Immunophenotypes of Acute Myeloid Leukemia
From Flow Cytometry Data Using Templates
Ariful Azad1 , Bartek Rajwa 2 and Alex Pothen 3∗
1

azad@lbl.gov, Computational Research Division, Lawrence Berkeley National Laboratory, California, USA
brajwa@purdue.edu, Bindley Bioscience Center, Purdue University, West Lafayette, Indiana, USA
3
apothen@purdue.edu, Department of Computer Science, Purdue University, West Lafayette, Indiana, USA

arXiv:1403.6358v1 [q-bio.QM] 22 Mar 2014

2

ABSTRACT
Motivation: We investigate whether a template-based classification
pipeline could be used to identify immunophenotypes in (and thereby
classify) a heterogeneous disease with many subtypes. The disease
we consider here is Acute Myeloid Leukemia, which is heterogeneous
at the morphologic, cytogenetic and molecular levels, with several
known subtypes. The prognosis and treatment for AML depends on
the subtype.
Results: We apply flowMatch, an algorithmic pipeline for flow
cytometry data created in earlier work, to compute templates
succinctly summarizing classes of AML and healthy samples. We
develop a scoring function that accounts for features of the AML data
such as heterogeneity to identify immunophenotypes corresponding
to various AML subtypes, including APL. All of the AML samples in
the test set are classified correctly with high confidence.
Availability: flowMatch is available at www.bioconductor.org/
packages/devel/bioc/html/flowMatch.html; programs
specific to immunophenotyping AML are at www.cs.purdue.edu/
homes/aazad/software.html.
Contact: apothen@purdue.edu

1

INTRODUCTION

Can Acute Myeloid Leukemia (AML) samples be distinguished
from healthy ones using flow cytometry data from blood or bone
marrow with a template-based classification method? This method
builds a template for each class to summarize the samples belonging
to the class, and uses them to classify new samples. This question is
interesting because AML is a heterogeneous disease with several
subtypes and hence it is not clear that a template can succinctly
describe all types of AML. Furthermore, we wish to identify
immunophenotypes (cell types in the bone marrow and blood) that
are known to be characteristic of subtypes of AML. Pathologists use
these immunophenotypes to visualize AML and its subtypes, and a
computational procedure that can provide this information would
be more helpful in clinical practice than a classification score that
indicates if an individual is healthy or has AML.
In earlier work, we have developed a template-based classification
method for analyzing flow cytometry (FC) data, which consists of
measurements of morphology (from scattering) and the expression
of multiple biomarkers (from fluorescence) at the single-cell level.
Each FC sample consists of hundreds of thousands or more of such
single-cell measurements, and a study could consist of thousands
of samples from different individuals at different time points under
different experimental conditions (Aghaeepour et al., 2013; Shapiro,
2005). We have developed an algorithmic pipeline for various
steps in processing this data (Azad et al., 2013, 2010, 2012). We
summarize each sample by means of the cell populations that it

