=Paper= {{Paper |id=Vol-2491/paper108 |storemode=property |title=Visualising the Training Process of Convolutional Neural Networks for Non-Experts |pdfUrl=https://ceur-ws.org/Vol-2491/paper108.pdf |volume=Vol-2491 |authors=Michelle Peters,Lindsay Kempen,Meike Nauta,Christin Seifert |dblpUrl=https://dblp.org/rec/conf/bnaic/PetersKNS19 }} ==Visualising the Training Process of Convolutional Neural Networks for Non-Experts== https://ceur-ws.org/Vol-2491/paper108.pdf
      Visualising the Training Process of
Convolutional Neural Networks for Non-Experts

 Michelle Peters[0000−0001−8884−730X]? , Lindsay Kempen[0000−0003−0556−0894]? ,
  Meike Nauta[0000−0002−0558−3810] , and Christin Seifert[0000−0002−6776−3868]

     University of Twente, P.O. Box 217, 7500AE Enschede, The Netherlands
cnn@michellepeters.eu, research@linths.com, {m.nauta,c.seifert}@utwente.nl



        Abstract. Convolutional neural networks are very complex and not eas-
        ily interpretable by humans. Several tools give more insight into the
        training process and decision making of neural networks but are not un-
        derstandable for people with no or limited knowledge about artificial
        neural networks. Since these non-experts sometimes do need to rely on
        the decisions of a neural network, we developed an open-source tool that
        intuitively visualises the training process of a neural network. We visu-
        alize neuron activity using the dimensionality reduction method UMAP.
        By plotting neuron activity after every epoch, we create a video that
        shows how the neural network improves itself throughout the training
        phase. We evaluated our method by analysing the visualization on a
        CNN training on a sketch data set. We show how a video of the training
        over time gives more insight than a static visualisation at the end of
        training, as well as which features are useful to visualise for non-experts.
        We conclude that most of the useful deductions made from the videos
        are suitable for non-experts, which indicates that the visualization tool
        might be helpful in practice.

        Keywords: Explainable AI · Convolutional Neural Network · Visuali-
        sation · Dimensionality reduction · Image recognition




1     Introduction

Image recognition has become a great beneficial technology in various fields. It
is being used for face recognition, visual search engines, e-commerce, healthcare
and much more. To classify images, a convolutional neural network (CNN) needs
to be trained. Neural networks have been found very useful for finding extremely
complex patterns [12]. Although image recognition is thus a very impressive and
useful technology, its complexity (and especially the high number of parameters)
makes it difficult to understand how a trained model makes its decisions and why
?
    Both authors contributed equally.
    Copyright c 2019 for this paper by its authors. Use permitted under Creative Com-
    mons License Attribution 4.0 International (CC BY 4.0).
2       Peters et al.

it gives certain results. Getting a better understanding and interpretation of the
model can help with debugging and improving the model, as well as generating
trust for non-experts [1]. We focus on facilitating the non-expert: an individual
without knowledge of neural networks who may not necessarily have a technical
background. The only knowledge required for our tool is a basic understanding
of classification. That is, a machine labelling input after learning from labelled
training data.
    The need to further interpret these models has given rise to numerous CNN
visualisation techniques [6]. We use the dimensionality reduction method Uni-
form Manifold Approximation and Projection (UMAP) [11] to plot the neuron
activations for every input in a single 2D graph. Our approach generates a visu-
alisation with three plots: (i) a 2D plot of the test data with the input images
as the data points, (ii) a simple 2D plot of the training data, and (iii) a line
plot of the accuracy of both the testing and training data. Most importantly,
we visualise throughout the CNN’s training phase, generating a video frame for
each epoch. We evaluate our tool by manually inspecting and interpreting the
videos, and question the accessibility for a non-expert. The data set we classify
contains grey-scale small sketches of various objects [5]. We limited us to 10
object categories.
    We have released a tool1 that intuitively visualises the training process of
a convolutional neural network. The tool can be simply adapted to visualise
other architectures of feedforward neural networks as well. We evaluated that
the visualisations can provide non-experts with a general insight into how a CNN
learns and how it can deduct the CNN’s decisions.


2     Related work

Much research concerns improving computational sketch classification [3, 5, 15,
16, 19]. The complexity of classifying sketches lies within the aspects being very
dependent on the person who drew it, such as their skill level. Using neural
networks is a valid approach to classifying these sketches. As neural networks in
general are not transparent and the task at hand is complex, this setup offers the
optimal testing ground to evaluate if our visualisation tool can help non-experts
gather insight of a neural network’s workings.


