Ismael (Real time Weather Forecasting using Multidimensional Hierarchical Graph Neuron (mHGN))
Real-time Weather Forecasting using Multidimensional Hierarchical Graph Neuron (mHGN)
BENNY BENYAMIN NASUTION RAHMAT WIDIA SEMBIRING AFRITHA AMELIA BAKTI VIYATA SUNDAWA GUNAWAN ISMAEL HANDRI SUNJAYA MORLAN PARDEDE JUNAIDI SUHAILI ALIFUDDIN MUHAMMAD SYAHRUDDIN ZULKIFLI LUBIS Department of Computer Engineering and Informatics Department of Telecommunication Engineering Department of Electrical Engineering Politeknik Negeri Medan Jalan Almamater No. 1, Kampus USU, Medan 20155 INDONESIA [email protected], [email protected]
Abstract: - Weather forecasting has been established for quite some time, but the quality is not yet satisfactory. The challenge to build a sophisticated weather forecast is high. Due to the difficulties in working on complex and big data, the research on discovering such weather forecast is still ongoing. It is still a big challenge to develop a self-sufficient machine that can forecast weather thoroughly. The new concept of Multidimensional Hierarchical Graph Neuron (mHGN) has opened up a new opportunity to forecast weather in real-time manner. The 91% of its accuracy in recognizing almost 11% distorted/incomplete patterns has suggested a strong indication that the accuracy of mHGN in forecasting weather will be high as well.
Key-Words: - Graph Neuron, Hierarchical Graph Neuron, Pattern Recognition, Weather Forecast
needs to be formulized in mathematical functions to Weather forecasting has been established for quite
1 Introduction
calculate parameters of weather is huge. If they exist, some time. People requires weather forecast to help
the functions are so much interrelated. Some weather planning their activities. By utilizing weather
experts even state that a leaf falling in Japan may forecast the plan is expected to be optimum, and at
cause rain in the US. The following is an example of the end the aim will be maximum. The challenge to
weather forecast taken from NDAA website. build a sophisticated weather forecast is still high [1]
[2] [3] [4] [5] [6] [7]. Due to the difficulties in working on complex and big data, the research on discovering such weather forecast is still ongoing [3] [5] [6] [8]. It is still a big challenge to develop a self- sufficient machine without an intervention of human being that can forecast weather thoroughly.
The obvious evidence that in preparing a weather forecast one or two weather experts have prepared a weather forecast is through the existence of forecaster ’s name on a weather report (See Figure 1, prepared by Hamrick). The reason of the involvement
of human being is that the number of variables that
Figure 1: An Example of US Weather Forecast
Since it is still difficult to have a weather forecast based on mathematical functions, it is a great opportunity to discover other solving methods, such us through utilizing artificial intelligent technologies. Although mathematical functions, that can determine the condition of weather, are not yet discovered, air- temperature, wind-speed, wind-direction, air- pressure, and air-humidity are all caused by physical states [9]. It means that what happens to weather condition is generally caused by particular physical patterns. So, time-series of several physical values will determine particular weather condition.
Multidimensional Hierarchical Graph Neuron (mHGN) has been proven to be capable of working as a pattern recognizer. The latest architecture to
prove its capability was the one that uses five-
Figure 2 : The Classification of the Earth’s Air and its
dimension 5X5X5X15X15 neurons. The architecture
corresponding temperature [9]
has been tested to recognize 26 patterns of alphabetical figures. Despite of 10% of distortion in
Similar situation governs on the surface of the all the figures, the architecture was able to recognize
earth. The wind-direction has its own characteristics. in average more than 90% of those patterns. This
On the equator, if we observe from the surface of the experiment result is a positive indication that mHGN
earth, the wind blows from the surface to the sky (See has a potential to be developed as a weather
Figure 3). However, if we observe the earth from the forecaster.
sky, on the equator the wind blows to the left (See Figure 4).
2 Weather Forecast
Weather forecasting normally utilizes meteorology [10] [9], a science about weather. The following is some fundamental concept of weather forecast that is
Figure 3 : Wind direction observed from the Earth’s
important to be first discussed, before working on
surface [11]
how to forecast the weather.
