNN) (Weinberger and

Saul, 2009) and Neighborhood Component Analysis

(NCA) (Goldberger et al., 2004).

Since the main focus of this work is to understand

the effect of dimensionality reduction with elemen-

tary matrix operations on privacy, we kept the reduc-

tion order as n − 1 which corresponds to a single fea-

ture removal from the overall dataset. After removing

one feature from the data via non-linear projection,

the data will lose its physical meaning, but as already

discussed in (Dwork et al., 2014b), it is not a certain

prevention mechanism for model inversion attacks es-

pecially the ones from the in-company intruders. As

a well-known fact, the Laplacian eigenvectors keep

most of the relevant information arising from the raw

data. Therefore, to ensure its privacy, as the second

phase of the implementation, the input matrix of the

reduced model should be perturbated. For this pertur-

ICISSP 2025 - 11th International Conference on Information Systems Security and Privacy

608

Figure 1: Illustration of the proposed approach.

bation, we followed a very basic idea arising from the

well-known LU decomposition (Golub and Van Loan,

2013). This decomposition has been in use for a long

time and it is also employed in several authentication

mechanisms (Li et al., 2013). The LU decomposition

consists of several operations based on permutation

(P) and elementary (E) matrices. The most important

property of both P and E matrices is that their inver-

sion is straightforward as the matrices are orthogo-

nal, which in turn simpliﬁes reversal of perturbation.

The mathematical model of this study is based on this

property.

3.1 Proposed Approach

Let X ∈ ℜ

m×t

represent a univariate time series data

collected from IIoT devices with corresponding labels

as y ∈ ℜ

m×1

. In standard machine learning pipeline

for time series, the features are extracted from the X

with a ﬁxed segment interval s where t = s × n and

the resulting data matrix is given as

X ∈ ℜ

m×n

. Once

the data matrix is obtained, it is always possible to re-

duce its dimension via linear or non-linear dimension-

ality reduction methods. In our approach, we used

one of the well-known manifold learning approaches,

namely the Laplacian Eigenmaps (LE). This method

is based on construction of a neighborhood graph of

the

X, and accordingly related weighted adjacency

(W ) and degree matrices (D). Then, the Laplacian of

the data matrix can be deﬁned as L = D −W . As dis-

cussed in (Belkin and Niyogi, 2003), it is indeed pos-

sible to construct an optimization problem to keep the

geometrical properties of the data in a lower dimen-

sional problem and the solution of this minimization

problem can be determined as a set of small eigen-

pairs of the generalized eigenproblem deﬁned in Eq.1

as follows:

Lv = λDv (1)

where λ is an eigenvalue and the v is the associated

eigenvector. If the reduction dimension is selected as

r, then V ∈ ℜ

m×r

will contain the eigenvectors associ-

ated with the r smallest eigenvalues of the generalized

eigenproblem given in Eq. 1. The reduced raw data

will be obtained as

= V . In this way, the raw data

will never be shared with the third parties since this

transformation is irreversible without knowing the as-

sociated eigenvalues of Eq. 1.

As dimensionality reduction preserves the intrin-

sic behavior of the data and is proposed as a solution

of the curse of dimensionality problem, it serves as

a strong candidate for maximizing the utility func-

tion in privacy preservation (Dwork et al., 2014b).

Even though the raw data still be stored at the in-

house computational environments, data behavior is

still vulnerable and intruders may use the reduced

data to build malicious machine learning models to

Privacy Preservation for Machine Learning in IIoT Data via Manifold Learning and Elementary Row Operations

609

violate data privacy. Therefore, we proposed a second

mechanism which will be realized at in-house compu-

tational systems to avoid internal threats arising from

collaborative environment (see Fig. 1).