2.1   Training phase visualisation

Most training visualisations show whether a model is improving during its iter-
ations, rather than how it is training and why it makes certain decisions. One of
these visualisations is the one proposed in [2], which proposes a way to visualise
a novel type of training error curve on three levels of detail.
    Since we want to show how the model trains, we have to look at more in-
formation than just the accuracy or error. Two tools that give insight into the
1
    https://github.com/Linths/TrainVideo
                  Visualising the Training Process of CNNs for Non-Experts       3

training process of a neural network are DeepTracker [8] and Tensorview [4].
DeepTracker is a proposed visual analytics system which helps domain experts
in giving a better understanding of what has occurred in the CNN’s training
process. TensorView uses visualisations of different attributes of the CNN, such
as the weights of the convolution filters, trajectories of the first two dimensions
of the convolution weights, and the activations of the filters. Both DeepTracker
and Tensorview specifically aid model-builders so they can improve their net-
work. However, since they give a lot of information that is only relevant to an
expert or model-builder, it also becomes less understandable for non-experts.
    Therefore, when building our visualisation tool, we need to find the right
amount of information to show, to give insight into the training process, without
losing the understandability for the non-expert.

2.2   Dimensionality reduction
Our goal is to make a CNN’s behaviour understandable for non-experts. This
behaviour is determined by how every neuron activates for the given images.
Because the number of neurons can grow large and the activations are essentially
a set of formulas, showing all this information can overwhelm non-experts. One
could show all exact neuron activity by plotting all separate activation values
per input image, taking a dimension per neuron. However, to make a human-
readable plot, tools such as t-SNE [9] and UMAP [11] reduce the dimensionality
to 2 or 3. These new dimensions are compressed versions of the old dimensions.
Dimensionality reduction (DR) approximates the neural network’s behaviour.
While the absolute DR values do not carry intuitive meaning, the relative values
do: generally, if two images get similar DR values, the neural network behaves
similarly to them. When it becomes clear what images the CNN considers similar,
one can theorise about what aspects the CNN based its decisions on.
    There is much variety in the existing DR approaches as well as the further
functionality of these visualisation tools. While t-SNE has been a very popu-
lar DR implementation [9], the more recent DR implementation UMAP shows
competition in visual and computational terms [11]. Comparative tests on bench-
mark data sets, such as COIL-100 [13], MNIST [7] and Fashion MNIST [18] – all
comparable to our data – have shown that UMAP consistently visualises global
structures significantly better than t-SNE and in considerably less time than
t-SNE. Therefore, we use UMAP as our DR method.
    Using t-SNE, Rauber et al. developed a 2D method that gives insight into
how an artificial neural network learns [14] over time, by overlaying all t-SNE
frames that were taken between training epochs, showing a t-SNE “trail” for
every input entry. The imagery however becomes cluttered by compressing the
whole timeline. One can also not see the additional information – such as the
changing performance of the neural network – evolve together with the net-
work’s activations. There are also tools that create dynamic DR visualisations.
TensorFlow’s Embedding Projector, is an open-source online web application
that allows for DR with rich functionality [17]. The tool shows the changing
t-SNE plots while the neural network is being trained. The tool does not have
4       Peters et al.




                                           Repeat
        Expert                                                                          Non-expert
        builds                            per epoch                                     investigates




      Test images                                ABC
                                                 CCA
                                                 70%
                                             Prediction data
                                                (testing)

      Train images       Trained CNN                           Visualisation frame   Visualisation video

                            ABC
                            CCA
                            70%
                        Prediction data
         CNN
                           (training)



                        Fig. 1. Tool process and stakeholders


this dynamic visualisation for UMAP. The original images are included in the
plots and they are colour-coded according to actual class. The tool is interactive
but lacks certain information such as accuracy.
    We conclude we will develop a tool that creates dynamic DR visualisations,
including performance statistics, by creating videos with the inter-epoch DR
plots as video frames. We use UMAP as DR method and include the input
images in the plots. The user-friendliness and increased interpretability that the
Embedding Projector offers with its rich interactivity could be an easy extension
for our tool in the future.

