Comparison of Dimension Reduction Methods for Multivariate Time

Series Pattern Recognition

Patrick Petersen

, Hanno Stage, Philipp Reis

and Jonas Rauch and Eric Sax

FZI Research Center for Information Technology, 76131 Karlsruhe, Germany

Keywords:

Pattern Recognition, Dimension Reduction, Motif Discovery, Time Series Data Mining.

Abstract:

Large volumes of time series data are frequently analyzed using unsupervised algorithms to identify pat-

terns. Multivariate time series’s time and space complexity poses challenges in this context. Dimensionality

reduction, a common technique in data science, provides a viable solution to improve time and space complex-

ity. Nevertheless, a crucial question arises concerning how the time advantage compares to the information

loss. This paper compares dimension reduction methods within unsupervised time series pattern recognition,

including rule-based, spectral, probabilistic, and unsupervised learning-based approaches. The comparison

involves both synthetic and real-world datasets for a comprehensive evaluation. The ﬁndings reveal the poten-

tial to accelerate pattern recognition algorithms by 90 %, with only 18 % information loss in the sense of the

F1 score.

1 INTRODUCTION

Time series analysis and pattern recognition are es-

sential in many ﬁelds such as healthcare (Kam et al.,

2010), automotive (Petersen and Sax, 2022), and ﬁ-

nance (Chan, 2007). A time series is a collection of

data points logged in chronological order. It is char-

acterized by trends, seasonality, and cycles (Dodge,

2008). These characteristics can be used to ﬁnd pat-

terns in the data and predict what will happen in the

future. Time series data offers valuable information

on system behavior and state, enabling Time Series

Pattern Recognition (TSPR) methods to identify re-

curring load situations. By identifying patterns in

time series data, it is possible to better understand how

different factors interact and how they inﬂuence the

overall system. In addition to the quality of the algo-

rithms, handling big data, especially in case of Multi-

variate Time Series (MTS), is a challenge. TSPR al-

gorithms in MTS require time-consuming numerical

computations, such as similarity measures and opti-

mization algorithms (Yeh et al., 2016; Bascol et al.,

2016), which can be costly and time-consuming.

These algorithms are iterative and require signiﬁcant

computational resources like CPU time and memory.

https://orcid.org/0000-0003-3203-5470

https://orcid.org/0009-0001-2653-4559

https://orcid.org/0000-0003-2567-2340

The time complexity for pattern search algorithms

ranges from O(m

log(m)) to O(m

), depending on

the length m of a Univariate Time Series (UTS) (Yeh

et al., 2016; Yan et al., 2017). For MTS, the time

complexity increases to O(nlog(n)m

) with n being

the number of dimensions (Alaee et al., 2020). While

resources are available through data centers and ser-

vices, they are limited and expensive. Besides the

computational effort for MTS, many algorithms lack

the multi-dimensionality ability to detect patterns be-

tween different time series. Dimension reduction

(DR) methods are potential solutions for this chal-

lenge. Clustering techniques have been successfully

applied to DR methods. However, to the best of the

author’s knowledge, DR has yet to be used in TSPR.

This contribution investigates how different DR meth-

ods inﬂuence the impact on the information loss and

the time efﬁciency for TSPR. This paper gives an

overview of different DR approaches and their advan-

tages and disadvantages. These methods are tested on

a synthetic dataset and on the real-world Commercial

Vehicle Sensor Dataset (AB, ).

Section 2 deﬁnes necessary terms and outlines the

state of the art of unsupervised TSPR algorithm and

DR methods. In Section 3, the concept of the unsu-

pervised TSPR framework is described. The evalua-

tion of the methods described is presented in Section

4. Section 5 concludes the result of this contribution.

Petersen, P., Stage, H., Reis, P., Rauch, J. and Sax, E.

Comparison of Dimension Reduction Methods for Multivariate Time Series Pattern Recognition.

DOI: 10.5220/0012428900003654

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

In Proceedings of the 13th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2024), pages 809-816

ISBN: 978-989-758-684-2; ISSN: 2184-4313

809

2 STATE OF THE ART

2.1 Unsupervised Pattern Recognition

Unsupervised TSPR of time series is a knowledge

discovery problem. For this problem, the following

terms need to be deﬁned:

Deﬁnition 1 (Time Series T (M

orchen, 2006)). A d-

dimensional time series w.r.t. a series of time points

T = {t

,...,t

} of length n ∈ N is T = {(t

)|y

i,1

,..., y

i,d

)

∈ R

∈ T,i = 1,··· ,n}. If d = 1, T

is called univariate, for d > 1 it is a multivariate time

series.

