An Efficient Algorithm for Clustering of Large-Scale Mass Spectrometry Data

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by  Fahad Saeed

An Efficient Algorithm for Clustering of
Large-Scale Mass Spectrometry Data
Fahad Saeed1,∗, Trairak Pisitkun1, Mark A. Knepper1 and Jason D. Hoffert1
1Epithelial Systems Biology Laboratory
National Heart Lung and Blood Institute (NHLBI)
National Institutes of Health (NIH)
Bethesda, Maryland USA
3 Abstract—High-throughput spectrometers are capable of pro- be used for clustering, and a graph theoretic framework that
1 ducing data sets containing thousands of spectra for a single allows us to use this metric for efficient cluster extraction.
0 biological sample. These data sets contain a substantial amount The novel algorithm introduced using the graph-theoretic
2 ofredundancyfrompeptidesthatmaygetselectedmultipletimes
framework has low computational complexity, thus allowing
inaLC-MS/MSexperiment.Inthispaper,wepresentanefficient
n algorithm, CAMS (Clustering Algorithm for Mass Spectra) for analysis of large datasets.
a clustering mass spectrometry data which increases both the Therestofthepaperisorganizedasfollows.Westartwitha
J
sensitivity and confidenceof spectral assignment. CAMS utilizes brief problem statement and background information relevant

4 a novel metric, called F-set, that allows accurate identification
to our discussions in section 2. In section 3, we introduce
of the spectra that are similar. A graph theoretic framework is
] definedthatallowstheuseofF-setmetricefficientlyforaccurate the graph theoretic framework and the algorithm for efficient
S clusteridentifications.Theaccuracyofthealgorithmistestedon extraction of clusters. Section 4 presents the experimental
D real HCD and CID data sets with varying amounts of peptides. resultsandtheperformanceofthealgorithmintermsofcluster
Our experiments show that the proposed algorithm is able to accuracy, cluster size. Section 5 concludes the paper with
s. cluster spectra with very high accuracy in a reasonable amount discussion and future work.
c of time for large spectral data sets. Thus, the algorithm is able
[ todecreasethecomputationaltimebycompressingthedatasets
while increasing the throughput of the data by interpreting low II. PROBLEM STATEMENTAND BACKGROUND
1 S/N spectra. INFORMATION
v IndexTerms—Clustering;Massspectrometry; Graph Theory;
4 Efficient Algorithms; Mass spectrometry data is complex and requires sophisti-
3 cated algorithms to do the data processing once the raw data
8 I. INTRODUCTION from the mass spectrometer is obtained. The raw data from
0 Mass spectrometry based proteomics is an emerging area themassspectrometeristhenfedtovarioussearchalgorithms
.
1 and has useful applications in biology such as studying the e.g. Sequest, Inspect. These search algorithms do a thorough
0 regulation of cellular processes [8], cancer molecular ther- job of searching the spectra against a known proteome data
3 apeutics [7] [11] and others [5]. Mass spectrometry often base. After the search is complete, each of the spectra is
1 generates thousand to millions of spectra that needs to be assigned a peptide (or a set of peptides with different sites
v: analyzed. The usual computational procedure invoked, after of modifications) to which it corresponds.
i the raw data is generated from the mass spectrometers is to There are a number of algorithms that have been intro-
X
search the spectra against a protein database. The algorithms duced for clustering mass spectrometry data. Tabb et. al [12],
r used for searching e.g. Sequest, Inspect, Xtandem etc, are MS2Grouper algorithm [13], Beer et. al. developed the Pep-
a
essentially brute force methods that try to deduce the peptide Mineralgorithm[1],Ramakrishnanet.al. [9],Duttaet. al.[2]
from a given spectra. Even algorithms that use advanced and Frank et. al. [4] are to name a few of these algorithms.
techniques to reduce the computational time e.g. tag-based The objective of this work is to formulate an algorithm that
for Inspect, two-pass database for X!Tandem etc. are still canaccuratelyandefficientlyclusterlargenumbersofspectra,
not computationally efficient enough for analyzing millions suchthatthespectrainagivenclustermustbelongtothesame
of spectra in a reasonable amount of time. peptide. More formally we define a cluster as follows:
It is common for the same peptides to get selected for Definition 1: Let there be N number of spectra S =
fragmentation multiple times in a given MS run, making {s ,s ,···,s } and the peptide corresponding to a spectra
1 2 N
fraction of MS/MS data sets redundant. Searching the same represented as P = {p ,p ,···,p }. Now let the peptide
1 2 N
spectra repeatedly, even with computationally efficient tools, corresponding to a spectra s represented by p where q =
q q
wastesalotoftimeandcomputationalresources.Theproblem {1,···,N}.