3   Approach
In this section, we describe our approach for producing dynamic visualisations
and interpreting them. To further facilitate the reproduction and expansion of
this study, our source code is available on GitHub1 .
    Simply put, our training visualiser takes in train and test images, runs them
through a trainable CNN and outputs a video visualising the training process
of the CNN. The main idea is to show how a CNN develops and improves on
classifying unseen images after more training. This is why we require test data
as well, even though we aim to visualise the training process. While a properly
performing neural network is crucial to our approach, there are only a few fur-
ther constraints. Our integrated CNN can be interchanged with any feedforward
                  Visualising the Training Process of CNNs for Non-Experts        5

neural network with a fully connected layer. Note that the resulting visualiza-
tion shows the original input images, thus if the network doesn’t have images for
input, only minor code tweaks are needed to show these as data points instead.
    Figure 1 shows how the tool operates and how the stakeholders are involved.
Per epoch of the CNN, it learns from the train data, classifies the test data and
creates a visualisation frame. After all epochs, the tool creates a video from those
frames.


4     Experimental Setup

For the experiment, we use our tool on one specific data set and one specific
neural network architecture. We manually evaluate the resulting visualisations
in detail.


4.1   Data Set

The data set we use was collected by having people sketch recognizable, specific
subjects [5]. It consists of 250 categories with 80 sketches of 1111x1111 pixels
each. They analyzed sketch recognition performance by humans, which was 73%,
to compare to the computational sketch recognition.
    We augmented the training data as follows: (i) horizontal flipping, (ii) ran-
dom rotation between 3.5 and 20.5 degrees clockwise or counterclockwise, (iii)
random shift between 20 and 100 pixels to right or left and to top or bottom (iv)
random rescale between 0.75 and 0.9 or between 1.1 and 1.25. All test and train
images are resized from 1111 x 1111 to 128 x 128, converted to tensor images
and normalized according to a normal distribution with µ = 0.8 and σ = 0.2
(determined empirically).
    We limit our experiments to 10 classes to increase the CNN’s performance
and our visualisation’s legibility. We created data sets, one corresponding to a
difficult classification task (further denoted as Hard ) and one corresponding to
a simple classification task (further denoted as Easy). Table 1 shows our two
data sets. Easy has arguably easily distinguishable images, e.g. apples and ants,
while Hard contains very similar images: types of bears, birds and cars. This
way, we can assess how our visualisation videos might provide understanding
in different situations. Moreover, showing a non-expert both videos might give
them additional insight into the CNN’s training process. For every class, we
split the data into 60 original train images (which amounts to 300 images after
transformations) and 20 test images.


4.2   Neural network architecture

Previous work on the sketch data set yielded an accuracy of ≈ 70% using 15
classes [3]. The authors used a CNN with two convolutional layers with ReLU
activations, each followed by a max-pool layer, and two fully connected layers
6        Peters et al.

Table 1. Overview of data sets. Similar
classes are grouped for data set Hard
                                                             Table 2. CNN hyperparameters
    Easy                  Hard
    Easy to classify      Hard to classify                         Parameter              Value
    airplane              bear (animal)                            # Classes              10
    alarm clock           panda                                    # Train images         3000
    angel                 teddy-bear                               # Test images          200
    ant                   cloud                                    Image width            128
    apple                 sheep                                    Batch size             25
    banana                pigeon                                   # Epochs               20
    basket                seagull                                  Learning rate          0.0001
    bed                   car (sedan)                              FC2 size               50
    bell                  suv
    calculator            van

                                         64@64x64
                                                            64@32x32
            32@128x128
                              32@64x64                                        1x(64*32*32)
1@128x128
                                                                                             1x50 1x10




Input    Convolution + ReLU     Max-pool      Convolution + ReLU      Max-pool      FC1      FC2 Output
           k=5, s=1, p=2      k=2, s=2, p=0     k=5, s=1, p=2       k=2, s=2, p=0


Fig. 2. Architecture of the CNN. The visualised component is red: the pre-activation
of the second fully connected layer.


(FC1 and FC2). In this work we use a similar architecture, that is shown in Fig-
ure 2. The differences between our architecture and that of [3] are the amount of
nodes in the FC layers, the amount of filters per convolutional layer, the stride
in the last max-pool layer, and that their FC1 has ReLU activations, where ours
does not. We apply dropout before FC1, and softmax on the 10 output nodes.
All parameters are determined empirically, optimising test accuracy, speed and
the visualisation (e.g., showing a clear clustering). Table 2 lists the final hyper-
parameters. We increased the number of epochs to show how the visualisation
changes when the model overfits.