Deﬁnition 2 (Subsequence t

i,l

(Noering, 2022)). A

subsequence t

i,l

∈R

n×d+1

of a time series T is a sub-

set of values from T of length l starting from index

i. This subsequence t

i,l

contains consecutive tuples



i+1

.. . t

i+l−1



Deﬁnition 3 (Pattern P (Noering, 2022)). A time se-

ries pattern P is a group of m (with m ≥ 2) similar

subsequences in a time series T excluding all triv-

ial matches. A subsequence t

i,l

, that is included in

a pattern P, is called a member M. Formally, P =

,. . .,M

] with each M

being a subsequence

with a starting index i and a length l. This includes

a distance threshold τ with dist(M

) ≤ τ, ∀x, y ∈

[1,. . .,m].

Deﬁnition 4 (Full-Dimensional Pattern P

full

). A full-

dimensional pattern P

full

of dimension d is a pattern,

where the distance of two members M

and M

in di-

mension k is dist(M

x,k

y,k

) ≤ τ, with {k ∈ N|1 ≤

k ≤d} in T .

Deﬁnition 5 (Sub-Dimensional Pattern P

sub

). A sub-

dimensional pattern P

sub

is a pattern of dimension b <

d, where d is the dimensionality of the time series.

The goal of TSPR is to ﬁnd patterns of unknown

shape, length, frequency of occurrence, and level

of detail in time series (Noering, 2022). Existing

methods for identifying those patterns include Dy-

namic Time Warping (Berndt and Clifford, 1994), dis-

cretization (Noering, 2022), or matrix proﬁles (Yeh

et al., 2016). Matrix proﬁles have found great interest

in unsupervised TSPR in recent years and are used as

a benchmark in this contribution. Nevertheless, the

nature of multivariate time series makes TSPR com-

putational intensive. To counteract the curse of di-

mensionality, DR methods are proposed in the follow-

ing.

2.2 Dimensionality Reduction of

Multivariate Time Series

The goal of DR methods is to ﬁnd a low-dimensional

data representation that retains the most relevant prop-

erties for a given problem. Such methods can be di-

vided into four categories: rule-based, spectral, prob-

abilistic, and unsupervised learning-based methods.

Rule-based methods apply rules to reduce dimensions

of time series, such as averaging the values of each in-

dex over all time series dimensions or unifying them

under one symbol based on their discretized sym-

bolic representation (Noering, 2022). Spectral meth-

ods (Chaudhuri, 2006; Hotelling, 1933) are based on

the idea that higher-dimensional data can be repre-

sented in a lower-dimensional domain using a lin-

ear or nonlinear transformation. Probabilistic meth-

ods (McInnes et al., 2018; van der Maaten and Hin-

ton, 2008; Cattell, 1965) view the data as samples

from an unknown probability distribution. A low-

dimensional latent random variable can be assumed

on which the data depends. Unsupervised learning-

based methods learn the internal structure of data

when supplied with it. AutoEncoder (AE) (Rumelhart

et al., 1986) architectures can create so-called bot-

tlenecks through which the data is routed. Thereby,

data is compressed to its essentials, which is equiv-

alent to a DR. Additionally, Long Short-Term Mem-

ory (LSTM) (Hochreiter and Schmidhuber, 1997) net-

works can process sequential data. Dictionary Learn-

ing (Mairal et al., 2009) allows sparse data encoding

by a linear combination of basis vectors, a so-called

Dictionary. For this, an optimization problem must be

solved. An overview of all methods considered in this

paper can be seen in Table 1.

Table 1: Overview of Dimension Reduction Methods.

Rule-Based Spectral Probabilistic

Unsupervised

Learning

Uniﬁcation PCA t-SNE Autoencoder

Averaging FPCA UMAP LSTM Autoencoder

Factor Analysis Dictionary Learning

Although the strengths and weaknesses of these

methods are well known, there is no research on the

impact of DR on TSPR in terms of information loss

and computational efﬁciency. For that purpose, the

concept of a comparative analysis is described in the

following.

ICPRAM 2024 - 13th International Conference on Pattern Recognition Applications and Methods

810

Preprocessing

Dimensionality

Reduction

Pattern

Recognition

Pattern

Recognition

Evaluation

Real Data

Synthetic Data

Data Sources

Figure 1: Overview of the concept for evaluating dimension reduction for pattern recognition.

