submitted, formatting to fit spec, better screenshots

Coursework-Reports/code.lyx

@@ -109,7 +109,7 @@ IoT Aggregation Algorithm Coursework
 November 2020
 \end_layout
 
-\begin_layout Right Footer
+\begin_layout Right Header
 Andy Pack / 6420013
 \end_layout
 

Coursework-Reports/report.lyx

@@ -36,7 +36,7 @@ customHeadersFooters
 \output_sync 0
 \bibtex_command default
 \index_command default
-\paperfontsize 10
+\paperfontsize default
 \spacing single
 \use_hyperref true
 \pdf_title "IoT Aggregation Algorithm Coursework"
@@ -83,13 +83,13 @@ customHeadersFooters
 \bottommargin 1.5cm
 \secnumdepth 3
 \tocdepth 3
-\paragraph_separation indent
-\paragraph_indentation default
+\paragraph_separation skip
+\defskip medskip
 \is_math_indent 0
 \math_numbering_side default
 \quotes_style english
 \dynamic_quotes 0
-\papercolumns 1
+\papercolumns 2
 \papersides 1
 \paperpagestyle fancy
 \tracking_changes false
@@ -109,7 +109,7 @@ IoT Aggregation Algorithm Coursework
 November 2020
 \end_layout
 
-\begin_layout Right Footer
+\begin_layout Right Header
 Andy Pack / 6420013
 \end_layout
 
@@ -159,6 +159,17 @@ d
 \end_inset
 
  inclusive.
+ 
+\end_layout
+
+\begin_layout Standard
+The use of string representation allows further processing and analysis
+ techniques to be used such as string pattern matching, Euclidean distance
+ and hashing operations.
+\end_layout
+
+\begin_layout Standard
+It is also an opportunity to reduce the required memory footprint.
  12 C 
 \begin_inset listings
 lstparams "basicstyle={\ttfamily}"
@@ -180,14 +191,55 @@ status open
 
 \begin_layout Plain Layout
 
-char
+chars
 \end_layout
 
 \end_inset
 
- representation instead, a window size of 2 halves the number of output
- samples and lowers the required memory to just 6 bytes.
- 
+ instead, a window size of 2 further halves the number of output samples
+ and lowers the required memory to just 6 bytes.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+	filename SaxBy2,4Break.png
+	width 100col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Demonstration of SAX aggregation with window size of 2 and alphabet of length
+ 4
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:Demonstration-of-SAX"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Section
@@ -195,9 +247,9 @@ Specification
 \end_layout
 
 \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.
+SAX is implemented in two stages, that of transforming the time-series into
+ Piecewise Aggregate Approximation (PAA) representation and then representing
+ this numeric series with a symbolic alphabet.
 \end_layout
 
 \begin_layout Subsection
@@ -205,27 +257,47 @@ PAA
 \end_layout
 
 \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
+PAA is an effective method for reducing the dimensionality of a time-series
+ by focusing on the trends and patterns of the data as opposed to individual
+ values.
+ It is a lossy operation that can be used to strike a balance between frequent
+ periodic sampling in order to keep the system responsive while reducing
+ the storage and processing requirements for such a large data stream.
+ This process is completed in two steps, Z-normalisation and aggregation.
+\end_layout
+
+\begin_layout Paragraph
+Z-Normalisation
+\end_layout
+
+\begin_layout Standard
+The standard deviation and mean of the data series were first calculated
+ using previously written functionality to calculate these values for arbitrary
+ arrays of numbers.
+ This normalisation process takes a series of data and transforms it such
+ that the output series has a mean of 0 and a standard deviation of 1.
+ This changes the context of the values 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.
+ This allows (somewhat) direct comparison of different time-series.
+\end_layout
+
+\begin_layout Paragraph
+Aggregation
 \end_layout
 
 \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.
+ to the mean of those values, reducing the length of the series by a scale
+ factor equal to the size of the group.
  
