=Paper=
{{Paper
|id=Vol-2874/paper7
|storemode=property
|title=Inversion of Artificial Neural Networks for WiFi RSSI Propagation Modeling
|pdfUrl=https://ceur-ws.org/Vol-2874/paper7.pdf
|volume=Vol-2874
|authors=Bence Bogdándy,Zsolt Tóth
}}
==Inversion of Artificial Neural Networks for WiFi RSSI Propagation Modeling==
https://ceur-ws.org/Vol-2874/paper7.pdf
Inversion of Artificial Neural Networks for
WiFi RSSI Propagation Modeling
Bence Bogdándy, Zsolt Tóth
Eszterházy Károly University, Faculty of Informatics, Eger, Hungary
bogdandy.bence@uni-eszterhazy.hu
zsolt.toth@uni-eszterhazy.hu
Proceedings of the 1st Conference on Information Technology and Data Science
Debrecen, Hungary, November 6–8, 2020
published at http://ceur-ws.org
Abstract
Wireless communication via access points has rapidly become widespread
in almost all aspects of human life. There is an abundance of Wi-Fi access
points in almost every building. Wi-Fi positioning systems take advantage of
the widespread use of the access points. Wi-Fi based indoor positioning tech-
niques use Wi-Fi fingerprinting to record the propagated signal of individual
access points. Recording the data of the propagation models can be used to
build a fingerprinting radio map. The built fingerprinting radio maps consist
of a set of coordinates, and an access point radio signal strength indication.
Artificial Neural networks have proven to be one of the most useful predic-
tion methods, given a big data set. Inversion of Artificial Neural Network
models is the process of creating a model that is capable of predicting a set
of possible inputs from a given output. The inversion of the neural network
which has been trained on the fingerprinting data set can create a novel po-
sitioning method. Received signal strength indication can be inverted into a
set of coordinates. This paper includes a description, and evaluation of pos-
sible metrics for calculating the error of indoor positioning in an evolutionary
artificial neural network inversion system.
Keywords: Indoor navigation, indoor positioning, machine learning, neural
network inversion
Copyright © 2021 for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0).
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1. Introduction
Indoor positioning has proven to be a challenge for the last few decades. Despite
the popularity and the general use of global positioning systems, indoor positioning
is yet to see widespread adoption. Many different theories and technologies were
employed in order to create an indoor localization system which is capable of gen-
eral adoption Wi-Fi positioning systems [11, 12] take advantage of the widespread
use of the Wi-Fi access points. Wi-Fi based indoor positioning techniques use fin-
gerprinting to record the propagated signal of individual access points. Recording
the data of the propagation models can be used to build a fingerprinting radio map.
The built fingerprinting radio maps consist of a set of coordinates, and an access
point radio signal strength indication.
Methods of modern data science [3] can be used to process the fingerprinting
data set in order to extract, and evaluate information. Furthermore, machine and
deep learning [8] can be used to learn and predict radio signal strength indication
values based on input coordinates. Artificial Neural networks have proven to be
one of the best prediction methods, given a big data set. Inversion of Artificial
Neural Network models [4–6, 10] is the process of creating a model that is capable
of predicting a set of possible inputs from a given output.
The inversion of the neural network which has been trained on the fingerprinting
data set can create a novel positioning method. Received signal strength indication
can be inverted into a set of coordinates.
A number of different metrics are required to train the evolutionary algorithm
behind the inversion method. Possible metrics include the mean squared error of
the coordinates, the error of the predicted RSSI based on the inverted values, and
the Jaccard index value of the set of original coordinates, and predicted coordinates.
This paper includes a description, and evaluation of possible metrics for calculating
the error of indoor positioning in a evolutionary artificial neural network inversion
system.
2. Related Works
2.1. Indoor Positioning and Navigation
Indoor Positioning is an actively researched, which aims to find ways to auto-
matically find the coordinates of users in indoor environments. Positioning and
Navigation has been a solved issue outdoors for decades. The use of satellite navi-
gation provides a communication which is stable and available in most conditions.