contains. (These terms are defined in Table 1 and illustrated in
Fig. 1.) Similar samples belonging to the same class are described
by a template for the class. A template consists of meta-clusters
that characterize the cell populations present in the samples that
constitute the class. We compute templates from the samples, and
organize the templates into a template tree. Given a sample to
classify, we compare it with the nodes in the template tree, and
classify it to the template that it is closest to. A combinatorial
measure for the dissimilarity of two samples or two templates,
computed by means of a mixed edge cover in a graph model
(described in the next section), is at the heart of this approach.
We have applied our algorithmic pipeline for templatebased classification to various problems: to distinguish the
phosphorylation state of T cells; to study the biological, temporal,
and technical variability of cell types in the blood of healthy
individuals; to characterize changes in the immune cells of Multiple
Sclerosis patients undergoing drug treatments; and to predict the
vaccination status of HIV patients. However, it is not clear if the
AML data set can be successfully analyzed with this scheme, since
AML is a hetereogeneous disease at the morphologic, cytogenetic
and molecular levels, and a few templates may not describe all of its
subtypes.
AML is a disease of myeloid stem cells that differentiate
to form several types of cells in the blood and marrow. It is
characterized by the profusion of immature myeloid cells, which
are usually prevented from maturing due to the disease. The
myeloid stem cell differentiates in several steps to form myeloblasts
and other cell types in a hierarchical process. This hierarchical
differentiation process could be blocked at different cell types,
leading to the multiple subtypes of AML. Eight different subtypes
of AML based on cell lineage are included in the French-AmericanBritish Cooperative Group (FAB) classification scheme (Bennett
et al., 1985). (A different World Health Organization (WHO)
classification scheme has also been published.) Since the prognosis
and treatment varies greatly among the subtypes of AML, accurate
diagnosis is critical.
We extend our earlier work on template-based classification here
by developing a scoring function that accounts for the subtleties of
FC data of AML samples. Only a small number of the myeloid
cell populations in AML samples are specific to AML, and there
are a larger number of cell populations that these samples share
with healthy samples. Furthermore, the scoring function needs to
account for the diversity of the myeloid cell populations in the
various subtypes of AML.
Our work has the advantage of identifying immunophenotypes
of clinical interest in AML from the templates. Earlier work on
the AML dataset we work with has classified AML samples using
methods such as nearest neighbor classification, logistic regression,

1

Table 1. Summary of terminology
Terms

Meaning

Sample

From FC data. Characterized by the collection of cell
populations included within it.

Cell population
(cluster)

A group of cells with identical morphology and
expressing similar biomarkers, e.g., helper T cells,
B cells. Computed from a sample.

Meta-cluster

A set of similar cell clusters from different samples.
Computed from similar clusters in samples.

Template

A collection of meta-clusters from samples of the
same class.

and the challenge is to determine the disease status of the rest
of the samples, 20 AML and 157 healthy, based only on the
information in the training set. The complete dataset is available
at http://flowrepository.org/.
The side scatter (SS) and all of the fluorescence channels are
transformed logarithmically, but the forward scatter (FS) is linearly
transformed to the interval [0,1] so that all channels have values
in the same range. This removes any bias towards FS channel in
the multi-dimensional clustering phase. After preprocessing, an FC
sample is stored as an n × p matrix A, where the element A(i, j)
quantifies the j th feature in the ith cell, and p is the number of
features measured in each of n cells. In this dataset, p = 7 for each
tube and n varies among the samples.

2.2
matrix relevance learning vector quantization, etc., but they have
not identified these immunophenotypes; e.g., (Biehl et al., 2013;
Manninen et al., 2013; Qiu, 2012).
Template-based classification has the advantage of being more
robust than nearest neighbor classification since a template
summarizes the characteristic properties of a class while ignoring
small sample-to-sample variations. It is also scalable to large
numbers of samples, since we compare a sample to be classified
only against a small number of templates rather than the much
larger number of samples. The comparisons with the templates
can be performed efficiently using the structure of the template
tree. It also reduces the data size by clustering the data to identify
cell populations and then working with the statistical distributions
characterizing the cell populations, in contrast to some of the earlier
approaches that work with data sets even larger than the FC data
by creating multiple variables from a marker (reciprocal, powers,
products and quotients of subsets of the markers, etc.).
Template-based classification has been employed in other areas
such as character, face, and image recognition, but its application to
FC is relatively recent. In addition to our work, templates have been
used for detecting the effects of phosphorylation (Pyne et al., 2009),
evaluating the efficiency of data transformations (Finak et al., 2010),
and labeling clusters across samples (Spidlen et al., 2013).

Identifying cell populations in each sample

We employ a two-stage clustering approach for identifying
phenotypically similar cell populations (homogeneous clusters of
cells) in each sample. At first, we apply the k-means clustering
algorithm for a wide range of values for k, and select the optimum
number of clusters k∗ by simultaneously optimizing the CalinskiHarabasz and S Dbw cluster validation methods (Halkidi et al.,
2001). Next, we model the clusters identified by the k-means
algorithm with a finite mixture model of multivariate normal
distributions. In the mixture model, the ith cluster is represented
by two distribution parameters µi , the p-dimensional mean vector,
and Σ, the p × p covariance matrix. The distribution parameters for
each cluster are then estimated using the Expectation-Maximization
(EM) algorithm. The statistical parameters of a cluster are used to
describe the corresponding cell population in the rest of the analysis.

