=Paper=
{{Paper
|id=Vol-3761/paper3
|storemode=property
|title=Interpreting Outliers in Time Series Data through Decoding Autoencoder
|pdfUrl=https://ceur-ws.org/Vol-3761/paper3.pdf
|volume=Vol-3761
|authors=Patrick Knab,Sascha Marton,Christian Bartelt,Robert Fuder
|dblpUrl=https://dblp.org/rec/conf/tempxai/KnabMBF24
}}
==Interpreting Outliers in Time Series Data through Decoding Autoencoder==
https://ceur-ws.org/Vol-3761/paper3.pdf
Interpreting Outliers in Time Series Data through
Decoding Autoencoder
Patrick Knab1,2 , Sascha Marton1 , Christian Bartelt1 and Robert Fuder2
1
University of Mannheim, Germany
2
Robert Bosch GmbH, Bühl, Germany
Abstract
Outlier detection is a crucial analytical tool in various fields. In critical systems like manufacturing,
malfunctioning outlier detection can be costly and safety-critical. Therefore, there is a significant need
for explainable artificial intelligence (XAI) when deploying opaque models in such environments. This
study focuses on manufacturing time series data from a German automotive supply industry. We utilize
autoencoders to compress the entire time series and then apply anomaly detection techniques to its latent
features. For outlier interpretation, we i) adopt widely used XAI techniques to the autoencoder’s encoder.
Additionally, ii) we propose AEE, Aggregated Explanatory Ensemble, a novel approach that fuses
explanations of multiple XAI techniques into a single, more expressive interpretation. For evaluation of
explanations, iii) we propose a technique to measure the quality of encoder explanations quantitatively.
Furthermore, we qualitatively assess the effectiveness of outlier explanations with domain expertise.
Keywords
Explainable Artificial Intelligence (XAI), Outlier Detection, Autoencoder
1. Introduction
Outliers represent exceptional instances that differ from a normal data distribution [1]. Artificial
intelligence (AI) is pivotal in outlier (anomaly) detection applications, particularly in domains
with high-dimensional data, such as time series. By analyzing patterns, trends, and dependencies,
algorithms can effectively identify outliers and anomalous events in various domains, ranging
from finance and healthcare to industrial processes [2, 1, 3]. In particular, manufacturing
processes generate vast amounts of time series data, making timely and accurate outlier detection
critical for maintaining operational efficiency and safety. However, opaque neural networks
(NN) often lack the interpretability necessary for high-stakes environments [4, 3]. Consequently,
explaining the model’s decisions through explainable artificial intelligence (XAI) is essential to
provide transparency and foster trust in automated decision-making [5, 6, 7].
This work utilizes convolutional autoencoders (CAE) to compress univariate time series
data for anomaly detection in an automotive manufacturing plant. A complete time series is
considered an outlier if the entire sequence deviates from the expected pattern. The purpose of
utilizing CAE is to learn specific manufacturing process features and map a time series into a
low-dimensional space at its bottleneck. An unsupervised anomaly detection algorithm then
uses these latent features to identify outliers. Therefore, we are interested in explaining how the
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Proceedings
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Figure 1: Aggregated Explanatory Ensemble - AEE. The aggregated explanation is represented by a
heat map in the background, with deeper shades of red indicating areas of greater significance for its
explanation in the time series. The black curve visualizes an anomalous time series, with the explanation
highlighting a disruption in the pattern between the 6300 and 7200 marks in the time series.
encoder transformation contributes to outlier detection by employing established XAI methods
(Section 2) like Grad-CAM [8], LIME [9], SHAP [10], and LRP [11, 12, 13], since we use the
CAE’s latent features for detecting outliers. The explanations of the XAI techniques mentioned
above lead to fluctuations due to their unique features. This diversity motivates us to combine
these explanations into a single, more comprehensive one: AEE - Aggregated Explanatory
Ensemble (see Section 3.2), visualized in Figure 1 for an anomalous time series instance. Since
ground-truth data for evaluating the produced explanations are often missing, counterfactuals
are widely recognized as an effective quantitative method for XAI techniques [14, 15]. In our
work, we implement a revised version of the quality measurement (QM) procedure, originally
proposed in [16], as detailed in Section 3.3. We assess the effectiveness of the techniques both
qualitatively and quantitatively (see Section 4) based on the underlying manufacturing process.
Our primary focus is on discussing their implications for erroneous time series data to gain
insights into the property of being an outlier as a complete time series.