is even more pronounced when data from multiple runs are Definition 2: A distance function δ(p ,p ) where p ∈
r t r
merged. The redundancy can reach up to 50% for large data P,p ∈P is defined as the levenstein distance of the peptides
t
sets [1], [3], [4]. correspondingtothespectras ands .Nowletthenumberof
r t
The main goal of the work presented in this paper, is to clusters be k and represented as K = {k ,k ,···,k } such
1 2 k
formulatean efficientand accurate algorithmfor clusteringof thatsetS isdividedintoksubsets.Then,thespectras ands
r t
large-scalemassspectrometrydata.Inordertoaccomplishthe where s ,s ∈S should belong to the same cluster k where
r t i
abovetask,weintroduceanovelmetric(calledF-set)thatcan k ∈K , if and only if, δ(p ,p ) =0 where p ,p ∈P.
i r t r t
Note, that during clustering of the spectra, the peptides are
y
not known; since the clustering of the spectra is performed nsit
e
before the searching. nt
I
a b c d e f g h i j k l m n m/z
III. PROPOSED GRAPH THEORETICFRAMEWORK AND y
ALGORITHM nsit
e
nt
In this section we propose the similarity criteria that we I
a b c d e f g h i j k l m n m/z
useforouralgorithmandtherationalebehindit.We willthen
y
introduce graph theoretic framework that allows us to use the nsit
e
similarity metric in an efficient way. This is followed by the nt
proposed clustering algorithm. AI a b c d e f g h i j k l m n m/z
{(b,d,f)(d,f,h)(f,h,l)(h,l,n)}
y
A. F-set metric nsit
e
Although there has been considerable effort in developing Int
algorithms for spectral data, all of the approaches have been a b c d e f g h i j k l m n m/z
{(b,d,f)(d,f,h)(f,h,j)(h,j,n)}
gearedtowardscountingthenumberofspectralpeaksthatare nsity
common between two given spectra. This information is then nte
usedtocreateasimilarityindexusedbythealgorithms[1],[4]. I a b c d e f g h i j k l m n m/z
Itmakessense tocountthenumberofpeaksthatarecommon {(b,d,g)(d,g,l)(g,l,m)(l,m,n)}
y
between two spectra and use that for similarity indexing. nsit
e
However,noiseandotherfactorssuchascompoundedspectra BInt a b c d e f g h i j k l m n m/z
cancreatefalsepositivesforsimilarity.Asimilarityindexthat
can mitigate these false positives is necessary for an efficient
Fig. 1. Section A of this figure shows three spectra. The first two
and accurate clustering algorithm. spectra map to the same peptides whereas the third spectra maps to
We introduce F-set metric in this paper for similarity. The a different peptide. Although, the last spectra is not mapped to the
basic idea of the metric is as follows:Itis possible for a peak same peptide as the first two spectra, weobserve significant overlap
between the peaks. However, if we make F-sets (of size 3) of the
to appear at a certain m/z by a randomchance. However,it is
samepeaksandspectra,itisclearthatthesetsformulateddonothave
far less likely for peaks to appear in consecutive succession
much in common for the non-related spectra, and much in common
just by chance. Thus, it makes sense to formulate a similarity for the spectra that are related, as shown in section B of the figure.
metricthatcountsthesetsofsimilarpeaksbetweentwogiven
spectra. We formally define the F-set metric below:
Definition 3: As before let the spectral data set be rep-
resented as S = {s ,s ,···,s }. Each spectra has two i.e. there is a high probability that a peak would appear at a
1 2 N
attributesi.e. m/z and the intensity of the peak.Let there be a randomplaceinaspectraduetonoise(andhencewouldresult
fragmentationspectrums =(m ,i ),(m ,i ),···,(m ,i ) in incorrect clusters if used as a similarity metric), but for
j 1 1 2 2 Q Q
that is extracted from the mass spectrometry data where m peakstoappearinsuccessiveorder(assets)fortwoun-related
d
represents the m/z ratio and i represents the intensity of the spectraislessplausible.Figure1showsthreespectra,ofwhich
d
peptide at position d and 1≤j ≤N. onlytwo arerelated.Itcanbeseen fromthe figurethattheF-
Now making sets of peak’s at m/z posi- set metricnotonly allowsdistinctionbetweenthe spectrathat
tions of size f. Then creating sets out of the are not similar but also allows us to identify spectra that are
spectra can be presented as a vector F(s ) = related i.e. map to the same peptide. Now we formulate the
i
{(m m ···m ),(m m ···m ),···,(m ,···, graph theoretic framework to take advantage of F-set metric
1 2 f 2 3 f+1 Q−f+1
m ,m )}. Then the F-set metric calculated for spectra s just defined.