2.3

Dissimilarity between samples

We calculate the dissimilarity between a pair of cell populations
by the Mahalanobis distance between their distributions. Let
c1 (µ1 , Σ1 ) and c2 (µ2 , Σ2 ) be two normally distributed clusters
and Σp be the pooled covariance of Σ1 and Σ2 . The Mahalanobis
distance d(c1 , c2 ) between the clusters is computed as follows:
d(c1 , c2 ) = 12 (µ1 − µ2 )> Σ−1
p (µ1 − µ2 ), where
(1)

2
2.1

METHODS
The AML Dataset

We have used an FC dataset on AML that was included in the
DREAM6/FlowCAP2 challenge of 2011. The dataset consists of FC
measurements of peripheral blood or bone marrow aspirate collected
from 43 AML positive patients and 316 healthy donors over a one
year period. Each patient sample was subdivided into eight aliquots
(“tubes”) and analyzed with different biomarker combinations, five
markers per tube (most markers are proteins). In addition to the
markers, the forward scatter (FS) and side scatter (SS) of each
sample was also measured in each tube. Hence, we have 359 ×
8 = 2, 872 samples and each sample is seven-dimensional (five
markers and the two scatters). Tube 1 is an isotype control used
to detect non-specific antibody binding and Tube 8 is an unstained
control for identifying background or autofluorescence of the
system. Since the data has been compensated for autofluorescence
and spectral overlap by experts, we omit these tubes from
our analysis. The disease status (AML/healthy) of 23 AML
patients and 156 healthy donors are provided as training set,

2

Σp = ((n1 − 1) ∗ Σ1 + (n2 − 1) ∗ Σ2 ))/(n1 + n2 − 2).
We compute the dissimilarity between a pair of samples by
optimally matching (in a graph-theoretic model) similar cell clusters
and summing up the dissimilarities of the matched clusters. In
earlier work, we have developed a robust variant of a graph matching
algorithm called the Mixed Edge Cover (MEC) algorithm that
allows a cluster in one sample to be matched with zero, one, or
more clusters in the second sample (Azad et al., 2010). The cell
population in the first sample could be either absent, or present,
or split into two or more cell populations in the second sample.
These can happen due to changes in biological conditions or due
to artifactual errors in clustering.
Consider two FC samples A and B consisting of ka and kb
cell populations such that A = {a1 , a2 , ..., aka }, and B =
{b1 , b2 , ..., bkb } where ai is the ith cluster from sample A and bj is
the j th cluster from B. The mixed edge cover computes a mapping
mec, of clusters across A and B such that mec(ai ) ∈ P(B) and
mec(bj ) ∈ P(A), where P(A) (P(B)) is the power set of A (B).
When a cluster ai (or bj ) remains unmatched under mec , i.e.,

(a) Template tree

(b) One phase of the
HM&M algorithm

T(S1, S2, S3, S4)

T(S1, S2)

S1

T(S3, S4)

S2

S3

S4

S3

S4

Fig. 1. (a) A hierarchical template tree created by the HM&M algorithm
from four hypothetical samples S1 , S2 , S3 and S4 . Cells are denoted with
dots, and clusters with solid ellipses in the samples are at the leaves of the
tree. An internal node represents a template created from its children, and
the root represents the template of these four samples. A meta-cluster is a
homogeneous collection of clusters and is denoted by a dashed ellipse inside
the template. (b) One phase of the HM&M algorithm creating a sub-template
T (S3 , S4 ) from samples S3 and S4 . At first, corresponding clusters across
S3 and S4 are matched by the MEC algorithm, and then the matched clusters
are merged to construct new meta-clusters.

