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  <front>
    <journal-meta />
    <article-meta>
      <title-group>
        <article-title>Voxel-Based Spatio-Temporal Visualization of Gameplay Traces with Anomaly Detection</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <string-name>Ling Liu</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Colan Biemer</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Günter Wallner</string-name>
          <xref ref-type="aff" rid="aff0">0</xref>
          <xref ref-type="aff" rid="aff1">1</xref>
        </contrib>
        <contrib contrib-type="author">
          <string-name>Seth Cooper</string-name>
          <xref ref-type="aff" rid="aff2">2</xref>
        </contrib>
        <aff id="aff0">
          <label>0</label>
          <institution>Eindhoven University of Technology</institution>
        </aff>
        <aff id="aff1">
          <label>1</label>
          <institution>Johannes Kepler Universität Linz</institution>
        </aff>
        <aff id="aff2">
          <label>2</label>
          <institution>Northeastern University</institution>
        </aff>
      </contrib-group>
      <pub-date>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>As video games take place across space and time, space-time visualizations are promising for conveying gameplay data, as they allow all the data to be shown at once and avoid, e.g., timeline scrubbing. However, space-time visualizations can sufer from clutter and occlusion of data. To address these issues, we explore AI techniques to visualize space-time gameplay traces. Clutter is reduced by aggregating the data of individual traces into voxels. To highlight areas of interest and reduce their occlusion, anomaly detection using isolation forests is used to visually emphasize voxels of interest, changing color and opacity. We present two case studies, based on StarCraft: Brood War and a custom platformer game, demonstrating the impact of the anomaly detection approach.</p>
      </abstract>
      <kwd-group>
        <kwd>eol&gt;gameplay visualization</kwd>
        <kwd>voxels</kwd>
        <kwd>anomaly detection</kwd>
      </kwd-group>
    </article-meta>
  </front>
  <body>
    <sec id="sec-1">
      <title>1. Introduction</title>
      <p>
        Modern single- and multiplayer video games feature a rich set of player behaviors, often contained in
playtraces encompassing movement data. However, movement data is complex to analyze and visualize
as it unfolds over space and time and becomes very large very quickly (cf. [
        <xref ref-type="bibr" rid="ref1">1</xref>
        ]). As such, traditional
visual analysis for 2D games, when faced with massive amounts of player data, often relies on multiple
views to present temporal and spatial data separately or resorts to animations. Such solutions (e.g., [
        <xref ref-type="bibr" rid="ref2">2</xref>
        ])
often require manual adjustments to the viewport and timelines to analyze the detailed information.
Multiple views, on the other hand, come with additional cognitive costs such as increased load on
working memory and efort for making comparisons [
        <xref ref-type="bibr" rid="ref3">3</xref>
        ]. Combining space and time in a single view —
such as in a space-time cube — is, however, prone to visual clutter and occlusions [
        <xref ref-type="bibr" rid="ref4 ref5">4, 5</xref>
        ], and thus only
feasible for the analysis of a small amount of movement traces.
      </p>
      <p>
        That, however, means that such solutions are not feasible for games such as multiplayer real-time
strategy (RTS) games like StarCraft: Brood War [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ] which involve large numbers of units moving
simultaneously. Furthermore, if movement data is augmented with further contextual data such as
key combat events these often get obscured. Even in singleplayer games, such as platform games,
multiple attempts can be considered in aggregate as a large number of players needs to be visualized
to understand common patterns. Given the large-scale nature, prior work has thus often resorted to
static or time-agnostic visualizations [
        <xref ref-type="bibr" rid="ref7">7, 8</xref>
        ], which — due to neglecting the time dimension — struggle
to convey dynamic player interactions.