Global Positioning Systems [7] have been part of everyday life, but not unlike other
technologies of today, it originates from the military. One might assume that since
GPS technologies have existed for so long and has enjoyed wide adoption in many
industries, indoor positioning must also be a well developed field. Indoor envi-
ronments provide a challenge as opposed to the outdoors; walls in buildings are
built to keep heat inside. However, insulation also provides a dampening effect
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on electromagnetic radiation. Therefore, satellites cannot be used to accurately
communicate with devices indoors.
For this reason, indoor positioning research has not enjoyed the attention like
global positioning systems did. Nevertheless, many different systems have been
developed for indoor positioning applications over the years. One of the most
widely adopted technologies for indoor positioning is the use of WiFi RSSI with
fingerprinting [1, 12]. WiFi-based Indoor Positioning and Localization techniques
use pre-installed WiFi enabled Access Points. The systems record connections with
devices, and measure the radio signal strength indication (RSSI) values. These
values can be used to build radio maps. Radio map data can be later transformed
into data sets, which provide the basis for indoor positioning applications.
2.2. Data Science
Data science has provided many innovations in the past decade, and seems to be a
very important part of computer science and life in general in the future.
Data recorded from WiFi fingerprinting can be parsed and transformed using
the tools of data science, such as statistical analysis. The process of data acquisition
was performed in the University of Miskolc’s Department of Information Science.
The data will be discussed in the Methods section of the paper. Once the data has
been loaded, and transformed various models can trained. After the training, the
trained models can be used for prediction of various target variables.
There are a number of machine learning models which have been used success-
fully to solve various complex tasks in the past decade. Models have been varied
over the years, always changing attention to the most recent when a significant im-
provement in prediction accuracy has been reached with a particular model. One of
the most versatile models has been the artificial neural network. Artificial Neural
Networks (ANN) have gained a reputation as one of the most significant machine
learning models over the years for solving problems which would otherwise seem
unsolvable. Deep learning is the collective term used for neural networks with deep
and complex structures.
2.3. ANN Optimization Methods
The goal of artificial neural networks is to use training data to modify the inner
connections called neurons of the network. Using the known input, and output
combinations of the data set, the neural network is able to iteratively modify its
own connections. This mechanism is able to automatically focus on important
connections in the network in order to increase prediction efficiency.
The most popular optimization method for this process is the gradient descent
algorithm, a backpropagation. Backpropagation uses the partial derivatives to cal-
culate the importance of certain neurons. The weight of the neurons are propagated
back from the end of the neural network. There are optimization algorithms for
neural networks other than gradient descent. These algorithms are usually Newton,
or quasi-Newton methods.
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After the network has been trained, new input data can be fed into the network
in order to predict unknown outputs. A section of the data set is usually reserved for
testing the model by comparing actual outputs with expected values. The difference
between these values is usually a metric of general performance of models.
3. Methods
3.1. Indoor Positioning Method
The proposed indoor positioning system maintains an active connection with all
users, while measuring and recording their WiFi RSSI values. The WiFi RSSI
values are fed into a novel artificial neural network inversion method in order to
determine possible locations of the users. The actual positions can be fine-tuned
using tracking of previous positions, and other methods.
3.1.1. Data Set
A dataset was previously collected [9] entirely for future indoor position prediction
tasks. The data set was recorded at the University of Miskolc in the Department
of Information Science. The data set consists of individual measurements, which
were measured using 𝑥, 𝑦, 𝑧 coordinates, WiFi RSSI values, and Bluetooth signal
measurements among other values. The data set consists of 67 features, and 1540
rows. The dataset consists of raw data, and had to be transformed into individual
data sets of certain WiFi Access points.
The 𝑋, 𝑌, 𝑍 coordinates were used for training, while the RSSI value was chosen
as a target for prediction.
3.2. Artificial Neural Network Inversion
After a neural network has been trained and tested, it can be used to calculate
predictions based on incoming data. The structure and the weight of the neurons,
as well as the inputs are fixed, while the output remains a variable. Therefore, the
trained network can be thought of as an approximated black box function 𝑓 . The
structure within the network does not describe the various transformations that
result in an output, it only provides a functional approximation.