2. Related XAI Approaches
The following section briefly mentions the XAI approaches used in this work. They were chosen
for their well-known status and ability to cover explainability from different aspects, e.g., local
vs. global and model-agnostic vs. model-specific explanations. These techniques share the
goal of providing post hoc explanations, but each employs different approaches to achieve
explainability.
CAM (Class Activation Mapping), proposed by Zhou et al. [17], is a local and model-specific
technique for explaining convolutional neural networks (CNN). Selvaraju et al. [8] enhanced
this approach with Grad-CAM, incorporating gradients into the explanation process. This
improvement removes the requirement for a global average pooling layer, making the method
applicable to a broader range of model architectures.
LIME (Local Interpretable Model-agnostic Explanations), proposed by Ribeiro et al. [9], is
another well-known local but model-agnostic technique. It achieves interpretability by locally
approximating the behavior of a complex neural network with an interpretable machine learning
algorithm.
SHAP (SHapley Additive exPlanations) is a game theory-inspired model-agnostic technique
proposed by Lundberg et al. [10], which can provide local or global explanations. It computes
Shapley values for the model’s data inputs, providing a global explanation that considers multiple
data instances simultaneously. Studies carried out in [4, 3] utilized SHAP to unravel the inner
workings of a complete autoencoder.
LRP (Layer-wise Relevance Propagation) aims at comprehending a model’s inner workings by
retroactively propagating the internal values of its layers. Following this strategy, LRP seeks to
assign relevance scores to different input features [11, 12, 13].
3. Application of XAI to Autoencoder
Notation. An univariate time series instance t is fed into the convolutional autoencoder via
the function t̂ = 𝐷(𝐸(t)), with encoder 𝐸, decoder 𝐷, and latent space 𝐿, where 𝐿 = 𝐸(t). The
output t̂ is a reconstruction of t. We denote explanation E as the output of an XAI technique
for a time series t.
3.1. Adapting XAI Techniques to Encoder
We employ a 1D convolutional autoencoder (1D CAE) to reduce feature dimensions and detect
anomalies in time series data (see Section 4.1 for more details). We apply XAI techniques to the
encoder since we use its output for anomaly detection. While the straightforward architecture
facilitates the application of the XAI methods introduced in Section 2, their utilization, although
widely applied in diverse machine learning scenarios, remains relatively limited within the realm
of 1D CAE, mainly when applied to time series data. We adapt these methods to improve their
capability to provide 1D explanations for 1D convolutional networks in the form of heatmaps.
The application of the XAI methods above yields two distinct types of explanations:
• Individual Feature Explanation: For each latent feature, 𝑙𝑖 ∈ 𝐿 (where 𝑖 is the feature
index), we generate a dedicated heatmap. This allows us to inspect how individual features
in t contribute to the reconstruction process (see Appendix A).
• Combined Feature Explanation: In addition to the individual views, we also create
a unified heatmap that integrates all latent features into a single representation (see
Figure 2a). This combined view provides a holistic understanding of how the interplay
between features in t influences the reconstruction process. All experiments and figures
in this paper use combined feature explanations.
3.2. AEE - Aggregated Explanatory Ensemble.
With the application of the covered XAI approaches (see Section 2), we generate a set of diverse
explanations. Each XAI technique provides distinct insights: Grad-CAM emphasizes spatial
relevance, LIME offers local interpretability, SHAP delivers global explanations, and LRP traces
relevance propagation (see Figure 2). By aggregating these methods, AEE leverages their
strengths for a holistic understanding of anomalies. We restrict AEE to a time series t that stores
the diverse explanations E𝑖 in an array E𝑥𝑖 , where 𝑖 indicates the index of t and 𝑥 denotes the
underlying XAI technique. To ensure equal consideration for each explanation, we individually
scale each element E𝑥𝑖 based on its importance scores. Mathematically, the scaled explanation
SE𝑥𝑖 is given by:
E𝑥𝑖 − min(E𝑥 )
SE𝑥𝑖 = ( ) × (𝑎max − 𝑎min ) + 𝑎min . (1)
max(E𝑥 ) − min(E𝑥 )
Here, 𝑎min and 𝑎max are the minimum and maximum values desired for scaling SE𝑥𝑖 . After
scaling, we compute the mean value for each point 𝑖 on the 𝑋 axis. We denote the aggregated
version as A𝑖 , where 𝑖 represents the aggregated value for the 𝑖th point of the time series t on
the 𝑋 axis, mathematically:
|𝑥|
1 𝑗
A𝑖 = ∑ SE𝑖 . (2)
|𝑥| 𝑗=1
Here, |𝑥| denotes the count of explanations stored in SE𝑥𝑖 . Alternatively, a weighting scheme
can be employed instead of equal contribution to assign more relevance to specific explanations.