2.1 The Regularity of Weather
The characteristics of weather on the earth is strongly influenced by the characteristics of the earth itself and its surroundings. Around the earth, there are several levels of air that has been classified by weather experts. They are (See Figure 2): Troposphere,
Stratosphere,
Mesosphere,
Thermosphere, and Exosphere. Each of those levels has its own characteristics. For instance, in the Troposphere and Mesosphere, the higher the altitude the lower the air-temperature will be. But, in the Stratosphere and Thermosphere is the situation
Figure 4: Wind direction observed from the sky [11]
different, the higher the altitude the lower the temperature will change.
2.2 Particular and Important Timeframes
The other thing that need to be considered is choosing the best time frame for learning data. As already mentioned, most of the time weather condition is more or less similar to the one at the same time frame in the same season. Additionally, weather condition will not change abruptly very often. Therefore, suitable and important time frame that contains unusual or extreme weather condition need to be recorded. The collected data can then be used as the training data. By doing so, patterns of such unusual or extreme weather conditions will be able to be
forecasted. In other words, the training data is the
Figure 5: Wind directions caused by High (upper) and Low (lower) air pressures [11]
data that constitutes unique patterns.
2.3 Methods of Forecasting
Plan recognizers have attracted researchers to construct a number of scenarios and to transform each scenario into hierarchical task decomposition or plan libraries. Based on such structures and libraries, they have built algorithms to infer the plan of an activity, for example an attack, or even a natural catastrophe. The probability of each step has been determined and calculated based on previous observations. Inspired by such technology, the associative memory mechanism of the mHGN also
Figure 6: Wind, Highs, and Lows pattern in January [11]
allows recalling and recognizing mechanisms based on incomplete input patterns. Hence, the mHGN can
be utilized as a forecaster of weather condition, with an assumption that the patterns of the condition are already stored in the mHGN.
Although regularities of weather condition exist, to anticipate dynamic characteristics of weather, patterns that are stored in the mHGN must be updated dynamically. So, this criterion is not suitable for an approach that takes a long time for the preparation and recognition process. In addition, it is required that the recognizing quality in a weather forecast
Figure 7: Wind, Highs, and Lows pattern in July [11]
must be consistently accurate. The reason is that the dynamic condition of weather can increase the false
These conditions shown by the figures above positive errors within weather forecasting. It is the indicate that the weather in general has several
case, if its quality depends on the number of the regularities. It means that a weather forecast can be
stored patterns, or on the size of patterns. Harmer et classified based on: 1) the area (longitude, latitude,
al. have warned of the same issue, that the constantly altitude) on the earth, 2) the season (January,
changing states of the environment of the computer February, till December) of the area, and 3) time-slot
or network, such as adding new applications, (morning, noon, afternoon, evening) of the season of
modifying file systems, can increase the false the area. An irregularity of weather will happen when
positive and true negative errors of a weather forecast something irregularly comes up, for instance
system.
mountain eruption, production of air-pollution from Interestingly in the mHGN, storing and recalling factories, or a comet hit the earth.
mechanisms are basically the same. So in terms of time consumption, the mHGN does not require a long time to recall and to store patterns. In terms of the complexity, the mHGN architecture is scalable and fairly straightforward to be expanded because every mechanisms are basically the same. So in terms of time consumption, the mHGN does not require a long time to recall and to store patterns. In terms of the complexity, the mHGN architecture is scalable and fairly straightforward to be expanded because every
level there are 5 neurons (1X5), on the fourth level mHGN suitable for such a dynamic update process.
there are 3 neurons (1X3), and on the top level there is only one neuron (1X1). So, the complete
3 Multidimensional
Hierarchical
composition of the mHGN from the base level until
Graph Neuron (mHGN) the top level is: 7X5, 5X5, 3X5, 1X5, 1X3, 1X1. To
this, the total number of neurons is: The need of handling multidimensional patterns for 35+25+15+5+3+1=84. Please note that the complete various purposes has been started long time ago.
composition can also be: 7X5, 7X3, 7X1, 5X1, 3X1, Although according to the previous publication, the
HGN —the previous version of the mHGN—can very The composition of the second option is less well recognize distorted 2D-patterns with up to 10% suitable than the one of the first option, due to the of distortion, the architecture that has been used is the total number of neurons in the composition of the one-dimensional HGN. So, for recognizing 2D- second option is less than the number of neurons in patterns (7X5 pixels), 324 neurons were deployed. the composition of the first option. The less number The architecture looks like the following. of neurons, the less accurate the recognition results
1X1.
will be. For the composition of the second option, the total number of neurons is: 35+21+7+5+3+1=72.