3 CONCEPT

3.1 Process

This paper evaluates ten DR methods for unsuper-

vised TSPR in MTS to investigate the advantages and

disadvantages of processing without DR. This is done

in an organized manner by predeﬁned concept (see

Figure 1). It consists of ﬁve steps: data acquisition,

preprocessing, optional DR, TSPR, and evaluation.

This paper uses synthetic and real datasets. Fur-

ther discussions are in Section 3.3 and 3.2. Z-

normalization, Piecewise Aggregate Approximation

(PAA), and Symbolic Aggregate approXimation

(SAX) can be used as optional preprocessing meth-

ods. This study aims to accelerate the search for pat-

terns in MTS using DR. However, this can result in a

loss of information in data representation (Wang et al.,

2016), making it necessary to examine the suitabil-

ity of reduced data for unsupervised TSPR. Matrix

proﬁles as TSPR algorithm is applied after prepro-

cessing, considering both the dimension reduced (up-

per path) and original (lower path) data. This paper

uses the implementation stumpy (Law, 2019), which

allows TSPR for UTS and MTS. The application of

TSPR to the dimensionally reduced and the original

data allows statements to be made about the inﬂuence

of DR on TSPR.

This study examines the results of dimension-

reduced time series compared to non-dimension-

reduced ones. Since the synthetically generated

data contains much less incorporated pattern sam-

ple points compared to the overall number of sam-

ple points, is considered to be unbalanced. Thus, F1

score (Sokolova et al., 2006) is used a metric to eval-

uate the precision and recall of TSPR algorithms. In

addition, the gain or loss of ∆F1

of the reduced data

F1 score F1

RPR

in comparison to the original data F1

score F1

is calculated by

∆F1

RPR

−F1

, (1)

with ∆F1

∈[−1, 1], where −1 means 100 % loss and

1 means 100 % gain of the dimension reduced data.

The computational efﬁciency ∆t

is analyzed by com-

paring the runtime of the dimension reduction t

and

the TSPR on the reduced data t

RPR

with the runtime

of the TSPR the original data t

∆t

−(t

RPR

)

, (2)

with ∆t

∈ [−1,1], where −1 means 100 % compu-

tational efﬁciency loss and 1 means 100 % computa-

tional efﬁciency gain of the dimension reduced data.

3.2 Discussion on Synthetic and

Real-World Data

One of the main beneﬁts of synthetic datasets is that

they are entirely labeled by nature. That is why they

require less time and effort to prepare for analysis

and experimentation. They are helpful in study ﬁelds

with privacy problems, since they also eliminate pri-

vacy and conﬁdentiality difﬁculties. Although syn-

thetic datasets can be tuned to produce ﬂawless re-

sults, they can also accidentally skew data or overﬁt

models. Despite their beneﬁts, synthetic datasets may

fail to capture real-world processes accurately. Be-

cause of their inability to capture intricacies in real-

world events when generalizing conclusions based

on synthetic data, undertaking extensive validation in

real-world contexts is still necessary.

Real-world datasets provide an excellent oppor-

tunity for investigating characteristics that synthetic

datasets may miss. Their variety and diversity al-

low for investigating features, discovering unexpected

patterns, and improving the validity and application of

study ﬁndings. Real-world datasets have advantages

but drawbacks, such as the time and money required

to gather and manage big, diverse, and representative

datasets. Data collection and labeling take time and

effort to assure quality and dependability. Concerns

about privacy and conﬁdentiality occur when dealing

with sensitive material, limiting access, and placing

legal and ethical constraints on research operations.

3.3 Synthetic Data Generation

To generate synthetic time series, a random

walk (Pearson, 1905) is utilized, as is also recom-

mended for pattern recognition in the literature (No-

ering, 2022). Therefore, a broader examination for

Comparison of Dimension Reduction Methods for Multivariate Time Series Pattern Recognition

811

100

150

200

250

300

Temporal sampling points (no unit)

−50

Value points (no unit)

(a) A 1-dimensional pattern with its template (red) and vari-

ations (blue shapes).

0 2000 4000

6000

8000 10000 12000

Temporal sampling points (no unit)

−100

100

(b) A synthetically created 1-dimensional time series with

a single pattern incorporated in several occurrences (blue

background).

Figure 2: Synthetic data generated via the random walk ap-

proach.

use cases other than driving TSPR may be conducted.

