Adaptive Piecewise Linear Approximation of Time Series [HANA, R, UI5]

HANA&R adaptive PLA

 HANA&R adaptive PLA

data.csv

segment.r

toSlopes <- function(ts){

  slopes <- diff(ts); 
  indexes <- 0:(length(slopes)-1);
  aux <- slopes*indexes;
  offset <- ts[1:length(slopes)] - aux;
  lngth <- rep(1,length(slopes));
	
  res <- data.frame(matrix(c(slopes, offset, indexes, lngth), ncol = 4));
  colnames(res) <- c("a", "b", "startp", "runlength");

  return(res);

};

fValue <- function(segs, x){
 return(segs[1,"a"]*x + segs[1,"b"]);
};

merge <- function(segs){

  slope <- weighted.mean(segs[,"a"], segs[,"runlength"]);
  start <- segs[1, "startp"];
  length <- sum(segs[, "runlength"]);

  if ( segs[1,"a"] == segs[2,"a"] ){
	offset <- segs[1,"b"];
  } else {
    offset <- fValue(segs[1,], segs[1, "startp"]) - (slope * segs[1, "startp"]) ;
  }  
  
  res <- data.frame( slope, offset, start, length);
  colnames(res) <- c("a", "b", "startp", "runlength");
  return(res);  
};

segdif <- function(segs, x1, x2){
  a1 <- segs[1,"a"];
  a2 <- segs[2,"a"];
  b1 <- segs[1,"b"];
  b2 <- segs[2,"b"];

  out <- (a1 - a2)*(x2*x2 - x1*x1)/2 + (b1 - b2)*(x2 - x1);
  return(out);
};

mergeCost <- function(segs){
  
  merged <- merge(segs);

  start1 <- segs[1, "startp"];
  end1 <- start1 + segs[1,"runlength"];
  
  cost <- segdif(rbind(merged, segs[1,]), start1, end1);
 
  start2 <- segs[2, "startp"];
  end2 <- start2 + segs[2,"runlength"]; 

  cost <- cost + segdif(rbind(merged, segs[2,]), start2, end2);

  return(abs(cost));
};

costVector <- function(segs){
  start <- 0;
  cost <- NULL;
  ## determine merge cost for each pair of segments
 
  for (i in 1:(length(segs[,1])-1))
  {    
    cost[i] <- mergeCost(segs[i:(i+1),]);    
  }
  return(cost);
};

bottomUp <- function(segs, minIndex){

  ## now adjust the data
  out <- segs;
  out[minIndex,] <- merge(out[minIndex:(minIndex+1),]);
  out <- out[-c(minIndex+1),];

  return(out);

};

bottomUpCost <- function(segs, cost, minIndex){

  ## now adjust the data
  out <- cost;   
  
  if (minIndex < length(segs[,"a"]))
  {
	out <- out[-c(minIndex+1)]; # eliminate cost for entry that is being deleted  
	out[minIndex] <- mergeCost(segs[minIndex:(minIndex+1),]); #recalculate cost after merge
  }
  else ## special case when we are eliminating the last entry
  {
	out <- out[-c(minIndex)]; # eliminate last cost entry
  }
  
  return(out);

};

segment <- function(ts, segments){
  slopes <- toSlopes(ts);
  cost <- costVector(slopes);

  while( length(slopes[,"a"]) > segments ){    
	## find minimum merge cost 
    minIndex <- which.min(cost); 

    ## now adjust the data    
	slopes <- bottomUp(slopes, minIndex);
	cost <- bottomUpCost(slopes, cost, minIndex);
		
  }
    
  return(slopes);
}

#### helper functions for display ####

segPlot <- function(segs){
  
  x <- 0;
  vec <- c(x,fValue(segs[1,],x));

  for (i in 1:length(segs[,"a"])){
    x <- x + segs[i,"runlength"];
    vec <- rbind(vec, c(x,fValue(segs[i,],x)));
  }
  return(vec);
};

series.hdbtable

table.schemaName = "IONESCUV";
table.tableType = COLUMNSTORE; // ROWSTORE is an alternative value

table.columns =
 [
 	{name = "index"; sqlType = INTEGER; },
  {name = "val";  sqlType = DECIMAL;  precision = 6; scale = 5; }
];

table.primaryKey.pkcolumns = ["index"];