One efﬁcient way of solving a linear equation sys-

tem is based on decomposition of the n-dimensional

coefﬁcient matrix A as the product of lower (L) and

upper (U) triangular matrices as A = LU. The proce-

dure is called the LU decomposition and start with

multiplying the matrix A from left with unit lower

diagonal elementary matrices to obtain an upper tri-

angular representation of the matrix A. An elemen-

tary matrix which can be useful for this purpose is

deﬁned as an identity matrix (I) with a nonzero ele-

ment in lower diagonal part and corresponds to the el-

ementary row operations (multiplication, subtraction

or addition). Formally any matrix obtained from iden-

tity matrix with a single elementary row operation is

called an elementary matrix (Strang, 2000). After a

successful decomposition, the matrix U can be writ-

ten as,

k−1

. . . E

A = U (2)

where k is the required number of the row operations

to transform the matrix A into upper triangular matrix

U. Then, if one multiply the both sides of Eq. 2 with

the inverses of each elementary matrix in a reverse or-

der one can obtain the LU decomposition as follows,

−1

. . . E

−1

k−1

. . . E

A = E

−1

. . . E

−1

A = E

−1

. . . E

−1

where L = E

−1

. . . E

−1

. Computing the inverse of

a unit lower elementary matrix E

is an operation that

is computationally very efﬁcient. If the non-zero en-

try of the E

is given as e

k j

where k and j are row and

column indices respectively, E

−1

will be simply equal

to the same matrix with −e

k j

. We will use this prop-

erty of unit lower elementary matrices to produce a

set of randomly selected elementary row operations to

modify the originally reduced data matrix

to a

For implementation, randomly produced indices and

a set of random elementary operation coefﬁcients are

produced at the on-site computational environment as

E and perform the operation

= E

. This opera-

tion easily be reversed by using the inverse of matrix

E. This matrix can be reproducible if the required

seed is available at any trusted third party. Note that

even if the elementary operations are reversed, still

the original feature space will be hidden at any party.

Therefore, the important beneﬁts of using this algo-

rithmic approach can be listed as follows:

• The raw data (X) and the original feature matrix

(

X) are never necessary to be shared with any third

parties.

• The perturbation with elementary row operations

can be easily reversed by any trusted third party

via the regeneration of matrix E with the shared

seed. The seed can be shared with the trusted

third party by any encrypted exchange algorithm

(such as the Difﬁe-Hellman key exchange algo-

rithm (Merkle, 1978)).

• Intruders from inside or outside of the collabo-

rative environment (such as a cloud system) can

only have access to

, which prevents the con-

struction of malicious models.

Even though the numerical results are promising,

there is a need for more investigations from theoreti-

cal and numerical perspectives.

4 NUMERICAL EXPERIMENTS

4.1 Dataset

We have used an experimental dataset collected at

a lab environment (Loparo, 2012). This dataset is

a well-known benchmarking dataset especially for

malfunction classiﬁcation based on vibration sig-

nals for production environment (Smith and Ran-

dall, 2015), (Sauﬁ et al., 2023). Experiments were

carried out using a 2-horsepower Reliance Electric

motor, with acceleration data collected from mea-

surement points both proximal and distal to the mo-

tor bearings. Faults were artiﬁcially induced in the

motor bearings through electro-discharge machining

(EDM), with defect sizes ranging from 0.007 inches

to 0.040 inches in diameter. These faults were intro-

duced individually at the inner raceway, rolling ele-

ment (ball), and outer raceway. The faulted bearings

were subsequently reinstalled in the test motor, and

vibration data was recorded under motor loads vary-

ing from 0 to 3 horsepower, corresponding to motor

speeds between 1797 and 1720 RPM. The dataset in-

cludes three fault cases in addition to normal condi-

tions: a) outer race, b) inner race, c) bearing. The ma-

chine learning model, therefore, can be considered as

a four-class problem. The distribution of the data with

respect to its labels in the original dataset is shown

in Fig. 2 using t-SNE reduction (Van der Maaten and

Hinton, 2008).