This shows that the number of neurons of the composition of the second option is 12 neurons less than the number of neurons in the composition of the first option. Note also, that the one-dimensional composition comprises 18 layers, whereas the two- dimensional composition comprises only 6 layers for the same patterns size of 35 on the base level.
Figure 8: One-Dimensional HGN architecture for
recognizing 7X5 2D Patterns [12]
3.1 Multidimensional Problems
The accuracy of the recognition results is quite The need to solve multidimensional problems has high, but in fact the one-dimensional HGN
been discussed since a long time ago. People are architecture does not visually nor physically
aware that to handle complex problems values taken represent 2D-patterns correctly. The following figure
from numerous dimensions must be considered and shows the structure of the transformation from 2D
calculated. Otherwise, the result that come up after architecture of the patterns to 1D architecture of
the calculation analyzing just a few parameters HGN on the base level of the hierarchy.
cannot be considered correct. In most cases, such a
condition has produced very high false positive and
true negative error rate. Another issue related to
solving multidimensional problems is the solving
Figure 9: Transformation of 2D Architecture to 1D
method that has been used. In a complex system, not
Architecture on the base level
only the number of dimensions is large, but how all the dimensions are interrelated and interdependent is
It can be observed from Figure 9 that in the 2D
often not clear.
architecture (left), the cells nr. 15 and nr. 16 are Weather system is a good example as a originally located far from each other, but in 1D
multidimensional system. Therefore, forecasting architecture (right) they are located next to another.
weather condition is also a kind of solving a On the other hand, in the 2D architecture the cells nr.
multidimensional problem. Not only air-temperature,
21 and nr. 26 are originally located close to each air-pressure, air-humidity, wind-direction, and wind- other, but in 1D architecture they are separated far
speed determine the condition of weather, season, from another. This is the evidence that the
time-frame, location (longitude, latitude, and recognition results may not be 100% correct.
altitude) play also a big role on affecting weather Therefore, an improved architecture that is
condition. Moreover, flora and fauna population, suitable to handle true multidimensional patterns has
factories development, people movement will also been developed. For example, to recognize 7X5 2D-
influence the condition of weather. However, the patterns, there are 35 neurons on the base level. On
conditions of those issues are hard to measure and not the first level there are 25 neurons (5X5), on the
clear what and how to measure it.
But, the phenomenon of its influence can still be measured. For instance, whenever in one area several factories have recently been established and the factories produce a lot of heat, the temperature in the area of the factories will be higher than the temperature away from them. This condition will cause weather condition that is not the same as the regular weather condition before the factories have been built. It means that the tangible measurements (such as: air-temperature, air-pressure, air-humidity, wind-direction, and wind-speed) can still be used to measure intangible conditions (such as: flora and fauna population, industries development, people movement). A problem that still exists is the interdependency amongst those tangible and intangible values. It is difficult to figure out a formula that constitutes such interdependency. This is a strong indication that such multidimensional problems may be solved using artificial intelligent approaches such as mHGN.
3.2 Multidimensional Pattern Recognition using mHGN
As is the case with a one-dimensional HGN, a pattern will be received by the GNs in the base layer. However, in a multidimensional HGN (mHGN), the pattern size now is the result of the multiplication of all the dimension’s sizes on the base layer. For example, the pattern size of a two-dimensional (2D) 7X5 mHGN array is 35. In a three-dimensional (3D) 7X5X3 mHGN array, the pattern size is 105. The following figure shows two examples of the visualized architecture.
Figure 10: mHGN configuration of 2D (7x5) (left) and 3D (7x5x3) (right) for pattern sizes 35 and 105 respectively
As already mentioned, for recognizing 7X5 2D- patterns the complete composition of mHGN in each layer respectively will be: 7X5, 5X5, 3X5, 1X5, 1X3, 1X1. Similarly, for recognizing 5X7X3 3D-patterns the complete composition of mHGN in each layer respectively will be: 5X7X3, 5X5X3, 5X3X3, 5X1X3, 3X1X3, 1X1X3, 1X1X1. These composition examples show that the size of each dimension plays
a big role in mHGN architecture, and determines how the best configuration should be. In other to gain the best recognition results, the configuration is concentrated on the greatest size of the dimensions on the base level.