mec(ai ) = ∅, we set d(ai , −) = λ, where the fixed cost λ is a
√
penalty for leaving a vertex unmatched. We set λ to p so that a pair
of clusters get matched only if the average squared deviation across
all dimensions is less than one. The cost of a mixed edge cover mec
is the sum of the dissimilarities of all pairs of matched clusters and
the penalties due to the unmatched clusters. A minimum cost mixed
edge cover is a mixed edge cover with the minimum cost. We use
this minimum cost as the dissimilarity D(A, B) between a pair of
samples A and B:
X
X
min (
d(ai , bj ) +
d(bi , aj )),
(2)
mixed edge
covers, mec

1≤i≤ka
bj ∈mec(ai )

1≤i≤kb
aj ∈mec(bi )

where d(ai , bj ) is computed from Equation (1). A minimum cost
mixed edge cover can be computed by a modified minimum weight
perfect matching algorithm in O(k3 log k) time where k is the
maximum number of clusters in a sample (Azad et al., 2010). The
number of cell clusters k is typically small (fewer than fifty for the
AML data), and the dissimilarity between a pair of samples can be
computed in less than a second on a desktop computer.

2.4

Creating templates from a collection of samples

We have designed a hierarchical matching-and-merging (HM&M)
algorithm that arranges a set of similar samples into a binary
template tree data structure (Azad et al., 2012). A node in the
tree represents either a sample (leaf node) or a template (internal
node). In both cases, a node is characterized by a finite mixture
of multivariate normal distributions each component of which is a
cluster or meta-cluster. Fig. 1 shows an example of a template-tree
created from four hypothetical samples, S1 , S2 , S3 , and S4 .
Let a node vi (representing either a sample or a template) in the
template tree consist of ki clusters or meta-clusters ci1 , ci2 , . . ., ciki .

A node vi is called an “orphan” if it does not have a parent in the
template-tree. Consider N flow cytometry samples S1 , S2 , . . . , SN
belonging to a class. Then the HM&M algorithm for creating a
template tree from these samples can be described by the following
three steps.
1. Initialization: Create a node vi for each of the N samples
Si . Initialize all these nodes to the set of orphan nodes. Repeat the
matching and merging steps until a single orphan node remains.
2. Matching: Compute the dissimilarity D(vi , vj ) between every
pair of nodes vi and vj in the current Orphan set with the mixed
edge cover algorithm. (using Equation (2))
3. Merging: Find a pair of orphan nodes (vi , vj ) with minimum
dissimilarity D(vi , vj ) and merge them to create a new node vl . Let
mec be a function denoting the mapping of clusters from vi to vj .
That is, if cix ∈ vi is matched to cjy ∈ vj , then cjy ∈ mec(cix ), where
1 ≤ x ≤ ki and 1 ≤ y ≤ kj . Create a new meta-cluster clz from
each set of matched clusters, clz = {cix ∪ mec(cix )}. Let kl be the
number of the new meta-clusters created above. Then the new node
vl is created as a collection of these newly created meta-clusters,
i.e., vl = {cl1 , cl2 , ..., clkl }. The distribution parameters, (µlz , Σlz ),
of each of the newly formed meta-clusters clz are estimated by the
EM algorithm. The height of vl is set to D(vi , vj ). The node vl
becomes the parent of vi and vj , and the set of orphan nodes is
updated by including vl and deleting vi and vj from it. If there
are orphan nodes remaining, we return to the matching step, and
otherwise, we terminate.
When the class labels of samples are not known a priori, the roots
of well-separated branches of tree give different class templates.
However, if samples belong to the same class – as is the case for
the AML dataset studied in this paper, the root of the templatetree gives the class-template. The HM&M algorithm requires
O(N 2 ) dissimilarity computations and O(N ) merge operations for
creating a template from a collection of N samples. Let k be
the maximum number of clusters or meta-clusters in any of the
nodes of the template-tree. Then a dissimilarity computation takes
O(k3 log k) time whereas the merge operation takes O(k) time
when distribution parameters of the meta-clusters are computed by
maximum likelihood estimation. Hence, the time complexity of
the algorithm is O(N 2 k3 log k), which is O(N 2 ) for bounded k.
The complexity of the algorithm can be reduced to O(N log N ) by
avoiding the computation of all pairwise dissimilarities between the
samples, for larger numbers of samples N , but we did not need to
do this here.

