Empirical Mode Decomposition for
Intrinsic-Relationship Extraction in Large Sensor
Deployments
Romain Fontugne

Jorge Ortiz, David Culler

Hiroshi Esaki

University of Tokyo /JFLI, CNRS

Computer Science Division
University of California, Berkeley

University of Tokyo

Abstract—In this paper we investigate the utility of empiricalmode decomposition (EMD) to identify intrinsically correlated
usage patterns among sensors in a large deployment. We use
data collected from almost 700 sensors in a 12-story building
measuring power, pressure, temperature, and other physicalphenomena. We discover that doing a correlation analysis on
the raw traces does not discriminate well enough to identify
meaningful relationships between sensors. We correlate the tracefrom a pump with the rest of the sensor traces and find that
simple correlation filters only 50% of the sensors as being
correlated with the behavior of the pump. In contrast, by runningthe correlation analysis on the constituent frequencies extracted
by the EMD process, we filter out over 99% of the sensors as being
correlated – with the highest correlation coming from sensors
that serve the same room as the pump. We believe our approach
can be used to construct inter-device correlation models that canhelp understand and identify misbehaving or inefficient usage
patterns.

I. I NTRODUCTION
Buildings consume an enormous amount of energy in countries around the world. In Japan, 28% of the energy produced
is consumed in buildings [12] while in the United States it
is as high as 40% [16]. Moreover, studies show that between
30-80% of it is wasted [5], [13]. Large commercial buildings
are typically instrumented with a large number of sensors
measuring various aspects of building operation. Although thisdata is typically used to assure operational stability, they may
also be used to measure, observe, and identify instances ofwasted use.
Identifying instances of wasted energy use is non-trivial.
System efficiency is defined as the ratio of the useful work
done to the energy it consumes. In the case of buildings,
we broadly define useful work as the energy used to support
occupant activities. From the perspective of the building thatmeans maintaining a comfortable temperature setting, providing power for plug-load devices, and providing adequate
lighting conditions; particularly in spaces that are occupied.
However, identifying efficient use of resources, especiallywhen a space is occupied, is difficult. Typically it involves
deep knowledge of the usage scenario and a meaningfulunderstanding of what it takes to support the activity. Furthermore, situations and activities differ greatly. The outside
weather changes, varying schedules affect occupancy, rooms
have lectures, class, or other office activities. Simply put, theprocess is time consuming, requires specialized knowledge,
and does not scale.
Devices are typically used together in some fashion. For
example, in an office setting a person enters their office,turns on their PC and lights, etc. When the person leaves
the office, they revert back to the state their devices were in
before arrival. If one of the items is not reverted to its prearrival state, waste occurs. The same is true about equipment
usage. When the outside temperature is low the heater turns
on. Waste occurs when abnormal in-concert usage patterns
arise. Fundamentally, understanding “normal” spatio-temporalusage patterns between devices could help identify problems
when devices are not being used correctly. We conjecture thatinefficient energy use can be identified through anomalies in
the correlation patterns between devices. We examine device
correlation patterns in this paper and look specifically atprocessing raw sensor traces, such that the correlations wefind are meaningful.
In this paper, we present early results for correlating usage
patterns across a large number of sensors in a single deployment. We analyze data from a 12-story office building at the
University of Tokyo. The deployment consists of almost 700
sensors monitoring a broad range of devices inside and outside
the building. Our initial observations and results include thefollowing:1) Raw-trace correlation analysis is too strongly influenced
by the common low-frequency trends in the data toidentify meaningful relationships.
2) Using a technique called empirical model decomposition(EMD) [7] removes this trend and helps identify truly
correlated sensor traces.
3) We can construct clusters of correlated sensors that are
spatio-temporally correlated, without a priori knowledgeof their placement.
In the rest of the paper we explain EMD and how we use
it, we show various examples of our technique on real-world
traces, and we discuss the implications and future work.
II. R ELATED W ORK
Recently, there has been increased interest in minimizing
building energy consumption. Our approach differs quite substantially from related work. Agarwal et al. [2] present a