Although increasing the dimensions of the composition reduces the number of GNs, there are however adverse consequences. The first and most important consequence is that the accuracy in recognising noisy patterns is diminished. Owing to fewer neurons being used, the higher layer GNs must contend with a larger part of a pattern for analysis. For instance, using a one-dimensional HGN composition, a noisy pattern can possibly be recognised as a pattern of either: S, Q, or H, and the percentage of the match would subsequently decide that pattern Q is the most likely match. On the other hand, a two-dimensional HGN composition would recognise the same noisy pattern as a pattern of Q. It will, however, do so without considering other possible matches i.e. S and H. The reason for this is that the GNs that recognise sub-patterns of S and H in the one-dimensional case may no longer exist in higher dimensional compositions. The second consequence is that the number of parameters each GN must hold in higher dimensional compositions would be higher. Although this will not affect the recognition accuracy and timing performance, the configuration for the distributed architecture will, however, become more complex.
3.2.1 Experiment Results
For the experiment, each GN is operated by a thread. We have scrutinized 2D-, 3D-, 4D- and 5D-pattern recognition. The compositions used in the experiment are: 15X15 mHGN, 5X15X15 mHGN, 5X5X15X15 mHGN, and 5X5X5X15X15 mHGN respectively. For instance, in the 15X15 pattern recognition the composition requires: 225 + 195 + 165 + 135 + + 105 + 75 + 45 + 15 + 13 + 11 + 9 + 7 + 5 + 3 + 1 = 1009 neurons per value of data. As for creating patterns, binary data is used, then two values (i.e 0 and 1) of data are required. Therefore, 2018 neurons are deployed in the 15X15 composition. So, 2018 threads have been run in parallel during this 2D pattern recognition. By using threads, the activity of neurons is simulated so that the functionalities are close to the real neuron functionalities.
The experiment has worked on all the patterns of
26 alphabets. Following the composition of the neurons, the alphabet patterns consist of 15X15 pixels. For the training purpose, the mHGN is first fed one-cycle with all the 26 non-distorted patterns. The order of the patterns during the training phase has been determined randomly. Then, to acquire the 26 alphabets. Following the composition of the neurons, the alphabet patterns consist of 15X15 pixels. For the training purpose, the mHGN is first fed one-cycle with all the 26 non-distorted patterns. The order of the patterns during the training phase has been determined randomly. Then, to acquire the
patterns.
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in total 200 distorted patterns have been prepared as
Figure 13: Ten different randomly 5.8% distorted patterns
testing patterns.
of alphabet “A”
There are 7 levels of distortion that have been
tested, they are: 1.3%, 2.7%, 4.4%, 6.7%, 8.0%, After collecting the results taken from testing 8.9%, and 10.7%. These levels have been so chosen
5200 patterns we can summarize how accurate the based on the number of distorted pixels. The sizes of
mHGN is, in recognizing different levels of distortion pixels represent the factor and the non-factor of the
of 26 alphabets. The summary is taken based on the dimension of the patterns. By doing so, we can
average accuracy values from all the steps. The observe all the possibilities of distortion. So, in total
following shows the summarized result taken from there are 5200 (26 x 20 x 10) randomly distorted
testing distorted patterns using five-dimensional testing patterns. The following Figure 11 shows 5
5X5X5X15X15 mHGN.
samples of different orders of the patterns:
Distortion (%) 1.3 2.7 4.4 6.7 8.0 8.9 10.7 1 ENWL
5X5X5X15X15 Patterns
I SPGHJDYAXQRCMFVOTUKZB
2 RPJSOQDVCKLEFGXYAT ZBUWTHMN
3 GBHRZC I YXSJKDANTQVEWFUPOLM
4 LN I FRXBKOCT ZAYGVUHPJQSWEDM
5 CETUNRHYGDBKFMI XVSQJ ZWOALP
E 100 100 100 100 100 100 F 100 100 99 94 89 83 85 74
Figure 11: Five different randomly ordered alphabets. 100
The following shows some results taken from
testing 4.4% randomly distorted patterns, and the
Accuracy for
97 77 63 60 mHGN was previously stored with alphabet patterns, 55
Each Pattern (%)
99 87 79 80 81 and 81 the order was
99 IEFXMQYJHPDKTORZCUALBGVWNS. 95 The
value on the right side of each alphabet show the 100
portion (percentage) of the pattern that is 100
recognizable as the corresponding alphabet. 100
PATTERNS RANDOMLY DISTORTED 4.4 %
Patterns Stored Distorted I Pattern A A 1 9A 2 Recognised patterns and their recognized portion (%) from 20 different randomly distorted patterns
20 Figure 14: The summary of the result using
20 5X5X5X15X15 mHGN
20 18 20 It can be seen from Figure 14 in the last column
Type 0 Order T O MMR
20 20 that the mHGN is able to recognize 91% of the 10.7%
20 20 distorted patterns of 26 alphabets. Some alphabets
20 20 (A, C, E, G, I, J, L, O, S, T, U, V, X, Y, Z) are even
20 20 100% recognizable. As already discussed, other patterns of alphabets, such as H, K, M, N, are not very
Figure 12: The result of al the 26 alphabets that are
well recognized because they are visually and
twenty times 4.4% randomly distorted.