2.5

Classification score of a sample in AML dataset

Consider a sample X consisting of k cell populations S =
{c1 , c2 , ..., ck }, with the ith cluster ci containing |ci | cells. Let T −
and T + be the templates created from AML-negative (healthy) and
AML-positive training samples, respectively. We now describe how
to compute a score f (X) in order to classify the sample X to either
the healthy class or the AML class.
The intuition behind the score is as follows. An AML
sample contains two kinds of cell populations: (1) AML-specific
myeloblasts and myeloid cells, and (2) AML-unrelated cell
populations, such as lymphocytes. The former cell populations
correspond to the immunophenotypes of AML-specific metaclusters
in the AML template, and hence when we compute a mixed edge
cover between the AML template and an AML sample, these

3

clusters get matched to each other. (Such clusters in the sample do
not match to any metacluster in the healthy template.) Hence we
assign a positive score to a cluster in sample when it satisfies this
condition, signifying that it is indicative of AML. AML-unrelated
cell populations in a sample could match to meta-clusters in the
healthy template, and also to AML-unrelated meta-clusters in the
AML template. When either of these conditions is satisfied, a cluster
gets a negative score, signifying that it is not indicative of AML.
Since AML affects only the myeloid cell line and its progenitors,
it affects only a small number of AML-specific cell populations in
an AML sample. Furthermore, different subtypes of AML affect
different cell types in the myeloid cell line. Hence there are many
more clusters common to healthy samples than there are AMLspecific clusters common to AML samples. (This is illustrated later
in Fig. 3 (c) and (d).) Thus we make the range of positive scores
relatively higher than the range of negative scores. This scoring
system is designed to reduce the possibility of a false negative
(an undetected AML-positive patient), since this is more serious
in the diagnosis of AML. Additional data such as chromosomal
translocations and images of bone marrow from microscopy could
confirm an initial diagnosis of AML from flow cytometry.
In the light of the discussion above, we need to identify AMLspecific metaclusters initially. Given the templates T + and T − ,
we create a complete bipartite graph with the meta-clusters in
each template as vertices, and with each edge weighted by the
Mahalanobis distance between its endpoints. When we compute
a minimum cost mixed edge cover in this graph, we will match
meta-clusters common to both templates, and such meta-clusters
represent non-myeloid cell populations that are not AML-specific.
On the other hand, meta-clusters in the AML template T + that are
not matched to a meta-cluster in the healthy template T − correspond
to AML-specific metaclusters. We denote such meta-clusters in the
AML template T + by the set M + .
Now we can proceed to compare a sample against the template for
healthy samples and the template for AML. We compute a minimum
cost mixed edge cover between a sample X and the healthy template
T − , and let mec− (ci ) denote the set of meta-clusters in T − mapped
to a cluster ci in the sample X. Similarly, compute a minimum
cost mixed edge cover between X and the AML template T + , and
let mec+ (ci ) denote the set of meta-clusters in T + mapped to a
cluster ci . These sets could be empty if ci is unmatched in the
mixed edge cover. We compute the average Mahalanobis distance
between ci and the meta-clusters matched to it in the template
T − , and define this as the dissimilarity d(ci , mec− (ci )). From the
formulation of the mixed edge cover in (Azad et al., 2010), we have
d(ci , mec− (ci )) ≤ 2λ. Hence we define the similarity between ci
and mec− (ci ) as s(ci , mec− (ci )) = 2λ − d(ci , mec− (ci )). By
analogous reasoning, the similarity between ci and mec+ (ci ) is
defined as s(ci , mec+ (ci )) = 2λ − d(ci , mec+ (ci )).
The score of a sample is the sum of the scores of its clusters. We
define the score of a cluster ci , f (ci ), as the sum of two functions
f + (ci ) and f − (ci ) multiplied with suitable weights. A positive
score indicates that the sample belongs to AML, and a negative score
indicates that it is healthy.
The function f + (ci ) contributes a positive score to the sum if
ci is matched to an AML-specific meta-cluster in the mixed edge
cover between the sample X and the AML template T + , and a nonpositive score otherwise. For the latter case, there are two subcases:
If ci is unmatched in the mixed edge cover, it corresponds to none of