Inversion is the process of predicting the input values based on a fixed neural
network and an output. The problem is that the approximated function of the
neural network is only linear from input to output. The 𝑓 −1 inverse function is a
non-linear function, as certain inputs (originally the outputs) can be assigned to
multiple outputs (originally the inputs). Therefore, no unique input values exist
which can be calculated from the outputs. The possible values create manifold
surfaces in the 𝑛-dimensional space, where 𝑛 denotes the number of inputs. Since
𝑓 −1 cannot be calculated using the original network’s weights, another method
must be used. This method is usually called 𝐼𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛. Two different methods of
neural network inversion are usually distinguished [4].
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On Figure 1 a figure of a two dimensional input space can be seen. Each
contour line consists of points, which when passed though the trained artificial
neural network, will produce the same output.
Figure 1. Contour Lines of Possible Input Combinations on a Two
Dimensional Surface.
3.2.1. Single-element Search
Single-element search methods are capable of calculating one possible input com-
bination for a given output. Because the value of only one input combination is
required, the methods used for neural network training can also be used to train the
network to be able to invert itself. However, different structures, and optimization
methods might be required for the inverse function.
One implementation of the single-element search methods for artificial neural
network inversion is the William-Linden-Kindermann(WLK) Algorithm [5, 6]. The
algorithm proposes a structure of different set of neurons for a given trained neural
network, which are trained by a modified backpropagation algorithm. The WLK
algorithm has seen real-life use, as it was noted by Jensen et. al. The algorithm
has been used for sonar performance analysis in submarines in order to determine
the position, and direction the submarine is going in order to avoid collision.
3.2.2. Multi-element Search
A different approach to the problem of generating possible input values from a
given output comes can be categorized as the multi-element search methods. These
methods are usually stochastic methods which are able to generate multiple possible
values using iterative fine-tuning to fit the given criteria.
The implementation of such method can be achieved with an evolutionary algo-
rithm. A genetic algorithm was used during the implementation to simultaneously
produce, and optimize a number of possible input combinations. The individuals
71
are optimized using the standardized selection, crossover, and mutation genetic al-
gorithm methods. A special repulsion method can be implemented between points
in order to try to evenly distribute individual points along the input manifold of
the space.
3.3. Error Metrics
The error values of the generated input combinations, and the original input values
have to be calculated in order to validate the inversion algorithm.
3.3.1. Distance Between Points
One way to calculate error is taking individual points in the predicted input com-
binations, and measuring the distance to the closest input point from the original
data set. Of course the comparison can only be drawn to input combinations with
the same output as the inversion input. As there are many different input combi-
nations for every output, this metric might not provide general error measurement.
In order to better see the difference between the generated points and the
original inputs is to calculate a weighted central point for both. The distance
between these weighted central points can be measured in order to calculate a
more general error between elements.
3.3.2. Jaccard Index
A third proposed error measurement for the input values is to calculate the Jaccard
Index of both value sets. The Jaccard Index calculates the similarity, and distance
between two sets of coordinates. The Jaccard index is measured by 𝐴∩𝐵 𝐴∪𝐵 , where 𝐴
and 𝐵 are finite sets. The Jaccard Index is frequently used in image recognition
tasks, where it is used to measure the similarity between the position of an object,
and a predicted position. Similarly, the paper proposes that the jaccard index can
be used to calculate similarity between a set of input values, and predicted set of
input values. On Figure 2, a visual representation of the jaccard index can be seen.
4. Implementation
4.1. Artificial Neural Network Inversion
The implementation of the inversion is in the Python programming language.
Python is already the language of choice for data science and machine learning,
therefore it was a natural choice for the implementation.
The implementation uses the Sci-kit Learn package, which contains a number
of modern data science and machine learning models. The MLPRegressor multi
layer perceptron model. The MLPRegressor is an easy-to-use implementation of
the artificial neural network. The network can be fine-tuned using the multitude of
72
Figure 2. Jaccard index.
optional parameters which can be passed during the initialization of the network.