3.3. Quality Measurement of Encoder’s Explanation
Given the interpretability constraints of the XAI results [5], we quantitatively analyze the
explanations generated by each method using a modified version of the quality measurement
function proposed by Schlegel et al. [16]. In this work, the XAI techniques focus on the
encoder’s explainability, resulting in a multi-regression task. Using the reconstruction error as a
quality measurement would involve the decoder, misleading the measurement of the encoder’s
explanation. Instead, we aim to analyze the projections of the original time series t, a randomly
perturbed version tcr , and a version perturbed based on explanation results tc in the latent space.
This approach operates independently of the decoder, focusing on explaining the techniques
applied to the encoder. Adversarial perturbations [18], which manipulate predictions, suggest
that the distance between tcr and t should be smaller than between t and tc . Thus, we define the
quality measurement for the encoder as:
𝑞𝑚𝑒 (t, t) ≤ 𝑞𝑚𝑒 (t, tcr ) ≤ 𝑞𝑚𝑒 (t, tc ). (3)
Here, 𝑞𝑚𝑒 measures the Euclidean distance between the original and perturbed time series in
the latent space. The underlying theory is that perturbations based on explanation results have
a more significant impact on the model’s predictions than random noise [14, 15]. The approach
applies to individual and combined feature explanations, revealing the importance of features
for the outlierness property of the instance.
4. Experimentation
4.1. Experimental Setup
Dataset. As introduced in Section 1, our demonstration employs univariate time series data
originating from a production plant. More specifically, it covers one process in a manufacturing
line consisting of multiple processes. The dataset consists of 18,412 time series instances, each
containing 8,192 data points. The test station (end of the line) automatically labels the data to
Table 1
Anomaly Detection Performance Measurements. The table contains the precision, recall, and
F1-score performance metrics of the developed anomaly detection pipeline for the test set.
Class Precision Recall F1-Score Support
0 (OK) 1.00 1.00 1.00 5441
1 (NOK) 0.89 0.63 0.74 38
indicate normal operation (OK) or an error (not OK—NOK) during production; NOK accounts
for 0.68% overall. This information can be used to assess whether the found outliers correspond
to actual errors identified by the test station.
Anomaly Detection Pipeline. Our 1D CAE architecture comprises three convolutional layers
with ReLU activation functions, followed by max-pooling layers and a bottleneck layer with a
three-dimensional latent space (see Appendix B). We divide the data into three sets to train the
AE: a training set for model training (0.66% NOK), a validation set (0.74% NOK), and a separate
set for testing (0.70% NOK) the model’s performance.
We intentionally include known anomalies in the training process, as instances with NOK
labels may contain errors originating from other processes in the manufacturing line that the
time series does not cover. In addition, the proportion of abnormal instances is low enough (less
than 1%) that the autoencoder continues to learn to reconstruct the time series correctly without
learning anomalies. The pipeline consists of an anomaly detection mechanism that utilizes
the latent feature space as input (see Appendix C). Specifically, we employ the density-based
spatial clustering of applications with noise (DBSCAN) algorithm [19]. Table 1 presents the
performance metrics of the anomaly detection pipeline, categorized into NOK and OK classes.
These results are based on the evaluation of the test dataset.
4.2. Qualitative Evaluation - Anomaly Interpretation
In the following, we discuss the utility of XAI techniques to interpret the encoder, focusing
on understanding why specific instances lead to anomalies by leveraging domain-specific
knowledge of the underlying manufacturing process. We examine an exemplary time series
classified as NOK for all explanation techniques in Figure 2 and Figure 3. The illustrative
case diverges notably in its final third segment, as the pattern is expected to exhibit distinct
characteristics compared to the preceding two thirds of the time series (see Appendix D). We
explicitly demonstrate the anomalies shown here using examples that are easy to visually
understand as outsiders.
We initiate with Grad-CAM (Figure 2a), revealing a heatmap that distinctly accentuates
positions later in t, precisely aligning with observable areas of technical failures in the manu-
facturing process. This targeted explanation effectively identifies the specific region preceding
real-world anomalies. Subsequently, LIME (Figure 2b) highlights the same area as CAM, but
its interpretation is more straightforward because of its apparent intensity. Moreover, it also
subtly indicates regions in intermediate areas of the time series. SHAP (Figure 2c) pinpoints
the same critical area of primary importance, consistent with the findings of the previous
methods. Compared to the preceding, the final standalone method LRP (Figure 2d) diverges
Grad-CAM Heatmap - Anomaly
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(d) LRP
Figure 2: Individual XAI Results. The XAI results are presented in the form of heatmaps. The black
portions of the images denote the time series signal. These displayed instances were identified as
abnormal by the AE’s pipeline. The heatmap in the background indicates feature importance using
varying intensities of red. We must evaluate color intensity individually as XAI techniques calculate
feature importance differently.
in its explanation. Although it does not explicitly emphasize the most pronounced pattern, it
assigns varying degrees of importance to different segments and provides valuable insights for
manual analysis by a domain expert.