physically very similar. In fact, if this architecture is used to recognize different states of the same
alphabet, such as regular-A, bold-A, and italic-A as The following shows 10 samples of distorted patterns of the alphabet “A” taken from the alphabet, such as regular-A, bold-A, and italic-A as The following shows 10 samples of distorted patterns of the alphabet “A” taken from the
accuracy value.
Regarding the real time capability, the process of
the 2D mHGN architecture is much faster than its 0 0 0 0 0 0 1 1 1
previous version of 1D architecture. The reason of 0 0 0 0 0 0 0 0 1
this is due to the less number of neurons that has been 0 1 2 3 4 5 6 7 8
Figure 16: Two examples of data representation for 8
used. As already mentioned, 2018 GNs are used
levels value
within this 2D architecture, whereas for the same
15X15 pattern size 25538 GNs will be required It can be seen from Figure 16 that the data is within 1D architecture.
represented using binary values. Additionally, the The following figure shows the differences of
number of bit differences between any two levels is recognition accuracy amongst 15X15, 5X15X15,
linear with the value difference between the two 5X5X15X15,
levels. By doing so, the pattern recognizer will work architectures when recognizing 10.7% distorted
and
5X5X5X15X15
mHGN
more accurately. The following figure shows an patterns of alphabets.
example of recorded data taken from a single value
measurement and each value has 8 levels.
Comparison Result 15X15
Distortion = 10.7 %
5X15X15
5X5X15X15
5X5X5X15X15
H Time (t) 23 63 69 55
Figure 17: Data of 8 level value build a 2D-Pattern
It can be seen from Figure 17 that the recorded
Recognition Accuracy for
53 42 63 55 values from parameter of 8 levels data construct a
Each Pattern (%) N
two-dimensional pattern of 30X8 architecture.
63 73 73 99 Utilizing these recorded data, the pattern recognizer
can predict in 6 hour time if the same thing will occur
again. It means that if values have been recorded and
the same pattern is recognized by the pattern
75 82 98 92 recognizer, then the same thing is predicted to happen
again in 6 hour time.
75 83 90 91 So, to predict what will occur in 6 hour time using
Average
Figure 15: Differences of recognition accuracy amongst
30X8 mHGN architecture, the recognizer need to be
four different architectures
fed with data measurement recorded from 7 days and
6 hours ago until now. Not only predicting something that will occur in 6 hour time, the 30X8 mHGN
architecture can also be used to predict something As already mentioned in 2.3, recognizing patterns of
3.3 Time-Series in Pattern Recognition
that will occur in 12 hour time. But the recognizer for time series problem utilizes data that has previously
this purpose is fed with data measurement recorded been recorded regularly in timely manner. For
from 7 days only. In this case, the pattern is not fed instance, if the parameter that need to be recorded is
with 30X8 binary data, but with only 29X8 binary
a single value, and the recording tempo is every six data. This is the same case when a pattern recognizer hours, then there will be 4 values recorded every day.
is fed with incomplete data (only 97% data), but the In order to constructs the recorded values as a pattern,
recognizer is still able to recognize the pattern. the data representation of the recorded values need to
Similarly, to predict something that will occur in 18
be developed so, that they can fit into a pattern hour time, the recognizer is fed with data recognition architecture. The following figure shows
measurement recorded from 6 days and 18 hours ago two ways of representing recorded data for 8 levels
(only 93% data). This case is described in section of measurement.
3.2.1 that after stored with 27 patterns, 5X5X5X15X15 mHGN is able to recognize incomplete/distorted (89%) patterns with 91% of result accuracy.