The test patterns may include all randomly produced

forms. Nonetheless, the synthetic data must be ver-

iﬁed as a suitable foundation for a valid comparison

of DR. As a result, restrictions are put on the syn-

thetic time series data to meet the given objectives,

which are deﬁned as follows in the current study: The

synthetic MTS can either contain full-dimensional

or sub-dimensional patterns without time warping or

shifts in pattern variances. Pattern class instances

should have different noise levels and amplitude val-

ues, as sensor signals are noisy. Time series data

should be within a predeﬁned range, but seasonality

and wear and tear may be present.

Using the random walk approach, the n-

dimensional random walk generates random se-

quences of arbitrary length. It creates pattern tem-

plates and variations to assemble multiple patterns

in a time series with random connections. Five dis-

tinct trends are created: strong-up, up, stay, down,

and strong-down. When the trend time is exceeded,

a new trend type is selected randomly, but two super

trends cannot follow each other. The resulting curve

is smoothed using linear convolution and scaled or

squashed according to predeﬁned values.

Variations are made by adding white Gaussian

noise and amplitude scaling individually for each di-

mension, resulting in a variable signal-to-noise ratio

(see Figure 2a). The desired order of pattern oc-

currences is randomly created, and multi-dimensional

patterns appear within the time series. A symmetrical

random walk with random length and white Gaussian

noise connects the patterns. The link and patterns are

shifted along the value axis, preventing value jumps

within the series (see Figure 2b). The resulting series

is smoothed and covered with white Gaussian noise,

and the same procedure is applied for all dimensions.

The method generates 100 three-dimensional time se-

ries with 10k data points with obvious patterns by ad-

justing scaling or noise parameters. Amplitude differ-

ences or noise levels can control the obviousness. To

ensure application relevance, the randomly generated

data must be correlated to some degree, allowing for

multivariate TSPR and DR. Real-world sensor data is

correlated to some degree, allowing for multivariate

TSPR and DR. For example, the angle of an acceler-

ator pedal and measurement data of an Inertial Mea-

surement Unit (IMU). Synthetic data can embed sim-

ple patterns, which search algorithms can easily ﬁnd

due to their conciseness. However, this is unrealistic.

Three datasets with different cross-instance dis-

tances CR

dist

and pattern amplitudes MA were created

to test the effectiveness of DR and TSPR in different

difﬁculty levels (see Table 2).

dist

|P|

∑

n=1

∑

i, j=1

|Z (M

) −Z (M

)|, i ̸= j, (3a)

MA =

|P|

∑

n=1

∑

max(Z (M

)), (3b)

where Z is the Z-Score normalization, |P| the number

of patterns, m the number of members in each pattern,

and N the total number of members over all patterns.

Table 2: Overview of the cross-instance distances and pat-

tern amplitudes of three generated benchmark datasets.

Case CR

dist

I 2.95 0.94

II 3.57 0.86

III 4.32 0.75

4 EVALUATION

The evaluation aims to examine ten used DR meth-

ods for unsupervised TSPR in MTS. Therefore, the

beneﬁts and drawbacks of DR for TSPR versus non-

reduction processing are investigated. A synthetic

dataset (see Section 4.1) and a real-dataset (see Sec-

tion 4.2) are used to compare the DR methods in

TSPR.

ICPRAM 2024 - 13th International Conference on Pattern Recognition Applications and Methods

812

4.1 Synthetic Data

4.1.1 Selection of Suitable Methods for

Dimension Reduction

Three-dimensional time series are synthetically gen-

erated as a full-dimensional TSPR problem. As pre-

processing, only z-normalization has been applied.

These dimensions were reduced to one dimension to

evaluate the effectiveness of different DR methods.

The hypothesis that larger amplitude and smaller dis-

tance make patterns easier to ﬁnd is conﬁrmed by pat-

tern search results. For cases I and II, F1 values are

good, while for case III, the values are worse. This

correlation is also observed for reduced time series,

indicating that pattern difﬁculty is not a signiﬁcant

factor in evaluating reduction methods (see Figure 3).

0.0 0.2 0.4

0.6

0.8 1.0

Original MTS

FPCA

Dictionary Learning

Avaraging

LSTM AE

PCA

Uniﬁcation

UMAP

t-SNE

Case

III

Figure 3: Results of pattern recognition with and without

prior dimensionality reduction on different pattern proper-

ties (Table 2).

It can be seen from the results that Factor Anal-

ysis (FA), Functional PCA (FPCA), and AE are the

most promising DR methods due to performing the

best throughout the different cases.