 \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.
+Following Z-normalisation and aggregation, the original time series has
+ been reduced to a given length of samples with a mean of 0 and standard
+ deviation of 1.
 \end_layout
 
 \begin_layout Subsection
@@ -233,13 +305,70 @@ SAX
 \end_layout
 
 \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.
+SAX is an extension to the PAA representation that uses an alphabet of symbols
+ instead of numeric values.
+ Following Z-normalisation as part of the PAA process, a time-series of
+ data will follow a Gaussian distribution profile.
+ Each value describes how many standard deviations it is away from the mean
+ of the series (how far away from the central Gaussian peak it is), an approxima
+tion of the value could be found by dividing the area of the Gaussian profile
+ into segments and referring to each by a character.
+ Each data value can now be described by a segment identifier.
+ These segments should not be of equal width, however - values are likely
+ to be closer to the mean, referring to these by a single character would
+ be unproductive.
+ Instead the Gaussian profile is divided into segments corresponding to
+ equal probabilities or areas under the curve.
+\end_layout
+
+\begin_layout Standard
+These segments are realised using breakpoints, the standard deviations that
+ describe the edges of each segment.
+ By comparing each datum to subsequent breakpoints the segment that the
+ value lies within can be identified and the corresponding character retrieved
+ for representation.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\align center
+\begin_inset Graphics
+	filename SaxBy4,8Break.png
+	width 100col%
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption Standard
+
+\begin_layout Plain Layout
+Demonstration of SAX aggregation with window size of 4 and alphabet of length
+ 8
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:Demonstration-of-SAX-2"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Section
@@ -249,8 +378,34 @@ Implementation
 \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 
+ This rotation mechanism lies between receiving the full data buffer on
+ the processing thread and passing it to the 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+handleFinalBuffer(buffer)
+\end_layout
+
+\end_inset
+
+ function for display.
+ 
+\end_layout
+
+\begin_layout Standard
+The length of the output buffer is calculated using the full data buffer's
+ length and the group size with which it is divided.
+ This size is used to allocate a new buffer to store the PAA representation
+ of the data.
+ 
+\end_layout
+
+\begin_layout Standard
+From here the input buffer is Z-normalised using the 
 \begin_inset listings
 lstparams "basicstyle={\ttfamily}"
 inline true
@@ -271,15 +426,20 @@ status open
 
 \begin_layout Plain Layout
 
-buffer.h
+sax.h
 \end_layout
 
 \end_inset
 
  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
+ mean and then divides by the standard deviation (the mean and standard
+ deviation are stored as members of the buffer prior to passing to the function).
+ 
+\end_layout
+
+\begin_layout Standard
+Following this, the buffer is aggregated using the same 4-to-1 aggregation
  function 
 \begin_inset listings
 lstparams "basicstyle={\ttfamily}"
@@ -293,12 +453,258 @@ aggregateBuffer(bufferIn, bufferOut, groupSize)
 
 \end_inset
 
- as the group size is variable.
+ used previously.
+ This functionality was used as the group size is variable and the same
+ required windowing and average function is used, as such it could be reused
+ with the desired aggregation level.
+ Figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Demonstration-of-SAX-2"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+ shows an output using a window size of 4 instead of figure 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:Demonstration-of-SAX"
+plural "false"
+caps "false"
+noprefix "false"
+
+\end_inset
+
+'s width of 2.
  The output from this function represents the PAA form of the initial data
  series.
 \end_layout
 
 \begin_layout Standard
+The 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+handleFinalBuffer(buffer)
+\end_layout
+
+\end_inset
+
+ function takes a 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+Buffer
+\end_layout
+
+\end_inset
+
+ struct as input which is defined as being a collection of 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+floats
+\end_layout
+
+\end_inset
+
+.
+ In order to maintain this structure and compatibility with the non-SAX
+ aggregation, the buffer is passed to this function in PAA form without
+ SAX conversion to a string.
+ In order to complete the system, the buffer must be 
+\emph on
+stringified
+\emph default
+ within this final method following a pre-processor check that SAX is being
+ used.
+ 
+\end_layout
+
+\begin_layout Standard
+SAX symbolic representation is completed using the 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+stringifyBuffer(buffer)
+\end_layout
+
+\end_inset
+
+ function of the 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+sax.h
+\end_layout
+
+\end_inset
+
+ header.
+ This function allocates a string of suitable size before iterating over
+ each value of the buffer and calling 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+valueToSAXChar(inputValue)
+\end_layout
+
+\end_inset
+
+ to retrieve the corresponding 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+char
+\end_layout
+
+\end_inset
+
+.
+ As the breakpoints are a constant for a given number of segments and would
+ require computation, the values for the breakpoints are defined by the
+ pre-processor based on the number of segments defined by the 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+SAX_BREAKPOINTS
+\end_layout
+
+\end_inset
+
+ macro.
+\end_layout
+
+\begin_layout Standard
+For each value, the breakpoints are iterated over.
+ Specific cases are defined for the beginning and end of the breakpoints
+ as these are one-sided inequalities.
+ For the rest, the value is compared to two neighbouring breakpoints.
+ A true condition for any of these checks indicates that the correct segment
+ for the value has been identified.
+ The same return value, 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+SAX_CHAR_START + i
+\end_layout
+
+\end_inset
+
+, is used in every case.
+ 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+SAX_CHAR_START
+\end_layout
+
+\end_inset
+
+ is a macro used to define the first character of the alphabet being used
+ for SAX representation (likely either 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+'a'
+\end_layout
+
+\end_inset
+
+ or 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+'A'
+\end_layout
+
+\end_inset
+
+), 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+i
+\end_layout
+
+\end_inset
+
+ is the iteration variable for the loop, it is used as an offset from the
+ alphabet start and is evaluated to a 
+\begin_inset listings
+lstparams "basicstyle={\ttfamily}"
+inline true
+status open
+
+\begin_layout Plain Layout
+
+char
+\end_layout
+
+\end_inset
+
+ for return.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Note Comment
+status open
+
+\begin_layout Plain Layout
 This final buffer is handled using 
 \begin_inset listings
 lstparams "basicstyle={\ttfamily}"
@@ -333,43 +739,6 @@ stringifyBuffer(buffer)
  which performs the SAX symbolic representation.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename SaxBy2,4Break.png
-	width 30col%
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption Standard
-
-\begin_layout Plain Layout
-Demonstration of SAX aggregation with window size of 2 and alphabet of length
- 4
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:Demonstration-of-SAX"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
 \end_inset
 