      </p>
      <p>To address these limitations, we propose an AI-assisted 3-dimensional spatio-temporal visualization
framework that: (1) aggregates raw trajectories into voxels to reduce visual clutter, and (2) applies
anomaly detection to highlight regions of interest. We built a voxel-based aggregation method for
spatio-temporal game data that preserves the essential details of the movement and reduces the clutter.</p>
      <p>We took a framework for anomaly detection — isolation forests [9] — and applied it to create a
visualization that emphasizes rare movements: by increasing the transparency of voxels containing more
common movements, rarer voxels are emphasized. Prior work in game analytics [10, 8] has highlighted
the importance of outliers that deviate from common movement behavior as those are often more
informative (e.g., for detecting unintended paths).</p>
      <p>
        To demonstrate our approach, we conducted case studies across two diferent game genres: a real-time
strategy game, StarCraft: Brood War [
        <xref ref-type="bibr" rid="ref6">6</xref>
        ], and a custom-built platformer game, Recformer. By applying
our model to these two types of game data, we visually filtered out common movements and retained the
interesting patterns that game researchers are more likely to be interested in. The case studies provide
a subjective visual comparison of the isolation forest-based emphasis versus two simpler baselines: a
sliding-window emphasis and an emphasis based solely on speed.
      </p>
    </sec>
    <sec id="sec-2">
      <title>2. Related Work</title>
      <p>Gameplay Analytics. As video games become increasingly complex, the field of game analytics has
emerged as a valuable asset for understanding various aspects of player behavior [11]. Drachen and
Schubert [12] proposed that game analytics can be based on four types of information: the attributes of
the character, the involved events, the spatial information of the character, and the changes in all these
types of information over time. Our work particularly focuses on the latter two, specifically movement
across space and time simultaneously. Movement – given its complexity – is, however, challenging to
analyze and visualize and a variety of solutions have been proposed within the field of information
visualization [13].</p>
      <p>
        Movement Visualization for Games. The field of game analytics has drawn upon this large
heritage in geovisualization and cartography. Early work in visual game analysis has, for instance,
advocated the use of geographic information systems (GIS) software [14]. Since then several methods
have been proposed in the games literature ranging from visualizing individual paths (e.g., [
        <xref ref-type="bibr" rid="ref5">5, 15</xref>
        ]) to
diferent forms of aggregation (e.g., [ 16, 8]), and covering both 2D (e.g., [8, 16]) as well as 3D (e.g., [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ])
representations. For the sake of the completeness it should also be noted that solutions that abstract
from the actual geographic coordinates such as by focusing on semantic locations (e.g., [16] have been
presented as well. Our focus is, however, on the actual spatio-temporal trajectories. In doing so, our
work particularly relates to the one of Sufliarsky et al. [
        <xref ref-type="bibr" rid="ref5">5</xref>
        ] in the sense that we adapt the concept of
a space-time cube. However, we utilize aggregation to overcome issues of clutter when representing
larger amounts of trajectories. In doing so, we draw upon work by Wallner and Drachen [
        <xref ref-type="bibr" rid="ref7">7</xref>
        ] who used
alpha shapes to construct boundary polygons enclosing the points of the trajectories. However, their
work focused on a 2D dimensional snapshot, rather than conveying movement over time.
      </p>
      <p>Volume Visualization. In other words, we view movement as volumetric data. In this sense, our
approach also relates to work in volume rendering [17] which has been heavily utilized in medical
imaging. However, its application in the context of gameplay analysis has not yet been fully explored
to the best of our knowledge, although some solutions such as the 3D heatmaps ofered by Unity
Analytics [18] touch upon it to a slight degree. One of the major challenges in volume rendering
naturally lies in the ability to handle occlusions and reveal the inner structures of the volume (see
also [17]) for which semi-transparency is essential (e.g., [19]) and which we also utilize in our approach.</p>
      <p>Anomaly Detection in Game Data. To detect anomalies (rare) movements, we used Isolation
Forest [9], an anomaly detection algorithm that finds more eficient isolated data through random
features and recursive algorithms. Its adaptability to high-dimensional data makes it suitable for
analyzing numerous player trajectories. The efectiveness of the algorithm in game analysis has been
demonstrated in previous work, such as for collusion detection in multiplayer games [20].</p>