TS.constroller.js

sap.ui.controller("r_pal_sample.view.Master", {

	onInit : function() {
		//Raw Data plot using Viz Line Chart
		var oDatasetRaw = new sap.viz.ui5.data.FlattenedDataset({
			dimensions : [ {				
				axis : 1,
				name : 'index',
				value : '{index}'
			}
			],
			measures : [ 
			{
				name : 'val',
				value : '{val}'
			} ],

			data : {
				path : "/rawData"
			}
		});

		var oVizFrameLine = this.getView().byId("idVizFrameLine");
		oVizFrameLine.setDataset(oDatasetRaw);

		//Segementation plot using VizFrame with 'timeseries_line' visualization
		var oVizFrame = this.getView().byId("idVizFrameCombined");
		oVizFrame.setVizType('timeseries_line');
		
		oDatasetVizFrame = new sap.viz.ui5.data.FlattenedDataset({
			dimensions : [ {
				name : 'index',
				value :  '{INDEX}',
				dataType:'date'
			} ],

			measures : [ {
				name : 'val',
				value : '{VAL}'
				} 
			} ],

			data : {
				path : "/segmentation(granularity=5)/Results"
			}
		});
	
	 oVizFrame.setVizProperties({
                general: {
                    layout: {
                        padding: 0.04
                    }
                },
                valueAxis: {
                    visible: false,
                    title: {
                        visible: false
                    },
                    label: {
                        formatString: 'u'
                    }
                },
                timeAxis: {
                	visible: false, 
                    title: {
                        visible: false
                    },
                    levelConfig: {
                        "year": {
                            row: 2 
                        }
                    }
                },
                plotArea: {
                    dataLabel: {
                        visible: false
                    }
                },
                legend: {
                	visible: false,
                    title: {
                        visible: false
                    }
                },
                title: {
                    visible: false,
                }
            });
		
		oVizFrame.setDataset(oDatasetVizFrame);
		feedValueAxis = new sap.viz.ui5.controls.common.feeds.FeedItem({
            'uid': "valueAxis",
            'type': "Measure",
            'values': ["val"]
        });
        oVizFrame.addFeed(feedValueAxis);
        
        feedTimeAxis = new sap.viz.ui5.controls.common.feeds.FeedItem({
            'uid': "timeAxis",
            'type': "Dimension",
            'values': ["index"]
        });
        oVizFrame.addFeed(feedTimeAxis);
	},

	onSegChange : function(event) {
		var newGranularity = Math.round(event.getParameters().value);
		oDatasetVizFrame.bindData({
			path : "/segmentation(granularity=" + newGranularity + ")/Results"
		});
	}

});

TS.view.xml

<core:View controllerName="r_pal_sample.view.Master" xmlns:com="sap.ui.commons" xmlns:core="sap.ui.core" 
	xmlns:html="http://www.w3.org/1999/xhtml" xmlns:l="sap.ui.layout" xmlns:viz="sap.viz.ui5" xmlns="sap.m">
	<Page id="TextPage" title="Segmentation">
		<l:HorizontalLayout>
				<viz:Line id="idVizFrameLine" width="600px" height="500px">
					<viz:legend>
						<viz:types.legend.Common visible="false"/>
					</viz:legend>
					<viz:title>
						<viz:types.Title text="Original Data" visible="true"/>
					</viz:title>
				</viz:Line>
				<com:Slider change="onSegChange" height="400px" max="99" min="1" stepLabels="true" vertical="true" width="50px"/>
				<viz:controls.VizFrame id="idVizFrameCombined" uiConfig="{applicationSet:'fiori'}" width="600px" height="500px"/>
		</l:HorizontalLayout>
	</Page>
</core:View>