4.2 Data Pre-Processing Pipeline and

Machine Learning Models

In the experimental setup, we have created four sce-

narios for comparing and evaluating the machine

ICISSP 2025 - 11th International Conference on Information Systems Security and Privacy

610

Figure 2: Distribution of the original features in 2-

dimensional t-SNE projection space.

learning accuracy performance and privacy preserva-

tion properties. In the ﬁrst setup, we created our

baseline, which is the application of several tradi-

tional machine learning algorithms on the dataset.

We considered three main types of machine learn-

ing approaches: a) linear models (logistic regression

(LR) and Support Vector Machine (SVM)), b) tree-

based models (Decision tree (DT), Random Forest

(RF), c) an instance-based model (k nearest neighbors

(KNN)). All experiments are realized with a 10-fold

cross-validation. To extract features from the X, we

choose the segment length as 1000, then extract stan-

dard statistical features such as the mean, standard de-

viation, root mean square, variance, and median. Note

that since we have restricted our discussion to the im-

pact of the proposed approach on privacy preserva-

tion, we did not implement more sophisticated feature

extraction methods.

4.3 Comparison of ML Accuracy

Values: Utility Perspective

In general, any privacy preservation technique should

have a balance between utility and privacy. In the ﬁrst

set of experiments, we compared the performance of

various machine learning approaches with respect to

different execution paths. The execution paths con-

sidered in these experiments can be listed as follows,

• Case-I: Apply ML methods with 10-fold cross-

validation to the

• Case-II: Apply ML methods with 10-fold cross-

validation to the LE applied reduced data

• Case-III: Apply ML methods with 10-fold cross-

validation to the perturbed

= E

X for various

different number of elementary row operations,

• Case-IV: Apply ML methods with 10-fold cross-

validation to the perturbed

= E

for various

different number of elementary row operations,

In Figs. 3, 4, and 5, we represents the change of

the accuracy values for algorithms under four execu-

tion path discussed above. For LE application, we

considered the reduction dimension as r = 4 without

optimizing the intrinsic dimension.

Figure 3: Accuracy behaviour of Decision Tree algorithm

under different execution scenarios.

In Fig.3, the effect of low number of eleman-

tary matrix operations on utility for both Case-III and

Case-IV is depicted. As we can see from the ﬁgure,

Case-IV has also positive impact on utility with re-

spect to Case-III even for high number of row opera-

tions.

Figure 4: Accuracy behaviour of Logistic Regression algo-

rithm under different execution scenarios.

However, in Fig.4, both Case-III and Case-IV cre-

ates a dramatical decrease on accuracy of the LR al-

gorithm. This can be expected since the LR algo-

rithm is driven by a linear hyphothesis function and

Privacy Preservation for Machine Learning in IIoT Data via Manifold Learning and Elementary Row Operations

611

elementary row operations are malfunctioning the ex-

isting linear relations in between the data samples.

The same effect can be visible for the SVM algorithm

(see Table.1). The instance based algorithm, KNN,

Figure 5: Accuracy behaviour of KNN algorithm under dif-

ferent execution scenarios.

also produced a similar behavior with the DT algo-

rithm and it presented in Fig 5. The comparison of

the whole algorithms including the RF and SVM for

the Case-IV, is shown in the Table 1.

4.4 Comparison of Data Distributions:

Privacy Perspective

In the second experiment, we presented the change in

the data distribution with respect to the given labels

by using linear (PCA) and non-linear (t-SNE) dimen-

sionality reduction. As shown in Figs. 3 and 5, the

low number of elementary row operations does not af-

fect the utility in terms of the accuracy of the DT and

KNN algorithms. Therefore, we selected the num-

ber of the elementary row operations 500 for Case-III

and Case-IV and created the 2-dimensional represen-

tations of all cases with PCA and t-SNE. As clearly

seen from Fig. 6, the LE method (Case-II) does not

affect the data distribution; however, even for a very

small number of perturbations (relatively to the data

dimension where n = 6650), linear projections of the

data change entirely in both Case-III and Case-IV. It

can also be considered as an explanation of the accu-

racy behavior of LR and SVM algorithms with Case-

III and Case-IV (see Table 1). A similar behavior

can be observed from the non-linear projection of the

data in Fig. 7. However, in this ﬁgure one can ob-

serve that Case-IV signiﬁcantly affects data distribu-

tion while the separability of the data is still protected.