    </sec>
    <sec id="sec-3">
      <title>3. System Overview</title>
      <p>In this section we describe the general data processing pipeline that converts the raw data into the
voxel format used for visualization and anomaly detection. The system takes as input the playtrace
trajectories for the individual units, along with an associated team (in this work, either team 0 or team
1), in the form of sampled , ,  coordinates, where ,  are the spatial and  the time coordinate. It
produces a voxel description with a base color and emphasis value (used to control transparency and
color brightness) for each voxel.</p>
      <p>Our system aims to detect less common, anomalous player movements and emphasizing those in
spatio-temporal game data by combining voxel-based visualization and isolation forests. As isolation
forests are an unsupervised learning approach, they enable automated analysis without manual labeling.</p>
      <p>A game’s original 2D coordinates are discretized into a rectangular 3D grid. The granularity of the
voxel structure is determined by the discretization factor  . A larger  results in coarser  resolution,
fewer grid cells, and smaller data files. The grid sizes are as below :
 ≈
2
 = ⌊(max −  min)/ ⌋ + 1
 = ⌊(max −</p>
      <p>min)/ ⌋ + 1
+ (we use Python round, ties-to-even)
the window around (, , ) as
As result, the voxels are approximately isotropic in three directions and visually symmetrical.</p>
      <p>This gives a 3D grid of  ×   ×   voxels. For each voxel, let  be the sum of step distances (that
is, the distance between samples for units in the  dimension) within the voxel and  the number
of samples with nonzero step distance. For voxel (, , ), let the neighborhood window size be odd
integers , ,  with half-widths  = ( − 1)/2 ,  = ( − 1)/2 ,  = ( − 1)/2 . We define
Ω(, , ) = {︀ (, , ) ∈ [1, ]×[1,  ]×[1,  ] : | − | ≤ 
, | − | ≤ 
, | − | ≤ 

︀}</p>
      <sec id="sec-3-1">
        <title>Each voxel containing samples then has three parameters associated with it:</title>
        <p>voxel_speed = /
window_speed = ∑∑︀︀ΩΩ</p>
        <p>move_count = 
In cases where the denominator is zero, the associated value is set to zero. Voxels also store which
teams had samples in them. Voxels with no samples are set to null.</p>
        <p>For isolation forest anomaly detection, we used NumPy’s [21] sklearn [22] module. Voxel data is
lfattened into a 3 ·   ·   ·   array, and the sklearn.preprocessing.StandardScaler is used
to set the mean to 0 and variance to 1 for normalization. Then unsupervised anomaly detection is
performed at the voxel level using sklearn.ensemble.IsolationForest with hyperparameters:
n_estimators = 100
max_samples = "auto" = min(256,  )
max_features = 1.0
random_state = 42</p>
        <p>This is used to compute an anomaly score for each voxel-level feature vector, assigning higher
anomaly scores to voxels that deviate from the learned distribution. The final output is a structured
VTR (Visualization Toolkit [23] Rectilinear Grid) file for interactive visualization in ParaView [ 24] –
an open source visualization platform. We use the anomaly score and team to visualize the voxels.
More anomalous voxels are emphasized with brighter colors and more opacity, while less anomalous
voxels are de-emphasized with duller colors and less opacity. Diferent colors represent diferent team
compositions within a voxel: red represents only team 0, blue represents only team 1, and green
represents both team 0 and team 1. All color scales have the same opacity curve control points. We
also visualize an image of the level or map along with the voxels to provide environmental context for
interpretation of the movement data.</p>
      </sec>
    </sec>
    <sec id="sec-4">
      <title>4. Visualization Application Comparisons: Two Case Studies</title>
      <p>Here we illustrate the proposed voxel-based anomaly detection approach by means of two games from
two diferent genres: StarCraft: Brood War, a popular multiplayer RTS game, and Recformer, a basic
custom-built platforming game.</p>
      <p>We present visual comparisons of the isolation forest with two baseline methods: First, using only
voxel speed directly, in which the emphasis value is just the voxel speed normalized across all voxels.
Second, the emphasis value is based on a sliding window for local pattern detection. For each voxel, we
checked a 3 × 3  × 5  neighborhood and calculated a rarity score based on the spatial distribution
pattern in the sliding window.</p>
      <p>Furthermore, we used isolation forest as the unsupervised anomaly detection method itself to assign
emphasis values. Each voxel is represented by its local statistical features, and the isolation forest
estimates how outlier-like that voxel is compared to the overall distribution. Voxels deemed more
anomalous receive higher emphasis values.</p>
      <p>The resulting visualizations (voxel speed, sliding window, and isolation forest) are shown in Figures
1 and 2. We used the same settings for all visualizations. All values are normalized to the range of 0–1.
