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\pdf_title "IoT Aggregation Algorithm Coursework"
\pdf_author "Andy Pack"
\pdf_subject "IoT"
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IoT Aggregation Algorithm Coursework
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November 2020
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Andy Pack / 6420013
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\begin_layout Section
Description
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\begin_layout Standard
Symbolic Aggregation Approximation (SAX) was implemented as an in-network
 data processing technique, compressing the representation while allowing
 further processing on this symbolic string.
 Figure 
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plural "false"
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 shows two rounds of SAX output following data collection, a window size
 of 2 was used and an alphabet of length 4, i.e the characters 
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a
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 through 
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d
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 inclusive.
 12 C 
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floats
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 total 48 bytes of data, this can be reduced by a factor of 4 using 
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char
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 representation instead, a window size of 2 halves the number of output
 samples and lowers the required memory to just 6 bytes.
 
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\begin_layout Section
Specification
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\begin_layout Standard
SAX is implemented in two separate steps, that of transforming the time-series
 into Piecewise Aggregate Approximation (PAA) representation and then representi
ng this numeric series with a symbolic alphabet.
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\begin_layout Subsection
PAA
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\begin_layout Standard
The standard deviation and mean of the data series were first calculated,
 these are required for Z-normalisation.
 This normalisation process takes a series of data and transforms it into
 one with a mean of 0 and a standard deviation of 1.
 This changes the context of the value from being measured in lux to being
 a measure of a samples distance from the mean, 0, in standard deviations.
 This allows comparison of different time-series.
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\begin_layout Standard
Following Z-normalisation, the size of the series is reduced by applying
 a windowing function.
 This takes subsequent equally-sized groups of samples and reduces the group
 to the mean of those values.
 
\end_layout

\begin_layout Standard
As a result of these two actions, the original time series has been reduced
 to a given length of samples with a mean of 0 and standard deviation of
 1.
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\begin_layout Subsection
SAX
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\begin_layout Standard
With the result of the above, the remaining step is to replace each sample
 value with a symbol to represent it.
 The amount of symbols to be used is given, each will represent the same
 probability range when considering a Gaussian distribution of mean 0 and
 standard deviation of 1.
 This can be achieved by using standard deviation breakpoints defined such
 that the area under Gaussian curve between breakpoints is the same.
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\begin_layout Section
Implementation
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\begin_layout Standard
The SAX functionality was added as an alternative buffer rotating mechanism
 over the original 12-to-1/4-to-1/12-to-12 aggregation system.
 The length of the output buffer is calculated such that it can be allocated.
 From here the input buffer is Z-normalised using the 
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normaliseBuffer(buffer)
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 function from the 
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buffer.h
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 header.
 This function iterates over each value in the buffer, subtracts the buffer's
 mean and then divides by the standard deviation.
 Following this, the buffer is aggregated using the same 4-to-1 aggregation
 function 
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aggregateBuffer(bufferIn, bufferOut, groupSize)
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 as the group size is variable.
 The output from this function represents the PAA form of the initial data
 series.
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This final buffer is handled using 
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handleFinalBuffer(buffer)
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 where a pre-processor directive checks whether SAX is being used.
 If so the PAA buffer is 
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 using 
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stringifyBuffer(buffer)
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 which performs the SAX symbolic representation.
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Demonstration of SAX aggregation with window size of 2 and alphabet of length
 4
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name "fig:Demonstration-of-SAX"

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