Classifying Intelligence Tests Patterns Using Machine Learning Methods

Georgios Liapis

, Loukritira Stefanou and Ioannis Vlahavas

Aristotle University of Thessaloniki, Thessaloniki, Greece

Keywords:

Intelligence, Raven Matrices, Machine Learning, Pattern Classiﬁcation.

Abstract:

Intelligence testing assesses a variety of cognitive abilities and is frequently used in the evaluation of people

for jobs, army recruitment, scholarships, and the educational system in general. Licensed psychologists and

researchers create and analyze intelligence tests, setting the difﬁculty layer, grading them, and weighing the

results on a global scale. However, developing new model tests is a time-consuming and challenging pro-

cess. In this study, we lay the groundwork for developing a model that classiﬁes the IQ patterns, in order to

generate new IQ Raven tests. More speciﬁcally, we analyze Raven’s Progressive Matrices Tests, a nonverbal

multiple-choice intelligence test, and their patterns using a variety of Machine Learning (ML) techniques. In

such intelligence tests, the question’s data includes mostly abstract images aligned in a grid system, with one

missing element and a pattern that connects them by threes in horizontal and vertical order. These tests have

been labeled based on several factors, such as the number of images, the type of pattern (e.g. counting, adding,

or rotating), or their complexity and in order to classify them, various ML methods are used. Results of the

current study act as a deﬁning basis for the use of advanced Neural Network models, not only for classiﬁcation

but also for the generation of new IQ patterns.

1 INTRODUCTION

Intelligence is one of the most intriguing research

topics, and many people believe that evaluating it is

crucial. Many attempts have been made throughout

history to develop tests that would make this assess-

ment feasible and valid. The Raven Progressive Ma-

trices (John and Raven, 2003) are tests that achieve

Intelligence Quotient (IQ) assessment, amongst other

things, and are utilized by numerous organizations

across the world. They are based on a grid of nine

elements, each of which is related to the ones in the

same row (or column), and the ﬁnal element is miss-

ing. The individual must ﬁrst identify the pattern that

connects these ﬁgures to ﬁnd the missing one.

In recent years, technology has advanced signif-

icantly, and many attempts have been made to ad-

dress previously unsolved problems, particularly in

the area of picture identiﬁcation and classiﬁcation.

Attempts to classify pictures with topics ranging from

animals to handwritten symbols have been effective

(noa, ). With the use of methods, like Machine Learn-

ing (ML), and in particular, Neural Networks (NN),

such challenges can be solved in a variety of ways.

Despite the fact that Artiﬁcial Intelligence (AI) has

https://orcid.org/0000-0003-1124-4257

https://orcid.org/0000-0003-3477-8825

numerous applications in image classiﬁcation, iden-

tifying and classifying patterns is a novel, intriguing,

and challenging aspect. This is because discovering

hidden relationships between image elements differs

from identifying speciﬁc elements in a picture.

In this paper, we propose AI methods that can

classify Raven IQ tests based on custom labels for

how they handle the pattern. More speciﬁcally, we

categorize the kind of pattern, whether it was about

adding or subtracting elements, or some parts of the

elements were moving, or there were elements that

existed on a vertical or horizontal axis.

The method of ﬁnding the images online turned

out to be challenging. Web scraping was used to ﬁnd

pictures with the necessary features, but very few of

them were in the right format. Unfortunately, pic-

tures with Raven patterns in a certain type of grid, that

were of good quality and free of noise were uncom-

mon. We did manage to ﬁnd and collect an adequate

amount of data nonetheless.

Next, we build models using state-of-the-art AI

methods, that they can be trained to identify the pat-

tern in a very abstract way. To reach a high enough

level of efﬁciency, such algorithms require a large

number of resources and data, which is a signiﬁcant

limitation in this type of work.

Another challenge we had to overcome is the di-

Liapis, G., Stefanou, L. and Vlahavas, I.

Classifying Intelligence Tests Patterns Using Machine Learning Methods.

DOI: 10.5220/0011606500003411

In Proceedings of the 12th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2023), pages 717-724

ISBN: 978-989-758-626-2; ISSN: 2184-4313

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

717

mensions of the images. There is a high computa-

tional need when trying to diminish the images’ di-

mensions. However, we used our available computing

power as efﬁciently as possible to create models that

could perform well on average.