parameter-fitting approach for a Gaussian model to fit theparameters of an occupancy model to match the occupancy
data with a small data set. The model is then used to drive
HVAC settings to reduce energy consumption. We ignore
occupancy entirely in our approach. It appears as a hidden
factor in the correlation patterns we observe.
Bellala et al. [3] look at various buildings to develop a modelof efficient power usage using an unsupervised learning technique coupled with a Hidden Markov Model (HMM). They
also develop occupancy models based on computer network
port-level logs to help determine more efficient management
policies for lighting and HVAC. They claim a savings of 9.5%
in lighting on a single floor. Kim et al. [8] use branch-level
energy monitoring and IP traffic from user’s PCs to determine
the causal relationships between occupancy and energy use.
Their approach is most similar to ours. Understanding how IP
traffic, as a proxy for occupancy, correlates with energy use
can help determine where inefficiencies may lie.
In each of these studies and others [1], [4], [10], occupancy
is used as a trigger that drives efficient resource-usage policies.
Efficiency when unoccupied means shutting everything off andefficiency when a space is occupied means anything can beturned on. There is no question that this is an excellent way
to identify savings opportunities, however, we take a fundamentally different approach. We are agnostic to the underlying
cause or driver for efficient policies to be implemented. Moregenerally, we look to understand how the equipment is used inconcert. This may help uncover unexpected underlying relationships and can be used in an anomaly detection application
to establish “(in)efficient”, “(ab)normal” usage patterns. The
latter should identify savings opportunities in cases where thespace is unoccupied as well as occupied, because it has to
do with the underlying behavior of the machines and how
they generally work together. Our approach could help achieveboth generality and scale for such an application. This article
focuses on the first step of this application, the identificationof correlated devices.
III. DATASET
The data we used was obtained from a deployment ofsensors in a 12-story office building on the campus of the
University of Tokyo [6], [14]. The deployment consists ofalmost 700 sensors monitoring device power consumption,
ranging from plug-load devices to components of the heating,ventilation, and air conditioning system (HVAC) and lighting.
Sensors also reported temperature, pressure, device-state, andother information. Each sensor reports data on the order ofminutes. Over 500 GBs of data was collected over a 2-year
span.
For this investigation, we focus on a three-week spanin the summer of 2011 (from July 4th to July 24th). The
dataset captures regular work days, weekends, and one holiday(July 18th). This timeframe captures the typical usage ofthe equipment, triggered by occupant activity. For the initial
analysis, we focus on three sensors; two water pumps and alight feed. The first pump is an “electric heat pump” and islabled as EHP, the second is a “gas heat pump” and labeled as
GHP. The room lighting system serves the same room as the
EHP. The GHP serves a different room on the same floor. The
expanded portion of our analysis pivots around the EHP anddoes a pairwise comparison between it and all other sensors inthe building. Computationally, this approach does not scale toa large number of sensors. For future work, we will examinevarious heuristics to narrow the search space before running
pairwise comparisons.
IV. P ROBLEM STATEMENT AND I NITIAL APPROACH
In buildings, metadata is poorly and unsystematically managed within a single system domain. Moreover, with theever growing number of additional sub-meters, it is importantto quickly integrate sensor data from multiple systems tounderstand the full state of the building. It is also importantto understand how sensors are used in concert. Anomalies inusage may indicate underlying problems with the equipment
or inefficient/incorrect usage.
Figure 2 shows the raw traces for the three devices discussed
in the previous section (EHP, GHP, light). All three exhibit adiurnal usage pattern. On weekends, each draw less power.
For our initial analysis, we calculated the pairwise correlation
coefficient for all sensors in the set. The correlation coefficientfor the EHP and light is 0.7715 and the correlation coefficientfor the EHP and GHP is 0.6370. Running correlation acrossthem yields high correlation coefficients, mostly due to theirunderlying daily usage pattern.
Our initial results were not surprising. The diurnal pattern
dominates the comparison between the sensors. Weather isthe main driver for this behavior and it affects the readings inalmost all of the sensors in our dataset. Cross-correlation on
raw sensor data is insufficient for filtering intrinsically related
behavior. Upon closer examination of the data we assess thefollowing:
The main underlying diurnal trend occurs in almost all
the traces.
• Occupancy and room activities occur at random times
during the day and change at a higher frequency thanweather patterns.
• Sensors that serve the same location observe the same activities. Therefore, their underlying measurements should
be correlated.
•