4.1.2 Runtime Analysis of Dimension Reduction

DR in TSPR aims to save time by analyzing di-

mensionally reduced time series compared to original

data, speeding up the analytical process. The evalu-

ation of dimension reduction methods involves com-

paring their runtime with (2). Time series are synthet-

ically generated as a full-dimensional TSPR problem

with dimensions from 2 to 14 reduced to 1, 2, and

3 dimensions. Each reduction process is tested ten

times to compensate for measurement variations. For

this analysis, the top three reduction methods regard-

ing their F1 score, as mentioned in Figure 3, are used.

The loss and gain of computational efﬁciency

∆t

of dimension reduction by Principal Component

Analysis (PCA), AE, and FA is shown in Figure 4.

In this scenario, the training of the AE is done in

three epochs with a batch size of six, and there is no

need to retrain after each sample.

The inference times for individual methods are in-

signiﬁcant compared to the time required for TSPR.

A beneﬁt in speed is nearly always present compared

to multivariate TSPR on all initial dimensions, re-

gardless of the combination of initial or reduced di-

mensions. The lower the number of reduced dimen-

sions, the higher the beneﬁt. The percentage bene-

ﬁt also increases with the number of original dimen-

sions. However, AE training can have a negative im-

pact when the distance between the number of orig-

inal dimensions and the number of reduced dimen-

sions is less than three.

In conclusion, a reduction generally leads to a

speed beneﬁt. The higher the distance between the

original MTS dimensions compared to the reduced

time series, the higher the temporal beneﬁt. From Fig-

ure 4, it can be seen that the decision on how many

dimensions the original MTS should be reduced has

an impact on the overall performance of the TSPR al-

gorithm. Therefore, it is recommended to investigate

the optimal number of dimensions before analysis.

4.1.3 Dealing with Sub-Dimensional Patterns in

Reduced Dimension

To ﬁnd the optimal number of reduced dimension

y,opt

, the dimension reduction method FA is tested

by reducing a 10-dimensional MTS to all possible di-

mensions n

∈[1,2,... , 9]. The study aims to ﬁnd the

optimal number of components n

, which is the num-

ber of dimensions of the reduced time series T , to

achieve the best possible results in TSPR. However,

an additional problem arises during TSPR: the pat-

terns in the reduced times series T do not necessarily

have to be a full-dimensional TSPR problem. Speci-

fying the minimum number of dimensions in which

a sub-dimensional pattern should occur in a multi-

dimensional pattern search is necessary. The test is

performed in three cases:

1. Sub-dimensional TSPR problem with |k| ≥ 1.

2. Sub-dimensional TSPR problem with |k| ≥

3. Full-dimensional TSPR problem with |k| = n

The test results are displayed as heatmap matrices,

with each heatmap showing one of the three test cases

(see Figure 5).

The patterns’ dimensions n

are horizontally dis-

played, and the number of reduced time series’ di-

mensions n

are vertically displayed. The F1 score

Comparison of Dimension Reduction Methods for Multivariate Time Series Pattern Recognition

813

2 3 4

5 6

7 8 9 10 11 12 13 14

Number of Original Dimensions n

−100

100

∆t

[%]

2 3 4

5 6

7 8 9 10 11 12 13 14

Number of Original Dimensions n

−100

100

2 3 4

5 6

7 8 9 10 11 12 13 14

Number of Original Dimensions n

−100

100

FPCA

−100

100

−100

100

−100

100

−100

100

−100

100

−100

100

−100

100

∆F1

[%]

−100

100

∆F1

[%]

−100

100

∆F1

[%]

Metric:

∆t

∆F1

Number of Reduced

Dimensions n

Impact on Metric:

Gain

Loss

Figure 4: Loss and Gain of ∆F1

and computation time ∆t

of different dimension reduction methods in pattern recognition.

1 2 3 4 5 6 7 8 9 10

123456789

|k| ≥ 1

1 2 3 4 5 6 7 8 9 10

|k| ≥ b

1 2 3 4 5 6 7 8 9 10

|k| = n

0.00

0.25

0.50

0.75

1.00

F 1

Figure 5: Heatmaps displaying the F1 score of pattern

recognition after reduction with FA regarding different

numbers of dimensions as well as dimensions of patterns.

values are indicated in color, with dark values repre-

senting high scores and light values representing low

scores. The smaller n

, the more difﬁcult it is to ﬁnd

the pattern in the reduced time series. This is because

the fewer dimensions contribute to a pattern, and the

less FA can identify and reproduce it. The relation-

ship between the number of dimensions in a reduced

time series and the size of the pattern is inﬂuenced

by the number of dimensions. The smaller the pat-

tern dimensions in the original MTS and the larger

the number of dimensions reduced, the less well the

pattern is found. The best possible combination of

, n

, and min n

m,r

cannot be guaranteed and must

be determined at the beginning of each new analysis.