 

Coursework-Reports/screenshot.lyx

@@ -109,7 +109,7 @@ IoT Aggregation Algorithm Coursework
 November 2020
 \end_layout
 
-\begin_layout Right Footer
+\begin_layout Right Header
 Andy Pack / 6420013
 \end_layout
 
@@ -133,11 +133,15 @@ Andy Pack / 6420013
 \emph on
 Standard deviation thresholds of 400 for some activity and 1,000 for high
  activity.
+\begin_inset VSpace 15pheight%
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard
 \begin_inset Float figure
-placement bh
+placement h
 wide false
 sideways false
 status open
@@ -145,9 +149,9 @@ status open
 \begin_layout Plain Layout
 \align center
 \begin_inset Graphics
-	filename 12to1.jpg
+	filename last12to1.png
 	lyxscale 50
-	width 80col%
+	width 100col%
 
 \end_inset
 
@@ -180,7 +184,7 @@ status open
 \begin_layout Plain Layout
 \align center
 \begin_inset Graphics
-	filename 12to3.jpg
+	filename last4to1.png
 	lyxscale 50
 	width 100col%
 
@@ -215,7 +219,7 @@ status open
 \begin_layout Plain Layout
 \align center
 \begin_inset Graphics
-	filename 12to12.jpg
+	filename last12to12.png
 	lyxscale 50
 	width 100col%
 

Coursework/buffer.h

@@ -40,7 +40,7 @@ void // perform aggregation into groupSize (4 in the spec)
 aggregateBuffer(Buffer bufferIn, Buffer bufferOut, int groupSize)
 {
     int requiredGroups = ceil((float)bufferIn.length/groupSize); // number of groups
-    int finalGroupSize = (bufferIn.length % groupSize) * groupSize; // work out length of final group if bufferIn not of length that divides nicely
+    int finalGroupSize = bufferIn.length % groupSize; // work out length of final group if bufferIn not of length that divides nicely
 
     if(requiredGroups > bufferOut.length) // error check
     {

Coursework/coursework.c

@@ -1,10 +1,12 @@
 #define READING_INTERVAL 2 //in Hz
 #define BUFFER_SIZE 12 // length of buffer to populate
 
-#define SD_THRESHOLD_SOME 400 // some activity, compress above, flatten below
+// below thresholds are calibrated for the cooja slider
+// they are likely not suitable for using on the mote
+#define SD_THRESHOLD_SOME 400 // some activity, 4-to-1 above, 12-to-1 below
 #define SD_THRESHOLD_LOTS 1000 // lots of activity, don't aggregate
 
-#define AGGREGATION_GROUP_SIZE 2 // group size to aggregate (4 in spec)
+#define AGGREGATION_GROUP_SIZE 4 // group size to aggregate (4 in spec)
 
 #define INITIAL_STATE true // whether begins running or not
 
@@ -39,7 +41,7 @@ PROCESS_THREAD(sensing_process, ev, data)
     static struct etimer timer;
     if(isRunning) etimer_set(&timer, CLOCK_SECOND/READING_INTERVAL); // start timer if running
     