In order to uncover these relationships we must remove lowfrequency trends in the traces and compare the readings at highfrequencies.
V. M ETHODOLOGY
Empirical Mode Decomposition (EMD) [7] is a new technique used for detrending data. Specifically, EMD detrends
non-stationary, non-linear timeseries data. A non-stationary
signal is a signal whose mean and variance change over time.
EMD is a process, not a theoretical tool, and its main use isfor removing trends to enable more useful spectral analysis.

traceEHP

LightCorrelation coeﬀ. 0.7715

0.8
0.6
0.4
0.2
0

Correlation coeﬀ. 0.43909
IMF1

0.5
0
−0.5

Correlation coeﬀ. 0.49344
IMF2

0.5
0
−0.5

Correlation coeﬀ. 0.63469
IMF3

0.5
0
−0.5

residual

Correlation coeﬀ. 0.82132
0.4
0.2
0
−0.2
−0.4
100

Fig. 1.

200

300

400

500
600
Time (30min time bins)

700

800

900

1000

Decomposition of the EHP and light trace using bivariate EMD. IMFs correlation coefficients highlight the intrinsic relationship of the two traces.

We describe the EMD process as follows: for a signal X(t),let m1 be the mean of its upper and lower envelopes as determined from a cubic-spline interpolation of local maxima andminima. The locality is determined by an arbitrary parameter.
1) The first component h1 is computed: h1 = X(t) − m1
2) In the second sifting process, h1 is treated as the data,
and m11 is the mean of h1 ’s upper and lower envelopes:
h11 = h1 − m113) The procedure is repeated k times, until h1k is a function: h1(k−1) − m1k = h1k4) Then it is designated as c1 = h1k , the first functional
component from the data, which contains the shortest
period component of the signal. We separate it from therest of the data: X(t) − c1 = r1 , and the procedure isrepeated on rj : r1 − c2 = r2 , . . . , rn−1 − cn = rn
The result is a set of functions called intrinsic mode
functions (IMF); the number of functions in the set depends
on the original signal [9]. An IMF is any function with thesame number of extrema and zero crossings, with its envelopes
being symmetric with respect to zero. We run our correlation
analysis on the shared IMF outputs between a pairs of traces.
In order to ensure that the IMFs corresponding to two distinct
traces are on the same time scale, we use bivariate EMD [15]
to decompose two traces at once.
We use EMD to detrend each of the traces and pay

particularly close attention to the high-frequency IMFs. Our
hypothesis is that correlating at the higher frequencies will
yield more meaningful comparisons.
VI. R ESULTS
We test our hypothesis in this section by using EMD toremove low-frequency trends in the data and run correlation
calculation at overlapping IMF timescales. We discover that
EMD allows us to find and compare high-frequency instrinsic
behavior that is spatially correlated across sensors. We begin
with a small set of three sensors (EHP, GHP, light) and expand
our scope to include all the sensors in the dataset.
A. Initial analysis
Lets consider the simple example of Section IV where wewould like to know if the EHP trace is correlated with the twoother traces. Recall that the correlation coefficients of the raw
feeds was 0.7715 and 0.6370, corresponding to the light and
GHP, respectively. As stated in previous section this result iscorrect but not so meaningful, since most of the traces display
the same diurnal pattern. Figure 1 and Figure 3 show the EMD
decomposition of the three traces. For each trace, EMD has
retrieved three IMFs that highlight the higher frequencies of
the traces.
Figure 1 shows the normalized raw trace (top) and EMD
output IMFs and residual as well as the correlation coefficients

traceEHP

GHP

Correlation coeﬀ. 0.6370

0.8
0.6
0.4
0.2
0
−0.2

Correlation coeﬀ. 0.00602
IMF1

0.2
0
−0.2

Correlation coeﬀ. 0.06354
IMF2

0.2
0
−0.2

Correlation coeﬀ. 0.16764
IMF3

0.2
0
−0.2

residual

Correlation coeﬀ. 0.79378
0.4
0.2
0
−0.2
100

200

300

400

500
600
Time (30min time bins)