4 Multidimensional Graph Neuron for Real Time Weather Forecast 4.1 Global and Local Weather Forecast
In the previous section, time series value is described As many people have experienced, weather condition within a city may vary. At particular time, in one area
and represented so, that it can be predicted through it rains pouring, whereas two kilometers away from utilizing a pattern recognition, such as mHGN. In
case of weather forecasting, single parameter in a it the sun shines brightly. Similarly, at particular longitude and latitude the temperature on the earth
location, such as humidity, is not the only value that surface is 30 degree, whereas at the same coordinate determine the temperature of the same location
within 6 hour time. Several other parameters, such as but different altitude the temperature is -10 degree. This is the real situation that the result of global
air-temperature itself, wind-speed, wind-direction, weather forecast will be different to the local weather and air-pressure, need to be measured as well. It
means that the number of levels or a measured value
forecast.
Local weather forecasts seem to be important for will increase according to the number of parameters. many people, as local weather forecasts work on In case 5 parameters need to be measured and each
value contains 8 levels, the required pattern structure weather condition in more details. But, there are not many local weather forecast running in a country.
would be 30X40. The reason of this, is that a weather forecast generally Also described in the previous section that require sophisticated computational resources. A lot measuring a parameter at particular point of location and complex data need to be calculated and analyzed for several periods of time will generate a two by a weather forecast. If such weather forecast need dimensional pattern. If a series of points of location to be operated locally in small areas, very expensive need to be measured for several period of time, then infrastructures including hardware and software must the measured values will become a three dimensional
pattern. The following figure depicts how some part
be provided in a country. Generally, countries only provide country-wide (global) weather forecast,
of it will look like.
rather than local ones.
4.2 The Architecture of mHGN for Time- Series Weather Data
The utilization of mHGN has introduced a new approach that a local weather forecast can be operated using small and cheap equipment. The values of air-temperature, air-humidity, air-pressure, wind-speed, and wind-direction can be gained through ordinary sensors. The area that is covered by those sensors can be a 3D area, because such small sensors can be easily mounted in valleys or hills, or even vehicles. The sensors can be connected to a tiny computer, such as Raspberry Pi. The tiny computer will be responsible to run several GNs. The values
Figure 18: A row of data of 8 level value build a 3D-
taken from the sensors will then be worked out within
the GNs. The connectivity of neurons is developed within a tiny computer and through the Also described in the previous section that
Pattern
interconnectivity of the tiny computers. measuring parameters at particular point of location
As already discussed, parameters that need to be for several period of time will generate a two
known in a weather forecast are temperature, wind- dimensional pattern. If a series and linear of locations
speed, wind-direction, air-pressure, and air-humidity. need to be measured for several period of time, then
So, for every parameter that need to be forecasted one the measured values will become a three dimensional
architecture of mHGN need to be developed. But the pattern. If the location that need to be measured is an
values taken from the sensors will be utilized and 2D area, then the measured values will generate a 4D
shared to all the mHGN architectures, and the result pattern. Furthermore, if the location that need to be
of the prediction depends on the precision level of the measured is a 3D area, then the measured values will
parameter.
generate a 5D pattern. For example in case of forecasting the temperature, in July in a particular city the temperature is generally between 20 and 30 degrees.
If the architecture of mHGN will forecast the value of the temperature in this city with a precision level of 1 degree, then the output of mHGN must have 11 different values. If the temperature value should have
a precision level of 0.5 degree, then the output of mHGN must have 22 different values. Following those two examples, other scaling mechanisms should be straightforward.
As discussed in section 3.2, within the mHGN architecture the number of neurons on the base layer
is the product of dimension sizes. On the next layer Figure 20: The number of threads (dashed line) is the
same as the neuron size on the base level
above it, the number of neurons is less than the one
on the layer. Such an architecture creates the In short, to build a weather forecast for particular hierarchy of mHGN. The following figure shows an
location, five parameters need to be measured. They example of one-dimension architecture of mHGN, in
are: air-temperature, air-humidity, wind-speed, wind- which the base layer contains 9 neurons, and the
direction, and air-pressure. So, if one parameter is mHGN in total contains 25 neurons.
represented through 8-bit binary data, then for the measurement of 5 parameters 41-bit data is needed. For the time series, 21 series of measurement will be carried out. To cover the location, 3X3X3 measurement points will be deployed. So, the mHGN dimension will be 3X3X3X41X21.
5 Discussion
As is the case with pattern recognition of alphabets, patterns are more or less different to one another.