4.3     Visualisation
To make the training process visible and understandable for non-experts, we
visualise the training data, testing data and accuracy of training and testing per
epoch, as can be seen in Figure 5. For this, we take the pre-activation values
of FC2 layer, as shown in Figure 2. To visualise all data points from an epoch,
                  Visualising the Training Process of CNNs for Non-Experts       7

we save the original labels, predictions and pre-activation values of FC2 of each
image after it passes the neural network.
    For the test data plot, we want to display the images on the plot points, to
make it visible why a certain image was perhaps misclassified, why specific classes
are displayed as multiple clusters or why they appear close to specific other
clusters. We add a mask to each of those images with the colour corresponding
to the predicted label, and a red border if the image is misclassified, which is
most useful when the actual class of the image is difficult to determine from
the image and to give a quick overview of how many images within a certain
cluster are misclassified. This way, the plot represents three important parts
of information; (i) the actual class, which is represented by the image, (ii) the
predicted class, represented by the image colour, and (iii) the neuron activity,
represented by the location of the image in the plot figure.
    The training data plot is almost the same as the test data plot, however, we
only show simple dots instead of the images, since we want to focus on showing
the effect of the training phase on the test data, and thus we want to keep the
training data plot small.
    We present the test accuracy and train accuracy, to see whether the CNN
trains well, and to view the relation between the quality of the neural network
and the UMAP visualisation.
    To visualise the neuron activity, we use UMAP (with #neighbours=25) to
reduce the pre-activation node values of the FC2 to two dimensions. To keep this
dimensionality reduction consistent, we fix the UMAP seed. This way, when the
values in the nodes are only slightly changed after an epoch, the x and y values
of an image will also only slightly change, which makes for a visualisation video
which is easy to follow.
    However, since the absolute x and y values have no useful addition for non-
experts when they already have the relative locations of the plot points, we
decide to not show any values on the axis of the training and testing data plots.
This way, we avoid confusing the user with useless information.


4.4   Evaluation

Our visualisation needs to give useful insights into the decisions that are made
inside a neural network during the training process, while also considering the
level of knowledge and understanding of a non-expert user. To evaluate whether
our tool complies to these two conditions, we compare our dynamic visualisations
with static visualisations, look at which conclusions can be drawn from our
visualisations, and also look at which aspects can be confusing for non-experts
and can lead to wrong conclusions.


5     Results

In this section we show and interpret our visualisations for Easy and Hard. We
also examine whether the visualisations themselves, the observations and the
8       Peters et al.




Fig. 3. Visualisation frames of epochs 1, 9 and 20 of Easy, with epoch 9 as the supposed
start of overfitting.
                   Visualising the Training Process of CNNs for Non-Experts           9




Fig. 4. Visualisation frames of epochs 1, 9 and 20 of Hard, with epoch 9 as the supposed
start of overfitting. Clusters are manually highlighted for epoch 9.
10       Peters et al.

interpretations are accessible for non-experts. While our resulting visualisation
is a video, for clarity we will refer to video frames (Figures 3 and 4). We refer to
a specific frame with a shorthand, e.g. the visualisation of Easy after 3 epochs is
called “Easy-3”. The two output videos and the raw frames are available online2 .

5.1     Accuracy of the model
We build and tweak the neural network based on Easy, which consists of only
10 classes. With this data subset, we reach over 70% accuracy. We also test the
accuracy of our model on a data subset of 15 classes. For this, we use Easy,
with the addition of the crab, pineapple, snail, sponge bob and squirrel classes.
Before the model starts to overfit, at epoch 7, we achieve around 74% accuracy.
However, despite our neural network being resistant to more than 10 classes, our
visualisation becomes cluttered and less understandable when it has to present
more classes. Table 3 gives an overview of the accuracies of our model.


           Table 3. Accuracy of our model with the different data subsets.