700

800

900

1000

Fig. 3. Decomposition of the EHP and GHP trace using bivariate EMD. IMFs correlation coefficients highlight the intrinsic independence of the two traces.

higher than 0.36. As expected, the underlying trend is sharedby a large number of device. Although the highest score (i.e.
0.7715) corresponds to the light in the same room that the EHP
serves, there are 118 pumps, serving all areas of the building,with a correlation higher than 0.6. Using only these results, it
is not clear where the threshold should be set. The distribution
is close to uniform, making it difficult to know of how wellyour threshold discriminates against unrelated traces.

calculated on the IMFs for the EHP and light traces. The
correlation coefficients are 0.43909, 0.49344 and 0.63469
corresponding to the IMF1, IMF2, and IMF3, respectively.
Notice the high correlation between the high-frequency IMFs.
We know that the light and EHP serve the same room, andtheir high-frequency IMF correlation corroborates our priorknowledge. Figure 3 shows a complementary result, for the
EHP and GHP comparison. The correlation coefficients for the
EHP and GHP IMFs suggest that the two may be independent.
In fact, they are indepdent; they serve completely different
rooms in the building!
EMD allows us to remove low-frequency trends that add
noise to the original analysis. By comparing IMFs, we seeboth intrisically correlated and uncorrelated behavior. In thenext section we expand our analysis and show the effectivenessof our methodology.

Figure 4(b) shows the distribution of the average correlation
value for the IMFs of each trace and the EHP. The number oftraces correlated in the high frequency IMFs is significantly
smaller than the previous results. It’s clear from the distribution that only a small set of devices are intrinsically correlatedwith the EHP. In fact, only 10 traces out of 674 yielded ascore higher than 0.25. This allows us to easily rank traces bycorrelation.

B. Validation
To validate the effectiveness of our approach, we analyze
the same three-week time span for all 674 sensors deployedin the building. For each trace S we compute two scores: (1)the correlation coefficient between S and the EHP trace and(2) the average value of the IMF correlation coefficients.
Figure 4(a) shows the distribution correlation coefficients.
Notice that a large fraction of the dataset is correlated with
the EHP trace. Half the traces have a correlation coefficient

Upon closer inspection of the 10 most correlated IMF traces,
we find that there is a spatial relationship between the EHP
and the ten devices. In fact, there is a direct relationshipbetween score and distance from the areas served by the EHP.
Figure 5 shows a map of the floor that contains the rooms
served by this EHP. The EHP directly serves room C2. We
introduce a correlation threshold to cluster correlated tracesby score. We highlight rooms by the threshold setting on the
IMF correlation score. When we set the threshold at 0.5 we see

250(a) EHP trace# traces

200

150

100

50

0

−0.2

0
0.2
0.4
Correlation coefficient

0.6

0.8

0
0.2
0.4
0.6
Avg. IMFs correlation coeff.

0.8(a) Raw traces correlation coefficients(b) Light trace

250# traces

200
150
100

(c) GHP trace
Fig. 2. Traces from three different sensors captured in 2011 from July 4th
to July 24th. Data is normalized and aggregated into 30 minutes time bins.