This paper contributes to analyzing the way Raven

IQ tests work as patterns and can be used as a ﬁrst step

to create models that can generate new IQ tests.

Regarding the paper’s structure, we ﬁrst examine

related research that has been done in the classiﬁca-

tion of IQ tests, and then providing a general overview

of the major issues, such as human, artiﬁcial, and

machine learning. The creation and preparation of

our data set is covered in the following chapter, af-

ter which we introduce our models and analyze the

training procedure. We also include a discussion and

possible future work at the end.

2 RELATED WORK

Numerous attempts have been made to classify a va-

riety of images, but to the best of our knowledge, the

classiﬁcation of Raven IQ test images based on pat-

tern types is the ﬁrst of its kind.

One of the best known examples is the CIFAR

data set (Krizhevsky, 2009), which is a data collec-

tion that includes 50,000 training photos and 10,000

test photos with 10 different labels (airplane, automo-

bile, bird, cat, deer, dog, frog, horse, ship, and truck).

Three convolutional layers are followed by concen-

tration layers in the model that conducts the classiﬁ-

cation of these images.

Other pattern recognition problems that have been

solved, include topics like optical microscopy images

(Bulgarevich et al., 2018). In this work, the Random

Forest classiﬁer was used, with highly accurate re-

sults.

Regarding the combination of IQ tests and

AI methods, deep learning methods were used to

solve abstract visual reasoning domain problems

(Małki

nski and Ma

ndziuk, 2022). More speciﬁcally,

this paper reviews the work regarding traditional and

neural network models trying to solve Raven Progres-

sive Matrices. The difference between this approach

and ours is that we label and categorize the matrices

themselves, while the above research tries to solve the

matrix while having the answer as a label.

Based on these ﬁndings, we decided to use not

only traditional ML methods, but also Neural Net-

works, to classify IQ tests and compare our models

in such a diverse and complicated data set.

3 BACKGROUND

This section delves into the deﬁnition of intelligence,

its qualities, and how it is measured. In this section,

we also deﬁne artiﬁcial intelligence and analyze the

details of the methodologies we utilize.

3.1 Human Intelligence

There are numerous deﬁnitions of intelligence, as it is

such a complex aspect of human life. In a broad sense,

it’s deﬁned as ”the intellectual activity of capturing

the important elements of a situation and accurately

responding to its demands” (Heim, 1970). Many at-

tempts have been made to lay a foundation of its char-

acteristics and establish a theory about it.

The Intelligence Quotient (IQ) refers to a person’s

ability to deliberately adapt his spirit to new surround-

ings and requirements, as well as to new responsibili-

ties and living conditions (Stern, 1949).

A common practice to employ the processing

speed to given tasks is intelligence testing (IQ Tests).

The questions on IQ tests are designed to look at

a wide range of mental abilities, including the ones

mentioned above. There are samples for each type of

question that could come on an IQ test for each kinds.

The most common IQ tests were created by Raven

(John and Raven, 2003), and they consist of a grid of

9 shapes that follow one or more patterns horizontally

and vertically. For example, Figure 1 depicts a Raven

IQ test, with each circle changing by a certain amount

each time, and the correct answer is 6. Usually, these

tests have six to eight possible answers, of which only

one is correct.

Figure 1: Indicative IQ test.

3.2 Artiﬁcial Intelligence

Artiﬁcial intelligence (AI) is a ﬁeld of computer sci-

ence that specializes in computers that mimic human

intelligence (Barr and Feigenbaum, 1981). Machine

ICPRAM 2023 - 12th International Conference on Pattern Recognition Applications and Methods

718

learning arose out of the need for complex Artiﬁcial

Intelligence applications for which human was unable

to provide knowledge representation through analysis

and problem-solving. As a result, this role is carried

out by a computer, which, using data provided by the

user, employs various machine learning techniques to

draw his own conclusions from the information pro-

vided.

3.3 Machine Learning Methods

There are numerous traditional Machine Learning

(ML) technologies available that can be used in classi-

fying objects, like K-Nearest Neighbours (KNN), De-

cision Trees, and Random Forest. These models are

part of supervised learning, and they detect and clas-

sify patterns by analyzing labeled data.