                         Dataset Number of classes Accuracy
                         Easy    15                74%
                         Easy    10                70%
                         Hard    10                50%




5.2     Trends observed
We observe several trends in the visualisations for Easy and Hard after running
for 20 epochs.
    Throughout the whole timeline, Easy and Hard show clustering in the train
and test plots. Every frame contains several clusters of mainly the same ac-
tual and/or predicted class. Over time, these clusters separate more. The video2
shows relatively smooth transitions; it maintains the same data structure with
some slight to moderate shifts. Unexpectedly, the visualisation seems to flip hori-
zontally or vertically at a few points, but even then the relative positioning seems
consistent. Interestingly, a specific structure is only present in the train plots for
Easy-1 and Hard -1. We refer to the very distanced and closely knit groups of
just several points. We found out through simple tests that this happens when
there is too little coherence in the data to properly apply DR – logical to happen
after just one epoch.
    Generally, the image distancing in the test plot seems logical and easily inter-
pretable. Firstly, in Easy-4 and later, the apple cluster moves far away from all
the other points. This means the CNN has found a very specific way to predict
apples: the activation behaviour for apples is very different than for the other
2
     https://doi.org/10.5281/zenodo.3525091
                  Visualising the Training Process of CNNs for Non-Experts     11

               Table 4. Types of prediction-placement combinations

                                       Plot placement
            Prediction Predicted class Actual class Seemingly random
            Correct                 A                      B
            Incorrect        C              D              E



classes. As almost the whole cluster is predicted correctly, the strong pattern
the CNN learns is a useful one. By inspecting all the images, one can speculate
what was used as the discriminating characteristic for apples. We hypothesize it
is a combination of the round and simple form and the large whitespace.
    Secondly, in Hard -7 and later we find clusters that contain two to three
predicted classes. The partitioning almost completely matches our expectations
(Figure 1), grouping cars and bears. However, the tool does not group sheep with
clouds. To the contrary, the sheep are grouped with bears. This indicates the
CNN has ease separating sheep from clouds, but not from bears. We believe the
CNN focuses on legs which is a strong differentiator between sheep and clouds,
but not for sheep and bears. The bears that are matched with the sheep do look
similar as they are on all fours. Moreover, the CNN clearly distinguishes this
bear variant from bears that are sitting, standing on hind legs or lack a body.
    The train accuracy signals the model overfits around Easy-9 and Hard -9.
The clusters in the test and train plots continue to separate, even for Easy
where the visualisation seems to have stabilised. Easy-9 and Easy-20 are closely
similar, but Easy-20 shows a bit more separation. For Hard, these differences
are bigger. While Hard -20 has a significantly clearer separation of clusters than
Hard -9, the test accuracy does not actually increase. Note that the clusters here
concern images of the same predicted class. In reality, the model just polarizes
its activation behaviour. It becomes stricter in enforcing the patterns it claims
to see, but not the patterns that actually exist. It is important to keep in mind
that more exaggerated clustering does not always indicate a better model.


5.3   Situation types

There are multiple ways an image can appear in our visualisations. The back-
ground colour, thus predicted class, can either be correct or wrong. And the
position of the image can differ. Table 4 shows the different types of combina-
tions, and in Figure 5 we point out some examples of these types. For A, we show
a correctly classified apple, which is also placed correctly. For B, we point out
an alarm clock which is classified correctly but not placed with the other alarm
clocks. C is represented by a basket, classified as an apple, which is also placed
with the apples by UMAP. For D, we show two examples; bananas classified as
bells, and bells classified as bananas. However, UMAP places both with their ac-
tual class rather than their predicted class. That means that UMAP’s DR seems
to be better at identifying these images than the neural network’s final layers,
while they are given the same input: the pre-activation values of FC2. Lastly, E
12      Peters et al.




Fig. 5. Visualisation of Easy after 2 epochs. Several datapoints are highlighted with
their situation type.


is represented by a misclassified alarm clock, which is neither placed with the
other alarm clocks, nor its predicted class. There are also middle grounds of the
above-mentioned situations. For example, a combination of C and D. When an
image is classified incorrectly, but both the actual and predicted class are clus-
tered together, the image can be placed with both its actual and its predicted
class images. This means that the classes are probably really similar, such as the
types of cars in Hard.