Figure 19: The hierarchy of one dimension of size 9 of
However, in time series measurement data patterns
mHGN
that are constructed from the measured values of the sensors can be very similar to one another. Therefore,
In HGN and mHGN experiments, each neuron data representation of measured values before data is and its functionalities was operated by a thread.
fed to the architecture of mHGN plays a big role in However, the number of thread will be tremendous,
having very accurate results. False positive and true especially when the mHGN is used to work on
negative rate will also be indications to determine the multidimensional patterns. For example, 15X15
quality of mHGN in forecasting weather. architecture of mHGN requires 2018 neurons. This
The data that will be used to validate this work means that the number of threads that need to be run
will be the weather data taken from different cities is also 2018. Such a number of threads would be
and different countries. As mHGN is trained one- difficult to be run if the computer used for the project
cycle only, it is a challenge to choose which data is is a Raspberry Pi. The new approach to run neurons
the right data for the training purpose. When the is through utilizing threads in which the number of
appropriate training data has been applied, mHGN threads is only the same as the size of neurons on the
will then have a capability to forecast the air- base level. The following figure shows that instead of
temperature, air-humidity, air-pressure, wind-speed, utilizing 25 threads the new approach to implement
and wind-direction at particular longitude, latitude, mHGN architecture only requires 9 threads.
and altitude.
6 Conclusion
From the experiment results it is shown that mHGN has the capability to recognize multidimensional patterns. For simulating a weather forecast, we have presented results of up to 5D architecture. As already discussed in [12] and [13] there is no modification required if the architecture needs to be extended to bigger sizes of patterns. In the future this capability From the experiment results it is shown that mHGN has the capability to recognize multidimensional patterns. For simulating a weather forecast, we have presented results of up to 5D architecture. As already discussed in [12] and [13] there is no modification required if the architecture needs to be extended to bigger sizes of patterns. In the future this capability
recognizable. At this stage it is also observed that
2000.
mHGN still use a single cycle memorization and recall operation. The scheme still utilizes small response time that is insensitive to the increases in the
[9] F. K. Lutgens and E. J. Tarbuck, The number of stored patterns.
Atmosphere:
Introduction to Meteorology, Glenview, USA: Pearson,
An
2013.
7 References
[10] F. Nebeker, Calculating the Weather: Meteorology in the 20th Century, San
Diego, USA: ACADEMIC PRESS , 1995. [1] K. Anderson, Predicting the Weather:
Victorians and
[11] S. Yorke, Weather Forecasting Made Meteorology, Chicago and London: The
the
Science
of
Simple, Newbury, Berkshire, UK: University of Chicago Press, 2005.
Andrews UK Limited, 2011. [2] C. Duchon and R. Hale, Time Series
[12] B. B. Nasution and A. I. Khan, "A Analysis in Meteorology and Climatology:
Hierarchical Graph Neuron Scheme for An Introduction, Oxford, UK: John Wiley
Real-time Pattern Recognition," IEEE & Sons, Ltd, 2012.
Transactions on Neural Networks, pp. 212- 229, 2008.
[3] A. Gluhovsky,
"Subsampling
Methodology for the Analysis of Nonlinear [13] B. B. Nasution, "Towards Real Time Atmospheric Time Series," Lecture Notes
Multidimensional Hierarchical Graph in Earth Sciences , vol. 1, no. 1, pp. 3-16,
in The 2nd 2000.
Neuron (mHGN),"
International Conference on Computer and Information Sciences 2014 (ICCOINS 2014) , Kuala Lumpur, Malaysia, 2014.
[4] P. Inness and S. Dorling, Operational Weather Forecasting, West Sussex, UK:
John Wiley & Sons, Ltd, 2013 .
[5] P. Lynch, "The origins of computer weather prediction and climate modeling," Journal of Computational Physiscs, vol. 227, no. 2008, p. 3431 –3444, 2007.
[6] J. r. ı. Miksovsky, P. Pisoft and A. s. Raidl, "Global Patterns of Nonlinearity in Real and GCM-Simulated Atmospheric Data," Lecture Notes in Earth Sciences, vol. 1, no.
1, pp. 17-34, 2000. [7] T.
Vasquez, Weather Forecasting Handbook, Garland, USA: Weather Graphics Technologies, 2002.
[8] D. B. Percival, "Analysis of Geophysical Time Series Using Discrete Wavelet