4

the meta-clusters in the template T + , and we assign it a zero score.
If ci is matched only to non-AML specific meta-clusters in the AML
template T + , then we assign it a small negative score to indicate that
it likely belongs to the healthy class (recall that k is the number of
clusters in sample X). Hence

f + (ci )

=



s ci , mec+ (ci ) ,




− 1 s(c , mec+ (c )) ,
i
i
k




0,

if mec+ (ci ) ∩ M + 6= ∅,
if mec+ (ci ) ∩ M + = ∅,
and mec+ (ci ) 6= ∅,
if mec+ (ci ) = ∅.

The function f − (ci ) contributes a negative score to a cluster ci in
the sample X if it is matched with some meta-cluster in the healthy
template T − , indicating that it likely belongs to the healthy class.
If it is not matched to any meta-cluster in T − , then we assign it
a positive score λ. This latter subcase accounts for AML-specific
clusters in the sample, or a cluster that is in neither template. In this
last case, we acknowledge the diversity of cell populations in AML
samples. Hence we have
(


− k1 s(ci , mec− (ci )) , if mec− (ci ) 6= ∅,
−
f (ci ) =
λ,
if mec− (ci ) = ∅.
Finally, we define
f (X) =

X |ci | 1 +
(f (ci ) + f − (ci )).
|X|
2
c ∈X

(3)

i

Here |X| is the number of cells in the sample X. The score of a
cluster ci is weighted by the fractional abundance of cells in it.

3
3.1

RESULTS
Cell populations in healthy and AML samples

In each tube, we identify cell populations in the samples using
the clustering algorithm described in Section 2.2. Each sample
contains five major cell types that can be seen when cell clusters
are projected on the side scatter (SS) and CD45 channels, as
depicted in Fig. 2. (Blast cells are immature progenitors of myeloid
cells or lymphocytes.) The side scatter measures the granularity
of cells, whereas CD45 is variably expressed by different white
blood cells (leukocytes). AML is initially diagnosed by rapid
growth of immature myeloid blast cells with medium SS and
CD45 expressions (Lacombe et al., 1997) marked in red in Fig. 2.
According to the WHO guidelines, AML is initially confirmed when
the sample contains more than 20% blasts. This is the case for
all, except one of the AML samples in the DREAM6/FlowCAP2
training set, and the latter will be discussed later.

3.2

Healthy and AML templates

From each tube of the AML dataset, using the training samples, we
build two templates: one for healthy samples, and one for AML. As
described in Section 2.4, the HM&M algorithm organizes samples
of the same class into a binary template tree whose root represents
the class template. The template trees created from the healthy and
AML training samples in Tube 6 are shown in Subfigures 3(a) and
3(b) respectively. The height of an internal node in the template
tree measures the dissimilarity between its left and right children,

0.8

0.8

Normal

AML

0.6

Lymphoid blasts

0.4

1.5%
0.2

0.4

0.6

0.8

Myeloid blasts
Monocytes

28%

0.2

0.4

Myeloid cells

0.2

SS (log)

0.6

Lymphocytes

0.2

0.4

0.6

0.8

CD45−ECD (log)

APL

116
101
7
172
49
103
88
5
26
9
60
105
33
134
174
165
151
95
117
89
67
37
58

0

20

40

60

80 100

(b)

86
23
137
145
142
131
82
72
129
101
105
15
146
54
128
46
116
93
65
62
140
130
118
58
39
91
9
124
155
50
110
57
13
139
134
156
51
78
100
89
67
60
41
43
7
19
114
47
14
73
147
30
143
2
109
27
11
18
153
61
75
90
117
4
126
97
99
98
24
49
59
44
83
127
95
10
45
125
34
144
76
103
1
154
20
42
87
52
135
74
38
36
112
17
68
150
5
77
64
102
121
16
70
3
123
22
148
48
84
21
92
37
96
94
29
63
111
79
133
115
120
106
141
138
66
151
26
152
132
56
33
85
80
25
69
31
107
119
88
122
113
53
136
32
55
6
108
8
71
12
149
40
81
28
104
35