3.3.1 K-Nearest Neighbours

One of the best-known techniques for image classiﬁ-

cation is the k-Nearest Neighbors (KNN) algorithm.

One can utilize this algorithm with a limited set of

data, like ours, as it does not ”learn” any function

from the input. In fact, it is based on the distances

between feature vectors, being the pixels of the pho-

tographs in this example. As a result of its simplicity,

its performance can be used as a benchmark for other

models.

3.3.2 Decision Trees

One of the most well-liked tree-structured learning al-

gorithms is the decision tree. The internal nodes stand

in for the feature of a data set, branches for the rules

of the decision, and each leaf node for the result. The

values of the root’s attribute are compared to the val-

ues of the image’s attribute to predict a tag for an im-

age. It moves to the next node based on the compari-

son and follows the matched branch.

3.3.3 Random Forest

The Random Forest Algorithm is founded on the idea

of ensemble learning. It is a classiﬁer that uses sev-

eral decision trees on different subsets of the data set

and improves performance by using either the average

value or the majority vote of the trees (Cutler et al.,

2012).

3.3.4 Artiﬁcial Neural Networks

Another method is Artiﬁcial Neural Networks (NN),

a machine learning technology, that simulates the hu-

man nervous system. They combine people’s abil-

ity to grasp objects and circumstances with comput-

ers’ ability to quickly conduct operations, handle, and

store enormous volumes of data.

In relation to a human neuron, the one that has a

predetermined activation function receives the data as

weighted input and eventually makes predictions. In

essence, an activation function determines whether or

not to stimulate the cell. If not, new computations

must be made using the threshold, weights, and bi-

ases. A bias is a constant parameter used to modify

the output. The activation function may only in some

circumstances be step, sigmoid, hyperbolic, ramp, or

linear (Dongare et al., 2012).

Convolutional Neural Networks (CNN) are a type

of Deep Neural Network that is linked to the biologi-

cal structure of the brain, speciﬁcally, the part respon-

sible for vision perception (Hubel and Wiesel, 1962).

Each image via which CNN is trained is viewed as a

two-dimensional table. Their job is to reduce the pic-

tures to a format that is easier to alter while maintain-

ing the features that are necessary for a solid forecast.

4 METHODOLOGY

In this section, we describe how we created and la-

beled the data as well as how the models were built

for classifying new data.

4.1 Data Set Creation

There have been suggested few well-known data sets

that are similar to Raven IQ test matrices, like D-set

and G-set (Ma

ndziuk and

Zychowski, 2019), PGM

(Barrett et al., 2018a) and RAVEN (Zhang et al.,

2019) amongst others. These data sets offer a variety

of tests, that only include the possible answers along

with a label for the correct answer. For the scope of

this paper, a new data set with custom-made labels

was created. We employed two distinct methodolo-

gies and tools to ﬁnd the images that would comprise

the data set. First, we wrote scripts for scraping im-

ages from the internet using tags. Then we used tools

for a more specialized scrape of speciﬁc pages. We

obtained approximately 6000 images relevant to IQ

test questions using these methods. After removing

the duplicates and making the appropriate selection,

1500 images remained to be processed.

4.2 Labelling Methodology

Following the data collection, the next step was to la-

bel them, since the model would have to learn to dif-

ferentiate the IQ tests based on the patterns they in-

Classifying Intelligence Tests Patterns Using Machine Learning Methods

719

cluded. The way a test is created can help classify

it, based on aspects like the relation between the ele-

ments of each test (e.g. progression pattern), the ob-

jects (e.g. their shape) and the attributes (e.g. num-

ber) (Barrett et al., 2018b). There are also reviews on

how to solve various types of puzzles, problems, and

riddles. (Gardner, 2005) , (Hern

andez-Orallo et al.,

2016). All these can be noted as a baseline for our

label proposition.

The labels proposed are related to the pattern, how

it is changing, and the objects from which it consists.

These are the core elements that change the difﬁculty

and complexity of such IQ tests. The presence of

more objects and how these are related has an impact

on the time one needs to ﬁnd and decipher the pattern

as a whole. In more detail, there are four main labels:

• Pattern Orientation: The structure and the axis on

which the pattern is shown. Speciﬁcally, whether

it is constructed horizontally, vertically, or both.