Red and blue represent voxels with data from only one out of the two teams, and green represents voxels
containing both teams. Colors are mapped by fixing the hue while varying lightness and saturation,
producing a perceptually monotonic gradient. The transparency curve control points (value, opacity)
are:</p>
      <p>{(0, 0.1), (0.55, 0.4), (1, 1)},
Here, value refers to the scalar data value of the field used for opacity mapping in ParaView, which is
the same variable as for coloring. ParaView uses it for linear interpolation between adjacent control
points.</p>
      <p>StarCraft: Brood War StarCraft: Brood War data was obtained from the STARDATA dataset [25]. We
used a single replay (one complete match), parsed with TorchCraft [26]. From this replay we extracted
unit trajectories sampled at 8 Hz (8 fps), voxelized the coordinates into a 3D grid ( and  from map
coordinates;  from time), and aggregated motion statistics per voxel. We used the open-source library
Screp1 to parse the game origin replay file to obtain basic game information, including maps. We then
ifltered out defensive structures to focus on the analysis of mobile combat units (including aircraft
units). Since StarCraft: Brood War has a large map area and higher event density,  = 15 is used to
control the data scale and the stability of the rendering, producing a grid size of 32 × 32  × 32 .</p>
      <p>Resulting visualizations are shown in Figure 1. The time within each visualization progresses from
the bottom to the top.</p>
      <p>The voxel speed image shows that almost all voxels are transparent, with the green portion almost
entirely hidden within the red and blue voxels, making it hard to observe them. The direction of
movement of the two teams can be inferred by following the ,  axis along the  axis, but it is dificult
to infer any players’ decisions from these results.</p>
      <p>The sliding window image reveals the vast majority of the coloring is concentrated at the extremes
of the color gradient, making it dificult to discern the focus of the game.</p>
      <p>In the isolation forest image, the overall color transition of all voxels is smoother. The intensity of
the red and blue voxels increases towards the end of the game (top of the cube), and there are also many
green, non-transparent voxels near the two colors representing the individual teams, likely representing</p>
      <sec id="sec-4-1">
        <title>1Code available on GitHub: https://github.com/icza/screp</title>
        <p>w
o
d
n
i
W
w
o
d
n
i
W
the players’ final battle at the end of the game. With a slight rotation and adjustment of the viewing
angle, the green voxels can be seen through the red and blue voxels, likely representing the area of
intense fighting between the two teams. At the same time, some paths become transparent and filtered
out. There are probably some combat units moving in non-combat areas, such as advancing or mining.
For both teams, more abnormalities (more solid color) are shown at the top of the -axis, i.e., the end of
the game. This is also in line with the gameplay of StarCraft: Brood War, which involves collection,
construction, and development in the early stages rather than direct combat.</p>
        <p>Recformer [27] is a custom-built platforming game with simple geometric graphics, where the player
must run and jump to avoid enemies and pits, while collecting all the coins to complete a level. We
used a level with one coin at the end.</p>
        <p>Recformer data was gathered specifically for this work from players recruited on the Prolific
crowdsourcing platform. We recruited 20 participants who were paid $1 to play the game online and logged
their gameplay data. The median time spent was 3 minutes and 17 seconds, resulting in a median pay
rate of $18.26 per hour. The methods were approved by the authors’ IRB, and participants consented to
participate in the research before playing. As it was possible for each participant to play multiple times,
we gathered 180 playtraces in total.</p>
        <p>For singleplayer games, we consider all players’ game data as team 0, and all enemies as team 1. As
all the enemies in the Recformer level move along a fixed trajectory at a constant speed, we used a single
playtrace for them. For this platform game and its smaller maps, we used a finer  = 1 to preserve
more geometric detail. This resulted in a voxel grid of approximately 96 × 22  × 30  voxels.</p>
        <p>Note that, if viewed axis-aligned (-plane), the visualization in this case study resembles a heatmap.