50
0that the sensors that have a correlation higher fall within room
C2 – the room served directly by the EHP. As we relax thethreshold, lowering it to 0.25 and 0.1 we see radial expansion
from C2. The trace with the highest score, 0.522, is the tracecorresponding to the lighting system in the same room. The
two highest scores for this floor (i.e. 0.316 and 0.279) are thelight and EHP traces from next door, room C1. Lower values
correspond to sensors measuring activities in other rooms thathave no specific relationship to the analyzed trace. The results
show a direct relationship between IMF correlation and spatial
proximity and supports our initial hypothesis.
C. Limitations
EMD is useful for finding underlying behavioral relationships between traces of sensor data. However, when we set thetimescales smaller than a day, the results were not as strong.
The trace has to be long enough to capture the trend. For thisdata set, the underlying trend is daily, therefore it requires
there to be a significant number of samples over many days.
Although this was a limitation for this dataset, it really depends
on the underlying phenomenon that the sensors are measuring.
Its underlying trend is ultimately what EMD will be able toseparate from the intrinsic modes of the signal.
D. Discussion
EMD allows us to effectively identify fundamental relationships between sensor traces. We believe that identifying−0.2(b) Average IMFs correlation coefficients
Fig. 4. Distribution of the correlation coefficients of the raw traces andcorrelation coefficients average of the corresponding IMFs using 3 weeks ofdata from 674 sensors.

meaningful usage-correlation patterns can help reduce oversights by the occupants and faults that lead to energy waste. A
direct application of this is the identification of simultaneous
heating and cooling [11]. Simultaneous heating and coolingis when the heating and cooling system either compete with
one another or compete with the incoming air from outside.
If their combined usage is incorrect, there is major energy
waste. This problem is notoriously difficult to identify, since
the occupants do not notice changes in temperature andbuilding management systems do not perform cross-signal
comparisons. For future work, we intend to run our analysis on
the set of sensors that will allow us to identify this problem: theoutside temperature sensors, the cooling coil temperature, andthe air vent position sensor. If their behavior is not correlated
as expected, an alarm will be raised.
We can also apply it to other usage scenarios. In our traces,
we found an instance where the pump was on but the lights
were off; where, typically, they are active simulatenously. The
air conditioning was pumping cool air into a room without
occupants. With our approach this could have been identified

time in order to identify opportunities for energy savingsin buildings. We will use it to build inter-device correlation
models and use these models to establish “(ab)normal” usage
patterns. We hope to take it a step further and include a supervised learning approach to distinguish between “(in)efficient”
usage patterns as well.
ACKNOWLEDGMENTS
The authors thank Gabriel Rilling, Patrick Flandrin, Patrice
Abry, Pierre Borgnat for their source code and help on EMD,
Hideya Ochiai for sharing the data, Kensuke Fukuda andYoung Jon Won for constructive discussions. This research waspartially supported by the JSPS fellowship program. This work
is also supported in part by the National Science Foundation
under grants CPS-0932209 and CPS-0931843.
R EFERENCES

Fig. 5. Map of the floor where the analyzed EHP serves (room C2). The
location of the sensors identified as related by the proposed approach arehighlighted, showing a direct relationship between IMF correlation and spatial
proximity.

and corrected. In future work, we intend to package oursolution to serve these kinds of applications.
VII. C ONCLUSION
This paper set out to examine the underlying relationshipbetween sensor traces to find interesting correlations in use.
We used data from a large deployment of sensors in a building
and found that direct correlation analysis on the raw traces
was not discriminatory enough to find interesting relationships.
Upon closer inspection, we noticed that the underlying trend
was dominating the correlation calculation. In order to extract
meaningful behavior this trend has to be removed. We showthat empirical mode decomposition is a helpful analytical
tool for detrending non-linear, non-stationary data; inherent
attributes contained in our traces.
We ran our correlation analysis across IMFs, extracted fromeach trace by the EMD process, and found that the pump andlight that serve the same room were highly correlated, while
the the other pump was not correlated to either. In order tocorroborate the applicability of our approach, we compared
the pump trace with all 674 sensor traces and found a strong
correlation between the relative spatial position of the sensors
and their IMF correlations. The most highly-correlated IMFs
were serving the same area in the building. As we relax theadmittance criteria we find that the spatial correlation expands
radially from the main location served by the reference trace.
We plan to examine the use of this method in applications
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