As we can observe in Figure 2, the pattern exists

on both axes in all the tests.

• Process: The change of each process of the pattern

as an action. That is, whether it stays the same

or changes from shape to shape. The operation

is variable in Figure 2(A) because the quantity is

deducted from the right side of the ﬁgure on the

horizontal axis, while on the vertical axis from the

bottom side. On the other hand, we can see in

Figure 2(B) that the operation has the same impact

in all circumstances.

• Process Value: The value of the pattern and

whether it changes. It can be classiﬁed as either

variable or constant. Figure 2(A) shows a con-

stant quantity of ¼, but Figure 2(B) shows a vari-

able quantity that might be 1, 2, or 3.

• Pattern Kind: The general way the pattern is at-

tributed to the elements. There are numerous

types of inquiries that can be classiﬁed. They

were, however, generalized to the point that each

category represents a collection of subcategories.

– Quantity Change: They include operations be-

tween numbers and shapes, as well as multipli-

cation and subtraction operations.

– Movement: Rotation and simple form move-

ment are some examples.

– Existence: It encompasses not only the basic

existence of shapes or numbers but also their

combinations. The exact instance is shown in

Figure 2(C).

In Table 1, we can observe all the labels and their

values. These were used to categorize the data set for

the model to classify each IQ test.

Figure 2: Indicative IQ tests with different patterns.

After labeling the data, the next step was to train

our models. We must also note that all of our models

tried to classify the tests based on the Pattern Kind

label.

4.3 Training Results

We used a variety of methods, from traditional ones

(K-Nearest Neighbors, Decision Trees, and Random

Forest) to Neural Networks using the sklearn library

and TensorFlow. We also applied some feature extrac-

tion techniques and the Fourier transformation, which

represents an image as a sum of sinusoidal waves.

Furthermore, we converted images in the form of

a NumPy array to a Keras image array, which is a 4d

tensor with the dimension being the batch size, height,

width, and channels. This gave the ability to easily

manipulate the image tensor with the TensorFlow op-

erations.

Then, we scaled the pixel values of our image ten-

sor from the range [0,255] to [0,1] which helped the

models to learn more effectively.

Finally, the data set was ﬁrst split into training

(80%) and test (20%) and the test set to a validation

set for the cross-validation process during the training

of the NN.

4.3.1 K-Nearest Neighbors

We run multiple instances of the model, with different

values for k, and we ﬁnally used k = 3 for the training,

with a yield of F1 score of 46%, a low score taking

into account it is a simple classiﬁer considering the

probability of randomly guessing the correct class is

13%. Moreover, as shown in Table 2, the metrics with

the Fourier are lower, with an F1 score of 44%.

Nonetheless, there is a fairly good distribution of

predictions in the classes according to Figure 3, which

displays a table that is frequently used to describe the

performance of the model (Confusion Matrix).

4.3.2 Decision Tree

For the training of this model we set the max depth to

15 and the F1 score is 39%, as seen in Table 3 with

both Fourier transform applied or not, which is a quite

low percentage due to decision trees’ proclivity for

overﬁtting to training data.

ICPRAM 2023 - 12th International Conference on Pattern Recognition Applications and Methods

720

Table 1: Data set labels.

Pattern Orientation Process Process Value Pattern Kind

Horizontal Constant Constant Quantity Change

Vertical Variable Variable Movement

Both Existence

Table 2: Metrics for KNN results (with Fourier).

precision recall f1 score support

class 0 0.42 (0.42) 0.66 (0.64) 0.52 (0.51) 114 (114)

class 1 0.44 (0.44) 0.31 (0.25) 0.39 (0.32) 71 (71)

class 2 0.49 (0.50) 0.34 (0.36) 0.40 (0.42) 109 (109)

accuracy 0.46 (0.44) 294 (294)

macro avg 0.48 (0.45) 0.44 (0.42) 0.44 (0.41) 294 (294)

weighted avg 0.47 (0.45) 46 (0.44) 0.44 (0.41) 294 (294)

Figure 3: Confusion Matrix for KNN results (left simple,

right with Fourier).

4.3.3 Random Forest

For the random forest model we also set the max

depth equal to 15. The model has an F1 score of

48% without the Fourier, and 49% with the Fourier

applied, as depicted in Table 4.