5.4   Approachability for the non-expert
Our tool visualises only information that is useful for a non-expert. For the test
data, we visualise the actual class, the predicted class, the neuron activations
(which estimates the class compatibility), and the overall accuracy. The same
holds for the training data except for the actual classes. Since these are all
features that are easy to understand, also for non-experts, the tool seems very
approachable for people with little to none background knowledge about neural
networks.
    There are some aspect that might be confusing for non-experts, such as situ-
ation types B, D and E from Section 5.3. These situations are less intuitive since
non-experts might not fully understand the difference between the output of the
neural network, the activation values of the neurons, and the output of UMAP.
When these do not agree on an image, it can become confusing for the user as
to why an image is classified as one thing, but clustered with another. Other
                  Visualising the Training Process of CNNs for Non-Experts      13

confusing factors are the occasional flips of the visualisations between epochs
and the misleading clustering of a increasingly overfitting model (mentioned in
Section 5.2).
   Visualising the training process over time – rather than after it has finished
– can give insights into which features are recognized first, and when certain
images are clustered much quicker and further away from the rest of the classes.
Also, seeing certain classes cluster together or next to each other can provide
the knowledge that the neural network sees them as quite similar.



6   Discussion

In this section, we lay out factors that have influenced our research and the
consequences for the tool’s quality and our research’s validity.
    Ideally, our visualisation would be insightful for CNNs of various performance
levels. We examined results for CNNs scoring around 50% and 70% test accuracy.
Because of the challenging dataset, we were unable to get a higher accuracy
and check if our visualisation would then be insightful. The data set we used
is arguably hard to classify, as it only contains 80 instances per class and the
classes can still contain quite different drawings, e.g., the bears mentioned in
Section 5.2.
    The CNN overfits rather quickly. It allows for only eight visualisation frames
without overfitting. More frames would facilitate smoother transitions and might
be more understandable and less overwhelming for non-experts. To add, detail
might be lost by the lack of intermediate epochs.
    Dimensionality reduction in itself is flawed. A datapoint can have false neigh-
bours or missing neighbours due to the “compression” of dimensions. This could
make our visualisation misleading. We have not tested other dimensionality re-
duction methods than UMAP and we have only roughly optimized the UMAP
settings to minimize such mistakes. Also, we have not counted any of these mis-
takes in our current visualisation, but we did see UMAP struggling to apply DR
in Easy-1 and Hard -1.
    Because UMAP refits on the data for every epoch, the visualization frames
sometimes appear to be flipped horizontally or vertically. This makes the tran-
sitions between our frames less smooth. A solution to this is applying DR only
once, on the data of all epochs. We can then still visualise every epoch indi-
vidually by only displaying the appropriate data points. This approach could
however lower the DR quality as it has to fit significantly more data. Addition-
ally, it would disable “live visualisations”: visualising while running the CNN.
    We have not used a standardized method to evaluate understandability, e.g.
user studies. Our evaluation method concerned just two test cases and was not
quantified. Visual inspection is not completely objective as well. Though tasks
as determining clusters have no objective answer anyway: there’s no silver bullet.
All in all, our methodology could not produce statistical claims.
14      Peters et al.

7    Summary and Future work

We have built a CNN for the data set of human-made sketches with an accu-
racy of over 70% for 10 classes when using the easily distinguishable data subset
(Easy). For the data subset with classes that seem very similar (Hard ), the accu-
racy is slightly lower, due to the classes being more similar. During the training
of this convolutional neural network (CNN), we have created video visualisa-
tions which provide useful information such as the actual class, predicted class
and similarity between classes. Despite some situations which can be difficult to
understand by a non-expert, the videos are overall quite interpretable even by
people without prior neural network knowledge.
    Many options for improvement and addition have been left for the future.
Most importantly, we would like to apply user studies with non-experts in our
evaluation for a better scientific justification. That way, we can evaluate how
understandable the visualizations are in practice. Another useful addition for the
evaluation would be a thorough comparison of our tool with several other neural
network visualisations. It would be interesting to at least include methods that
are focused on the training process and/or DR, such as [2, 4, 8, 9, 14, 17]. With
user studies and tool comparisons, one can more properly assess the added value
of both the DR and training process aspect of the visualizations. Furthermore,
it could be interesting to see whether fitting the UMAP visualisation to the
result of the first epoch, or to all epochs after training, makes the visualisation
more easy to follow since clusters might not jump between epochs. Another
useful addition could be to add an automatic cluster detector, which can detect
the types in Table 3. Some methods can detect false or missing neighbours in
DR [10], which would add a quick overview for the user of which data points are
classified correctly but displayed within the wrong cluster. Moreover, a small but
very useful tool to give concrete and objective insight into how distinguishable
the classes are is a confusion matrix of the actual classes versus the predicted
classes. Lastly, the tool could be made into an interactive viewer. By being able
to switch certain options on or off, it could provide more information without
too much clutter. It could then also enable a 3D visualisation.


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