Figure 3 shows the aggregated explanation. Parallel to Grad-CAM and SHAP, the region
signaling an abnormal pattern is precisely accentuated, and the aggregated version amplifies
AEE Heatmap - Anomaly
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Figure 3: AEE XAI Results. This figure presents the results of the XAI analysis for the AEE approach.
The format and layout of these explanations are consistent with those shown in Figure 2.
the color representation, enhancing interpretability. Besides confirming the importance of the
known area, this approach offers additional insights into other parts of the time series, e.g., it
prioritizes early regions that indicate possible technical abnormalities. Repeated experiments
prove its explanations are more stable due to its aggregation property, mitigating the negative
implications of instability [20].
4.3. Quantitative Evaluation - XAI Quality Measurement.
Figure 4 depicts the QM (normalized Euclidean distances) distributions, where boxes represent
the interquartile range (IQR) from Q1 to Q3, with a median line (Q2). The fences extend ±1.5
times the IQR. The OK category includes 100 randomly selected instances, and the NOK category
comprises 38. The noise/shuffle box (green) represents QM values tcr , and the XAI box (red)
represents tc .
The visualization indicates that each QM XAI score consistently outperforms its QM noise
counterpart. The scores for the NOK cluster are significantly higher, demonstrating the effective-
ness of using explanations for outlier interpretation. LRP and LIME overlap between Noise and
XAI, while Grad-CAM and SHAP display a clearer separation in their explanations. The AEE
produces a significant result, indicating that aggregating multiple explanations sharpens the
distinction between relevant and irrelevant features within a time series, improving explanation
quality.
Aggregation Plot LIME Plot Grad-CAM Plot SHAP Plot LRP Plot
1 Grad-CAM Plot LIME Plot SHAP Plot LRP Plot AEE
1 1 1 1 1
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QM
XAI
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Plot Grad-CAM Plot 0.20.2 SHAP Plot 0.2 LRP Plot 0.2 0.2 0.2
0
0 0 0 0 0
false
false true
true false
false true
true false
false
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true
false
false
true
true
Anomaly
Anomaly Anomaly
Anomaly Anomaly
Anomaly Anomaly
Anomaly Anomaly
Anomaly
Noise
Noise XAI
XAI
Figure 4: Interquartile Range Quality Measurements. The visualization depicts quality measure-
ment scores for each XAI technique, categorized into true anomalies (NOK) and false anomalies (OK).
false
true
true
false
The
false
true
measurements
true
false
false
are further
true
true
stratified
false
false
true
noise (tcr - XAI shuffled), denoted by green, and XAI (tc -
into true
Anomaly Anomaly Anomaly Anomaly
aly Anomaly XAI perturbated), represented by Anomaly
Anomaly red.
4.4. Limitations and Future Work
Our study applied XAI techniques to CAE, leaving the potential for other architectures such
as variational autoencoders (VAE) [21] and recurrent neural networks (RNN) [22, 23, 7] unex-
plored. Additionally, the evaluation of these techniques was primarily based on qualitative
assessments, as anomalies required examination by domain experts. Future research on datasets
not requiring expert knowledge should consider integrating additional quantitative methods to
complement qualitative insights [24]. In addition, a clear distinction between explanation and
interpretation should be established [25], recognizing that not all explanations are inherently
human-interpretable [26], as it was sometimes the case in this scenario.
Furthermore, exploring different weighting schemes for AEE could enhance the interpretation
and accuracy of feature importance calculations in various scenarios. We outlined the experi-
mentation on the time series manufacturing use case. Future research could involve testing the
AEE approach across various data types, such as images or text. Regarding XAI approaches,
future work could focus on improving time series segmentation using foundation models [27],
particularly beneficial for LIME. Another promising direction is to direct the explanations
not toward the latent features themselves but the classes in the latent space that signify the
presence or absence of anomalies. Lastly, extending this methodology to multivariate time
series [28, 23, 29, 30] or even multimodal data [21] presents another intriguing avenue for future
exploration.