It distributes the most samples in the ﬁrst, and

most numerous, class, as shown in Figure 4, some-

thing that explains the models results.

Figure 4: Random Forest Confusion Matrix.

4.3.4 Convolutional Neural Networks (CNN)

For our CNN model, we used ﬁlters of varying sizes

and convolutional layers. We made two different

models, by changing the number of the convolutional

layers to two or three but with a similar structure,

which follows:

• First convolutional layer: ﬁlter size 32 and ReLU

activation function

• First layer of Pool: Max Pooling with a size of

2x2.

Table 3: Metrics for Decision Tree results (with Fourier).

precision recall f1 score support

class 0 0.40 (0.40) 0.39 (0.49) 0.39 (0.44) 114 (114)

class 1 0.32 (0.18) 0.35 (0.17) 0.34 (0.17) 71 (71)

class 2 0.42 (0.53) 0.41 (0.43) 0.42 (0.48) 109 (109)

accuracy 0.39 (0.39) 294 (294)

macro avg 0.38 (0.37) 0.38 (0.36) 0.38 (0.38) 294 (294)

weighted avg 0.39 (0.40) 39 (0.39) 0.39 (0.39) 294 (294)

• Second convolutional layer: ﬁlter size 32 and

ReLU activation function (This ﬁlter is size 64

when we have a third convolutional layer)

• Max Pooling’s second layer

• Third convolutional layer: ﬁlter size 64 and ReLU

activation function (This exists only on the second

model)

• Max Pooling’s second layer (This exists only on

the second model)

• Flatten Layer: convert the data to a one-

dimensional table before continuing to the next

layer

• First fully connected layer (Dense Layer) with an

output size of 64

• Second Dense Layer which has an output size of

three, same as the number of classes we predict

The learning rate, the number of epochs that the

model runs, and the batch size, which is the number of

training data repetitions utilized, were all ﬁne-tuned

during the training procedure of these models.

The accuracy of the ﬁrst model (two convolutional

layers), was high in many cases and loss was minimal

during the training, but this was not the case in the val-

idation set. As a result, we changed the batch size and

epochs. We notice that when we reduce the number

of epochs the model is able to generalize more effec-

tively. On the other hand, when we reduce the batch

size, the model’s F1 score also decreased. So, when

we altered these two parameters at the same time, the

model became more efﬁcient, and the classiﬁcation

became more uniform. Regarding the second model,

with three layers of convolutional, we reduced the

learning rate and followed the same methodology as

the ﬁrst model regarding the batch size and the epoch

parameters. This made our models more efﬁcient.

In Figure 5 we observe the confusion matrix for

the second model. The validation loss is limited to

1.31, and the F1 score is 56%, which is remarkable

considering that the ﬁrst models had a validation loss

of 1.8 and an F1 score of up to 54%.

Classifying Intelligence Tests Patterns Using Machine Learning Methods

721

Table 4: Metrics for Random Forest results (with Fourier).

precision recall f1 score support

class 0 0.44 (0.45) 0.92 (0.96) 0.59 (0.61) 114 (114)

class 1 0.83 (0.00) 0.07 (0.00) 0.13 (0.00) 71 (71)

class 2 0.67 (0.71) 0.29 (0.33) 0.41 (0.45) 109 (109)

accuracy 0.48 (0.49) 294 (294)

macro avg 0.65 (0.38) 0.43 (0.43) 0.38 (0.35) 294 (294)

weighted avg 0.62 (0.44) 48 (0.49) 0.41 (0.40) 294 (294)

Figure 5: Confusion Matrix for 3 layers Convolutional Neu-

ral Network model.

Last but not least, we used cross-validation, with 5

folds, 8 epochs, and 8 batch size, to ﬁne tune the best

CNN model. In Table 5, we can see the metrics of the

second model (three convolutional layers), where we

must note that the accuracy is 56%. During the cross-

validation process, we use a validation set for the ﬁnal

output, and we can see the results of the training in

Figure 6.

5 PERFORMANCE RESULTS

The results of the training and test procedure are pre-

sented and discussed in this section and we can ob-

serve a collective table of all the scores (Table 6).