4.2 Real-World Data

The Commercial Vehicles Sensor Dataset (AB, ) is

used to validate TSPR on a reduced dataset. The

dataset classiﬁes the activities of two dumpers dur-

ing regular use. Dumpers have various states, such

as idle, driving, loading, dumping, and engine-off, la-

beled in their MTS data. These states are less detailed

and suitable for classifying operating modes, but re-

curring events within these modes require unsuper-

vised TSPR. The data is z-normalized and analyzed

using a 100 Hz sampling rate for MTS acquisition.

Data reduction is performed using a 128-sequence

SAX dictionary with 256 symbols converted from let-

ters to ﬂoating point numbers, as both matrix pro-

ﬁles and DR methods work with numeric data. Time

250 500 750

1000

1250 1500 1750

2000

Time [s]

−2.5

0.0

2.5

11 110 00 0 22 22 2

(a) Reduce time series by FA with recognized patterns. The

top three patterns were drawn with different colored boxes.

0 12 24

Time [s]

−2.5

0.0

2.5

Pattern 0

0 12 24

Time [s]

Pattern 1

0 12 24

Time [s]

Pattern 2

(b) Extracted value curves of the patterns found in the re-

duced time series.

0 12 24

−2

gFx

0 12 24

gFy

0 12 24

−0.5

0.0

0.5

gFz

0 12 24

−2

0 12 24

Time [s]

−1

0 12 24

Time [s]

−2.5

0.0

2.5

0 12 24

Time [s]

speed

Figure 6: Results of real-world data pattern recognition.

frames during idle or engine-off mode are removed, as

they lack useful patterns and are irrelevant to the anal-

ysis. The dataset has seven dimensions, reduced using

FA for synthetic data and MTS reduced to one dimen-

sion. Pattern classes are represented by the same box

color, with value curves of pattern instances repre-

sented by different shades (see Figure 6a). Three pat-

terns with the smallest z-normalized Euclidean dis-

ICPRAM 2024 - 13th International Conference on Pattern Recognition Applications and Methods

814

tance are marked with colored boxes in the reduced

time series. Value curves are extracted and displayed

in separate diagrams for all classes (see Figure 6b).

The question remains whether these patterns in

the reduced time series are also present in the orig-

inal MTS. Therefore, as an example, the original

segments of the identiﬁed pattern 2 are investigated

(see Figure 6c). Positive and negative correlations are

evident between sensor values, mainly between gy-

roscope data in x and z direction and accelerometer

data in x and z direction. Patterns are found between

variables of gyroscope data in x direction, accelerom-

eter data in x, and z direction, indicating a link be-

tween correlation and patterns. However, some sen-

sors have little to no correlation to other sensors, such

as speed and accelerometer data in y direction. A cor-

relation between sensor values is necessary for DR,

especially for PCA methods, which use correlation as

a primary factor. Patterns 0 and 2 show similar re-

sults, indicating that patterns found for reduced time

series also occur in the MTS. However, higher vari-

ances or noise among pattern instances occur in a sub-

set of the dimensions, making them sub-dimensional

patterns. Utilizing upstream DR for TSPR results in a

time saving of 89 % compared to multivariate cases.

5 CONCLUSION & OUTLOOK

This paper compares various methods for dimen-

sion reduction in the context of unsupervised pat-

tern recognition. As a result, Autoencoder, Func-

tional Principle Component Analysis (FPCA), and

Factor Analysis (FA) produce dimensionally reduced

data with the least loss of ∆F1

using a synthetic

dataset. Furthermore, dimension reduction with FA

and FPCA yields a runtime advantage of up to 90 %

over a non-reduced pattern search while losing only

18 % of ∆F1

. This result is validated with the real-

world dataset Commercial Vehicles Sensor Dataset.

However, the speed beneﬁts must be weighed against

potential loss in accuracy and tested in advance, es-

pecially in the case of sub-dimensional pattern recog-

nition. Future studies can explore alternative pattern

algorithms, increase dataset diversity, investigate sub-

dimensional pattern recognition and variable pattern

lengths, and consider the temporal offset of patterns.

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