The neural network has been fine-tuned using hyperparameter tuning [2].
The chosen network is capable of predicting the output RSSI values based on
the coordinates, with the performance of 75% with a variance of 15%. The high
variance can be attributed to the usage of a single network structure for every WiFi
RSSI Access Point. Running a hyperparamter tuning algorithm for every access
point would undoubtedly yield better, unique network structures.
4.2. Evolutionary Inversion Implementation
A general genetic algorithm-based inversion method was implemented. The inver-
sion method is capable of the inversion of a single MLPRegressor. The inputs of
the inverter consists of the regressor, and optional genetic algoritm parameters for
fine-tuning. These parameters include the numberic bounds in which the parame-
ters are generated, population size, number of elites, and strategies for crossover,
and selection. On Figure 3, a flowchart of the genetic algorithm can be seen.
The invert method returns the inverted population of the given regressor. The
python code of the invert method can be inspected on Code Listing 1.
73
Figure 3. Flowchart of the Genetic Algorithm.
1 def invert ( self ,
2 desired_output : np . ndarray ) -> List [ np . ndarray ]:
3 self . logger . info (" GAMLPInverter . invert started ")
4 population = self . _ i n i t _ g a _ p o p u l a t i o n ()
5 for _ in range ( self . max _generat ions ) :
6 fitness_v alues = [ self . __fitness ( individual , desire d_outp ut )
7 for individual in population ]
8 sorted_fitnesses , s ort ed _of f sp rin g s = self . __ s or t _b y _f it n es s (
fitness_values , population )
9 elites = s or t ed _ of fs pri ngs [0: self . elite_count ]
10 c r o s s e d _ m u t a t e d _ o f f s p r i n g s = []
11 for _ in range ( self . popula tion_s iz e - self . elite_count ) :
12 parents = self . __selection ( sorted_fitnesses ,
so rte d_o ff s pr ing s )
13 c r o s s e d _ m u t a t e d _ o f f s p r i n g s . append ( self . __mutate (
14 self . __crossover ( parents [0] , parents [1]) ) )
15 population = [* elites , * c r o s s e d _ m u t a t e d _ o f f s p r i n g s ]
16 fitness_values , population = self . _ _ so r t_ b y_ f it n es s ( fitness_values
, population )
17 self . logger . debug (" population : " , population )
18 self . logger . info (" GAMLPInverter . invert stopped ")
19 return population
Listing 1.
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The method consists of standardized mechanisms of genetic algorithms. Imple-
mentation contains different implementations of selection, and crossover methods.
Selection methods include random, rank, tournament and roulette selection meth-
ods.
Crossover methods include one point, multi point, uniform, and arithmetic
crossover methods. These methods can be changed by passing a string to their
respective parameters.
Individual creation is implemented using numpy’s np.uniform method which
randomly draws samples from a uniform distribution within the passed parameters.
5. Conclusion
In this paper, a general outline of an artificial neural network inversion based indoor
positioning was presented. Inversion as an artificial neural network operation was
shown. Inversion could become the third natural operation of any neural network.
Artificial neural network implementations already contain the training, and predict
methods. Training freezes the input and output values in order to modify the
underlying structure of the network in order to increase performance. Prediction on
the other hand freezes the input, and weights of the network in order to predict new
values. Inversion has not seen widespread adoption as a possible third operation,
which freezes the weights and the output, to predict the possible inputs. This
method could be used to increase the explainability, and performance of neural
networks by exploring the different input values of a given output.
The two different categories of neural network inversion methods were outlined.
Single search methods use well known algorithms used in neural networks already.
However, these methods are only capable of producing one input combination at
a time. Multi element search methods use stochastic search methods, particularly
evolutionary algorithms. These methods provide a less stable search, but they are
capable of predicting all possible input values given a well defined evolutionary
algorithm.
A general implementation of a genetic algorithm was described in the python
programming language.
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