Both the k-Nearest Neighbors model yielded 47%

and the Random Forests model yielded 47%, while

Decision Trees performed at just 40%. In general, tra-

Figure 6: Train vs Validation Accuracy of Convolutional

Neural Network model with cross validation.

Table 5: Metrics for CNN results.

precision recall f1 score support

class 0 0.54 0.81 0.65 131

class 1 0.51 0.28 0.36 64

class 2 0.63 0.40 0.49 99

accuracy 0.56 294

macro avg 0.56 0.50 0.50 294

weighted avg 0.57 0.56 0.5 294

ditional machine learning models performed poorly in

image classiﬁcation.

This is expected, because their architecture is pri-

marily designed to accommodate structured data and

they are not well-suited for image classiﬁcation. Es-

pecially RGB images that have lot of dimensions; for

instance, a 268x268x3 image includes 3 channels for

RGB and 71.824 pixels per channel.

On the other hand, the processing of these many

dimensions is not challenging using CNN. These

models are predominantly employed for image clas-

siﬁcation, where they have the advantage of automat-

ically detecting essential traits without the need for

human intervention.

These results show that Raven IQ tests can be

custom labeled and classiﬁed, regarding their pattern

type, with a fair efﬁciency, given the size of our data

set.

6 DISCUSSIONS AND FUTURE

WORK

In this study, we propose a number of Machine Learn-

ing models that learn to classify Raven IQ tests on

custom-made labels based on their pattern types. In

particular, we constructed a data collection containing

pictures of multiple Raven IQ progressive patterns of

various types.

The next step was to build the data set’s labels,

which included not only the pattern’s orientation, but

also the process, its value, and its kind. These identi-

ﬁers refer to the pattern’s variation in qualities as well

as its changes from one ﬁgure to the next.

Following that, we built and trained traditional

machine learning models such as KNN, decision trees

and Random Forest. We also constructed two dif-

ferent Convolutional Neural Networks (CNN) models

that attempt to classify images. All the models were

trained to distinguish the patterns kind.

The results suggest that the CNN technique has

an advantage over traditional models in terms of accu-

racy. This was to be expected, given that these models

are designed for picture identiﬁcation and feature ex-

traction. We conclude that the CNN models learned

to classify the tests with reasonable accuracy, but they

still struggle to recognize more intricate information.

ICPRAM 2023 - 12th International Conference on Pattern Recognition Applications and Methods

722

Table 6: Collective results of the models.

Model Accuracy (test) Comments

Random Forest 47 % max depth =15

K-Nearest Neighbours 47 % K = 3

K-Nearest Neighbours 46 % K = 1

Decision Tree 40 % max depth =15

CNN (2 Conv) Weighted 52 % Batch Size = 8, Learning Rate 0.0007, Epochs 10

CNN (2 Conv) Weighted 54 % Batch Size = 8, Learning Rate 0.001, Epochs 6

CNN (2 Conv) 50% Batch Size = 4, Learning Rate 0.001, Epochs 10

CNN (2 Conv) 54 % Batch Size = 4, Learning Rate 0.001, Epochs 7

CNN (3 Conv) 57 % Batch Size = 8, Learning Rate 0.0004, Epochs 7

The nature and quantity of the data set’s images

precluded further investigation and more detailed re-

sults. Despite the fact that we have demonstrated that

Neural Network models can indeed identify hidden

patterns with some decent accuracy.

Our solution and proposed labels can be set to be

a way for classifying Raven IQ matrices in a more au-

tomated way. This suggests that models such as Gen-

erative Adversarial Neural Networks (GANs) may be

able to generate new and distinct IQ tests and patterns,

based on such patterns.

The lack of labeled data set with more examples

and pictures is a drawback since it did not allow us

to make our models more efﬁcient. There is also the

limitation that similar data sets may have different

kinds of images or tests format, something that may

be solved by using feature extraction techniques.

Future research will include larger and more ex-

tensive data collection, more detailed labels, and more

complex Neural Network models for classifying IQ

tests and patterns. Finally, using Generative Adver-

sarial Neural Networks, we will be able to test the

hypothesis of developing new IQ tests using cutting-

edge models.

ACKNOWLEDGEMENTS

We would like to thank Kejsi Rrasa for their help, and

support and for reviewing this paper before submit-

ting it.

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