Therefore, the numerical results show that Case-IV

improves the privacy (in terms of distribution of the

data) while preserving its utility.

5 DISCUSSION AND FUTURE

STUDIES

In this work, we proposed a hybrid mechanism based

on manifold learning (LE) and the elementary row

operations inspired by the well-known LU decompo-

sition. As shown in the numerical experiments sec-

tion, applying the low number of elementary row op-

erations retains the accuracy behavior, especially for

the tree and instance-based classiﬁers. This observa-

tion (after theoretical validation) can be used to es-

tablish a privacy preservation protocol that consid-

ers the reduction order r and the number of the el-

ementary row operations as parameters. Although

we employed accuracy as the only metric for eval-

uating the utility of the data, we plan to extend our

study to show the balance between utility and privacy

by covering several theoretical and practical aspects

arising from the privacy preservation literature. Be-

sides, in future work of this study, we will compare

our proposed approach with the state-of-the-art pri-

vacy preservation techniques discussed in Section 2.

Even though the numerical results depicted that the

proposed approach is promising for balancing utility

and privacy, several issues should be evaluated care-

fully. This study used visual data distributions as the

primary evaluation method for privacy preservation.

However, we plan to develop a solid privacy evalu-

ation procedure based on a technical privacy metric

such as entropy-based approaches deﬁned in (Wagner

and Eckhoff, 2018). Furthermore, we have used a sin-

gle IIoT dataset in our experiments, and it should also

be extended to a set of experiments. Lastly, we are

also planning to investigate the theoretical reasons for

the behavior of Case-IV to establish a solid explain-

able mechanism to improve the usability of the pro-

posed approach.

6 CONCLUSION

This study aims to propose a privacy protection mech-

anism that can balance utility and privacy. For the

implementation, the data owner selects the number

of the elementary row operations as a parameter and,

according to the privacy policy related to data, can

share the random seed required for the reproduction

of the matrix E with trusted third parties. If the util-

ity is the priority for the selected case, then the num-

ber of the elementary row dimensions (or the number

ICISSP 2025 - 11th International Conference on Information Systems Security and Privacy

612

Table 1: Comparison of the accuracy performance of several ML algorithms under various conditions.

# of Elementary Matrix Operations

Original LE 500 1500 2500 3500 4500 5500 6500

LR 0.72 0.77 0.31 0.29 0.29 0.29 0.29 0.29 0.30

KNN 0.81 0.82 0.80 0.76 0.75 0.72 0.70 0.69 0.67

SVM 0.79 0.78 0.29 0.29 0.29 0.29 0.29 0.29 0.29

DT 0.82 0.80 0.82 0.78 0.69 0.65 0.64 0.63 0.60

RF 0.83 0.80 0.82 0.79 0.76 0.74 0.74 0.71 0.69

Figure 6: Distribution of the features in 2-dimensional PCA projection space with several different application scenarios.

Figure 7: Distribution of the features in 2-dimensional t-SNE projection space with several different application scenarios.

Privacy Preservation for Machine Learning in IIoT Data via Manifold Learning and Elementary Row Operations

613

of nonzero elements in the matrix E) can be set to a

lower value. The numerical results are promising, and

future studies of this work will focus on developing

the theoretical basis of the proposed approach.

ACKNOWLEDGEMENTS

This research was supported by the European

Union in the Framework of ERASMUS MUNDUS

project (CyberMACS) (https://www.cybermacs.eu)

under grant number 101082683.

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