-    event_buffer_full = process_alloc_event();
+    event_buffer_full = process_alloc_event(); // event for passing full buffers away for processing
     initIO();
     
     static Buffer buffer;
@@ -59,6 +61,7 @@ PROCESS_THREAD(sensing_process, ev, data)
             buffer.items[counter] = light_lx; // STORE
             
             printf("%2i/%i: ", counter + 1, buffer.length);putFloat(light_lx);putchar('\n'); // DISPLAY CURRENT VALUE
+            //printBuffer(buffer);putchar('\n'); // DISPLAY CURRENT BUFFER
             
             counter++;
             if(counter == buffer.length) // CHECK WHETHER FULL
@@ -126,10 +129,15 @@ handleSimpleBufferRotation(Buffer *inBufferPtr)
 
     Stats sd = calculateStdDev(inBuffer.items, inBuffer.length); // GET BUFFER STATISTICS
     
+    printf("B = ");printBuffer(inBuffer);putchar('\n');
+    printf("StdDev = ");putFloat(sd.std);putchar('\n');
+    printf("Aggregation = ");
+    
     /* LOTS OF ACTIVITY - LEAVE */
     if(sd.std > SD_THRESHOLD_LOTS)
     {
-        printf("Lots of activity, std. dev.: ");putFloat(sd.std);printf(", leaving as-is\n");
+        //printf("Lots of activity, std. dev.: ");putFloat(sd.std);printf(", leaving as-is\n");
+        puts("None");
         
         outBuffer = getBuffer(1); // get a dummy buffer, will swap items for efficiency
         
@@ -139,7 +147,8 @@ handleSimpleBufferRotation(Buffer *inBufferPtr)
     /* SOME ACTIVITY - AGGREGATE */
     else if(sd.std > SD_THRESHOLD_SOME)
     {
-        printf("Some activity, std. dev.: ");putFloat(sd.std);printf(", compressing buffer\n");
+        //printf("Some activity, std. dev.: ");putFloat(sd.std);printf(", compressing buffer\n");
+        puts("4-into-1");
         
         int outLength = ceil((float)inBuffer.length/AGGREGATION_GROUP_SIZE); // CALCULATE NUMBER OF OUTPUT ELEMENTS
         outBuffer = getBuffer(outLength); // CREATE OUTPUT BUFFER
@@ -150,7 +159,8 @@ handleSimpleBufferRotation(Buffer *inBufferPtr)
     /* NO ACTIVITY - FLATTEN */
     else
     {
-        printf("Insignificant std. dev.: ");putFloat(sd.std);printf(", squashing buffer\n");
+        //printf("Insignificant std. dev.: ");putFloat(sd.std);printf(", squashing buffer\n");
+        puts("12-into-1");
         
         outBuffer = getBuffer(1); // CREATE OUTPUT BUFFER
         
@@ -192,16 +202,16 @@ handleSAXBufferRotation(Buffer *inBufferPtr)
 void
 handleFinalBuffer(Buffer buffer)
 {
-    printf("Final buffer output: ");
-    printBuffer(buffer);putchar('\n');
-    printf("Mean: ");putFloat(buffer.stats.mean);putchar('\n');
-    printf("Std Dev: ");putFloat(buffer.stats.std);putchar('\n');putchar('\n');
-    
+    printf("X: ");printBuffer(buffer);putchar('\n');
 #ifdef SAX
+    printf("Mean: ");putFloat(buffer.stats.mean);putchar('\n');
+    printf("Std Dev: ");putFloat(buffer.stats.std);putchar('\n');putchar('\n');    
+
     char* saxString = stringifyBuffer(buffer);
-    printf("SAX: %s\n\n", saxString);
+    printf("SAX: %s\n", saxString);
     
     free(saxString);
 #endif
+    putchar('\n');
 }
 /*---------------------------------------------------------------------------*/

Coursework/math.h

@@ -15,7 +15,7 @@ ceil(float in) // self-implement ceil func, no math.h
 }
 
 float
-sqrt(float in) // self-implement ceil sqrt, no math.h
+sqrt(float in) // self-implement sqrt func, no math.h
 {
     float sqrt = in/2;
     float temp = 0;

README.md

@@ -3,5 +3,5 @@ IOT Labs
 
 Using Coniki and Cooja in C.
 
-![4-into-1 aggregation](Coursework-Reports/12to3.jpg)
+![4-into-1 aggregation](Coursework-Reports/last4to1.png)
 ![SAX aggregation](Coursework-Reports/SaxBy2,4Break.png)