Q−1 Q x
and s can be formulated as
y B. Graph Theoretic Framework
In this section we present the graph-theoretic framework
|F(sx)||F(sy)| thatwouldallowustouseF-setmetricin anefficientmanner.
W(s ,s )= φ(F(s )[i],F(s )[j]) (1)
x y x y Definition 4: AweightedundirectedgraphG=(V,E)isa
Xi=1 Xj=1 graph where V is a set of vertices and E ∈V ×V is a set of
edges. Now let a weight w ≥0 associated with edge
φ(a,b)= 1 if a[i]=b[j] (2) e=(v ,v ) where e∈E aen=d(vvi,,vjv) ∈V.
(cid:26) 0 o.w. i j i j
A weighted undirected graph is created with vertices that
TheF-set,denotedbyW(s ,s ),canbeusedasasimilarity correspond to each of the spectra. The vertices are connected
x y
metric for spectra. The F-set makes set of m/z from the by weighted edges and each vertex corresponds to a single
spectra of size f and then compares it with the F-set of spectra. The weight on each edge between two given spectra
the other spectra. If there is a match of a F-set in the other is assignedusing the weightcalculatedusing the F-seti.e. the
spectraascoreof1isadded.Otherwiseazeroscoreisadded. weight assigned to the edge is equal to the F-set calculated
Therefore, the final score W represents the number of F-sets between two given spectra. More formally:
thatarecommonbetweenthetwogivenspectra.Therationale Definition 5: Given a graph G=(V,E) such that the num-
for comparing sets of m/z between two given spectra has to ber of vertices in the graph are equal to the number of
do with the probability of peaks appearing at random places spectra being considered i.e. |V| = |S| = N and an edge
connecting each vertex. Now vertices can be represented by A
V =v1,v2,···,vN. Then, the nodescan be labeled using the 10 22
following mapping function ∀v → s where v ∈ V,s ∈
i i i i B 9 C
S,1 ≤ i ≤ N. The weight on each edge is the F-set metric 36 22
9
that is calculated for the spectra i.e. w = W(s ,s ) where 40
e=(v ,v );s ,s ∈S,e∈E,v ,v ∈Ve. i j 23 14 89 10 12
i j i j i j
After the above procedure a graph is created that is
weighted, and the weight corresponds to the F-set metric D 7 E
calculated for a given spectra. The next step is to extract the 21 F 72
clusters using the graph that has been created. In order to
extractclusterstwomethodswereinvestigated;oneistrivialin A
which a threshold is chosen by the user; the second threshold
is chosen using SVM which our experiments suggested was
B 36 C
more effective in chosing the right threshold. After threshold
40
is chosen, the edges that have weight less than threshold are
89
eliminatedand the connectedcomponentsare reported,which
canbecalculatedinO(V +E)time.Thealgorithmisstatedin
D E
Algorithm1 and graphical representation of clusters is shown F 72
in Fig. 2 (b).
Fig. 2. The graph from with weighted edges calculated using F-
set metric is shown. The value of ζ is determined using the SVM.
Require: MS2 spectra data set: Thereafter, the edges having weight less than ζ are labeled with red
boxes(figa).Theseedgesaretheneliminatedandtheverticesthatare
Ensure: Clusters of spectra such that the cluster has
still connected are determined using DFS. These connected vertices
spectra that can be mapped to the same peptide:
are reported as potential clusters (fig b).