5. Conclusion
This paper contributes to the application of XAI techniques to CAEs for analyzing outlier
properties within the latent space of time series data in the operational context of a manu-
facturing plant. We employed well-established XAI methods to demonstrate the practicality
and effectiveness of these techniques in interpreting outliers. In addition, we introduced AEE,
an ensemble of multiple XAI techniques. We quantitatively evaluated the different explana-
tions using a QM approach specifically modified to fit the encoder of an AE. Moreover, the
application of XAI techniques provided explanations for these outliers, accurately highlighting
the abnormal segments within the time series. This alignment confirms the utility of XAI in
providing meaningful insights into anomalies and building confidence in the system through
the interpretation of XAI results.
Acknowledgments
This work was supported by the German Federal Ministry for Economic Affairs and Climate
Action (BMWK).
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A. Individual Feature Explanation
Figure 5 shows an instance that the pipeline classified as NOK, featuring the reconstructed
time series in red and the original time series in black. The underlying explanation is provided
through individual feature explanations, where a distinct heatmap visually explains each latent
feature.
(a) Heatmap Latent Feature One
(b) Heatmap Latent Feature Two
(c) Heatmap Latent Feature Three
Figure 5: Grad-CAM - Individual Feature Heatmaps. The images illustrate individual latent feature
explanations in the form of a heatmap generated by Grad-CAM. The black curve illustrates the original
time series, while the red curve represents its reconstruction.
B. Autoencoder Architecture
In the following, we present the defined search space of hyperparameters for tuning an AE
in this work. The search space has been explored by 100 runs and 500 epochs each. Figure 6
represents the building blocks we tuned during this process.
• The amount of CNN blocks consists of an optional dropout and max pooling layer. We
restrict this size to at least one and a maximum of three blocks. This number applies to
both the encoder and the decoder.
• In contrast to the number of CNN blocks, this number varies for DNN blocks between
the encoder and decoder parts. Both can have up to two DNN blocks.
Dense Reshaping
CNN_Transpose
CNN_Transpose
Bottleneck
UpSampling
UpSampling
Dropout
Dropout
Output
Flatten
Dropout
Dropout
Dropout
Dropout
Dropout
Dropout
Pooling
Pooling
Input
Dense
Dense
Dense
Dense
…
CNN
… CNN … …
Encoder Decoder
Figure 6: The Building Blocks of an Autoencoder: An Abstract Architecture. The AE’s architecture
comprises diverse blocks, each possessing unique internal attributes and dimensions. As a result,
the encoder and decoder are constructed separately, deviating from the conventional symmetrical
autoencoder. These blocks encompass convolutional layers and their associated operations alongside a
dense block that integrates dense and dropout layers.
• Each convolutional layer is optimized with a specific number of filters in its operation,
namely 16, 32, 64, and 128. Furthermore, the kernel size is tuned to either 8, 16, or 32.
While it is possible to consider additional values for these parameters, doing so would
increase the search space for the tuner.
• The dropout layer is optional for each CNN and DNN block. Possible dropout rates
range is 0.1, 0.2, 0.3, 0.4, and 0.5.
• Max pooling is another optional layer in the CNN-Block but with a fixed pooling size of
two.
• The range of neurons in a dense layer is 32, 64, 128, and 256, respectively.
• The activation function chosen for each layer in the autoencoder remains consistent,
namely, the ReLu, Tanh, Sigmoid, or Softmax function. However, only the output layer of
the decoder is individually tailored to these four functions.
C. Latent Space Plot
The encoder’s output projection is shown in Figure 7. This figure displays the latent variables
on a two-dimensional scale for easier interpretation. Each point on the plot corresponds to
a mapped instance, representing a complete time series from the test dataset. The colors
indicate the categorization by DBSCAN in the latent space: red points are outliers, orange
points represent instances with manually detected deviations yet considered OK, and green
points indicate cases with no apparent deviations, also classified as OK.
Figure 7: Latent Space Visualization. Two-dimensional latent space representation of the autoen-
coder’s features. Green and orange points represent instances assigned to two distinct clusters, while
red points are identified as outliers.
D. Exemplary Non-Outlier Time Series
Figure 8 displays an exemplary time series classified as a non-outlier alongside its reconstruction
by the autoencoder. The image demonstrates that the AE can meaningfully reconstruct the
input time series. Additionally, the pattern of this time series is typical for an instance without
apparent errors in this dataset.
Figure 8: Time Series Reconstruction. The figure illustrates a time series, depicted in black, classified
as OK. The corresponding reconstruction through the autoencoder is shown in red.