However, unlike a traditional heatmap which does not convey unfolding of the data over time, rotating
the view in our visualization — since the -axis encodes the time — allows to observe the dynamics of
movement patterns and anomalies.</p>
        <p>Resulting visualizations are shown in Figure 2. The player starts from the left and moves towards the
right, and the time progresses from the front to the back.</p>
        <p>The voxel speed image shows that most voxels are semi-transparent, with only a small number of
voxels at the beginning of the game showing a prominent intensity, likely representing players starting
the game collectively from the starting point.</p>
        <p>In the sliding window results, some enemy paths coloring faded, and again only the extremes of
the color gradient stand out. In particular, the players’ voxels exhibit almost exclusively extreme
transparency, making it dificult to explore the changes in player behavior.</p>
        <p>In the isolation forest view, the voxel color distribution for both teams is smoother, with most of
the enemy team’s red becoming uniformly opaque. As in this platform game, all enemies follow the
same path and speed. In addition to a few highlighted voxels at the beginning of the game, the blue
team’s voxels also show some brightness towards the middle of the game. Green voxels, representing
the simultaneous presence of both players and enemies within the area, are visible at the intersection
of red and blue voxels. Visually, these regions appear to correspond to areas where players employ
identical evasive strategies after approaching enemies. We can also notice that some bright blue voxels
are far away from the enemy. These are likely players who are wandering, waiting, or even pausing the
game. On some platforms where players might fall or need to avoid obstacles, we can observe along
the -axis that the intensity of the blue or green voxels gradually decreases. This is likely because the
players who are still playing the game have found a relatively fixed way to avoid the enemies, making
the voxels more opaque than at the beginning of the game. Considering that this is a relatively simple
platform game, this performance is understandable.</p>
        <p>The visual result also shows that most of the enemies’ voxels are translucent and similar. This also
verifies our idea of the anomaly detection pipeline, as enemies that always repeat the same action
patterns may be less interesting to game analysts in most cases.</p>
        <p>In summary of these two case studies, the voxel velocity visualization is uniformly transparent,
making it dificult to discern diferences. The sliding window highlights some end paths, but most
intermediate values still appear similarly colored. The isolation forest balances local prominence with
global data variation, but its results are more sensitive to visualization parameter choices.</p>
      </sec>
    </sec>
    <sec id="sec-5">
      <title>5. Conclusion</title>
      <p>This paper proposes a general voxelization visualization pipeline for transforming game playtrace
trajectory data from 2D into 3D voxel volumes for visual analysis, and using anomaly detection to
emphasize voxels of interest. We use the same steps across two distinct games; spatio-temporal
information is aggregated into a regular grid using a voxelization parameter; then an isolation forest
is applied to the normalized 3D feature vectors for unsupervised anomaly detection. All results are
written to a VTR file for overlay display in ParaView using color and transparency mapping. Overall,
this pipeline strikes a good balance between consistency across games and interpretable results, while
maintaining simplicity in implementation and flexibility in expansion. Our voxel-based anomaly
visualization provides a visual 3D approach to analyze complex intertwined game paths that is envisioned
to potentially be useful for tasks such as level design diagnosis, player behavior analysis, and detecting
unusual strategies.</p>
      <p>We still face the limitations that results can be afected by the discretization and parameter selection,
which can lead to unstable rarity and outlier scores in sparse regions; alignment of map textures and
voxel coordinates currently requires minimal manual fine-tuning; the isolation forest hyperparameters
are fixed for both datasets, and the feature dimensionality is currently low. However, being able
to adjust the discretization is not only a limitation but also a level-of-detail parameter. A rougher
discretization could reveal high-level issues, while a smaller one would enable a focus on more
finegrained movement. Future plans include: introducing automated map registration and cross-map
standardization; incorporating more unsupervised methods to enhance adaptability to a broader range
of games to promote the reproduction and reuse of this system. We would also like to perform a user
study to better understand the usefulness and ease-of use of these visualizations for game designers.</p>
    </sec>
    <sec id="sec-6">
      <title>Declaration on Generative AI</title>
      <p>During the preparation of this work, the author(s) used Grammarly in order to: Grammar and spelling
check, Paraphrase and reword, Improve writing style; and ChatGPT in order to: Citation management.
After using these tools/services, the authors reviewed and edited the content as needed and take full
responsibility for the publication’s content.
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