1) Read the Sequest search results (.dta) files
2) Enumerate the F-set of a given size for each of the
spectra independently
3) For each of the pair determine the F-sets that are the cluster be defined as ni where 1 ≤ i ≤ k. Now assume
common between them thatthenumberofspectraina clusterthatbelongtothesame
4) Generate the graph using the definition 5 in the peptidebedenotedbyxi.Then,theaccuracyofasinglecluster
paper can be defined as :
5) Run SVM on the F-set metrics that gives a ζ x
i
threshold ai = (3)
n
6) Eliminate the edges that are below the ζ threshold i
7) Determine the vertices that are still connected in and the average weighted accuracy (AWA) of the whole
the graph after elimination dataset under consideration is defined as:
8) Output the vertices that are still connected after
k
elimination as clusters a n
AWA= i=1 i i (4)
Algorithm 1: CAMS P k n
i=1 i
P
AWA takes into account the accuracy of each cluster and
IV. PERFORMANCE EVALUATION gives a global view of the accuracy for a given dataset.
The performance evaluation can be divided into two parts.
A. Quality assessment
ThefirstpartdealswithassessinghowgoodtheF-setmetricis
at distinguishing between related and unrelated spectra. The 1) Quality with increasing F-set size: The objective of
second part of the evaluation relates to the accuracy of the the first part of quality assessment, is to see how does the
clusters using the algorithm with different mass spectrometry quality of the clustering behaves using increasing F-set size.
data sets. Consideringtheframeworkthatweintroducedinthepaper,the
Before we go any further, let us define the quality metric increasing size of F-set must correspond to higher accuracy.
that we use in this paper. The quality of the clustering can In orderto confirm this, we choose a CID and HCD data sets
be divided in two parts. The first part is the quality of the used in our other studies [10].
individual cluster and the second is the quality of clustering Fig.3showstheaverageweightedaccuracywithincreasing
overall. If we just take an average of the individualquality of size of the F-set. In general, the average weighted accuracy
theclusteritmaybemisleading,sincethenumberofelements increases with increasing F-set size for both CID as well as
in each cluster may be different. Therefore, we defined the HCD data sets. Theaccuracyseemsto be levelingoff atF-set
accuracy as a weighted accuracy that allows us to determine size of 7 or more. The increase in accuracycan be seen more
the quality of the clustering for each cluster as well as the pronouncedin CID data sets as comparedto HCD. The HCD
overallqualityofallclusters.Theweightedaccuracyisdefined data sets have better accuracy with lower F-set size due to
as follows: better Signal-to-noiseratio as comparedto CID. The fact that
Assumetherearekclusters.Nowlettheaccuracyofasingle accuracyincreasessignificantlywithincreasingF-setsizeeven
cluster i be denoted by a and the total number of spectra in for CID data sets shows the effectiveness of F-set metric. We
i
V. CONCLUSIONS AND FUTUREWORK
100
In this paper, we have presented an efficient clustering
algorithm suitable for large scale mass spectrometry data. A
%)
A(CCURACY 80 sthimeilaalrgiotyrithmmet,ribcas(ecdalloedn tFh-esets)paitsialfolromcuatliaotends,aannddinutseendsiitny
WEIGHTED 60 oinftrtohdeucpeedakthsatinalalowspsetchtrea.usAe ogfrathpeh-itnhteroordeuticcedfrFam-seewt morektriics
AVERAGE foonrncoluvsetlersiinmgilsaprietcytrma.eAtricde(tFa-isleedt)awlgaosridthesmcricibteedchannidqureigboaroseuds
40 HCD time complexity and quality assessment were presented. The
CID graphtheoreticframeworkallowsclusteringofverylargemass
spectrometrydatasetsin areasonabletime.We usedCID and
1 2 3 4 5 6 7 8 9 10 11 12
HCD data sets with different conditions to assess the quality
SIZEOFF-SET
of the produced clusters. Our experiments suggest that the
Fig.3. TheaverageweightedaccuracyisshownwithincreasingF-set proposedalgorithmallowsnear-perfectclustersforlarge-scale
size for CID as well as HCD data sets
mass spectrometry data. The execution time of the algorithm
is upper-bounded by O(N2), but observed execution time is
close to linear with increasing number of spectra.
Thepaperpresentedis partofthe ongoingworkoncluster-
|F−set|=7
|F−set|=8 ingofmassspectrometrydataandweplantoexpandthework
400 |F−set|=9 in the future. We would like to investigate both theoretical
O(N2)
andapplication-orientedaspectsofclusteringlarge-scalemass
300 spectrometry data.
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