0

10

20

30

40

Dissimilarity between
samples (templates)

(a)

AML positive patients

100
80

(d)

CD38
CD34
CD117
HLA−DR
CD45
SS

20

40

60

0.0

(e)

0.2

0.4

CD38
CD34
CD117
HLA−DR
CD45
SS

0.6

(f)

0.0
0.2
0.4
0.6
Expression levels of markers

0

60
40
20

Meta-clusters in the healthy template

Fraction of samples present in a meta-cluster (%)

(c)

80

100

Healthy individuals

0

Fraction of samples present in a meta-cluster (%)

Dissimilarity between
Dissimilarity
between
samples (templates)
samples
(templates)

Fig. 2. Cell types identified on the side scatter (SS) and CD45 channels for a healthy and an AML positive sample. Cell populations are discovered in the
seven-dimensional samples with the clustering algorithm and then projected on these channels for visualization. A pair of clusters denoting the same cell type
is marked with the same color. The proportion of myeloid blast cells (shown in red) increases significantly in the AML sample.

Meta-clusters in the AML template

Fig. 3. The healthy and AML templates created from Tube 6. (a) The template-tree created from 156 healthy samples in the training set. (b) The template-tree
created from 23 AML samples in the training set. Samples in the red subtree exhibit the characteristics of Acute Promyelocytic Leukemia (APL) as shown
in Subfigure (f). (c) Fraction of 156 healthy samples present in each of the 22 meta-clusters in the healthy template. Nine meta-clusters, each of them shared
by at least 60% of the healthy samples, form the core of the healthy template. (d) Fraction of 23 AML samples present in each of the 40 meta-clusters in the
AML template. The AML samples, unlike the healthy ones, are heterogeneously distributed over the meta-clusters. (e) The expression levels of markers in the
meta-cluster shown with blue bar in Subfigure (d). (Each horizontal bar in Subfigures (e) and (f) represents the average expression of a marker and the error
bar shows its standard deviation.) This meta-cluster represents lymphocytes denoted by medium SS and high CD45 expression and therefore does not express
the AML-related markers measured in Tube 6. (f) Expression of markers in a meta-cluster shown with red bar in Subfigure (d). This meta-cluster denotes
myeloblast cells as defined by the SS and CD45 levels. This meta-cluster expresses HLA-DR− CD117+ CD34− CD38+ , a characteristic immunophenotype
of APL. Five AML samples sharing this meta-cluster are similar to each other as shown in the red subtree in Subfigure (b).

5

whereas the horizontal placement of a sample is arbitrary. In these
trees, we observe twice as much heterogeneity in the AML samples
than among the healthy samples (in the dissimilarity measure),
despite the number of healthy samples being five times as numerous
as the AML samples. The larger heterogeneity among AML samples
is observed in other tubes as well. The template-tree for AML
partitions these samples into different subtrees that possibly denote
different subtypes of AML. For example, the subtree in Fig. 3(b) that
is colored red includes samples (with subject ids 37, 58, 67, 89, and
117) with immunophenotypes of Acute Promyelocytic Leukemia
(APL) (discussed later in this section).
Together, the meta-clusters in a healthy template represent a
healthy immune profile in the feature space of a tube from which
the template is created. We obtained 22 meta-clusters in the healthy
template created from Tube 6. The percentage of samples from the
training set participating in each of these meta-clusters is shown
in Fig. 3(c). Observe that 60% or more of the healthy samples
participate in the nine most common meta-clusters (these constitute
the core of the healthy template). The remaining thirteen metaclusters include populations from a small fraction of samples. These
populations could correspond to biological variability in the healthy
samples, variations in the FC experimental protocols, and possibly
also from the splitting of populations that could be an artifact of the
clustering algorithm.
The AML template created from Tube 6 consists of forty metaclusters (almost twice the number in the more numerous healthy
samples). Fig. 3(d) shows that, unlike the healthy samples, the
AML samples are heterogeneous with respect to the meta-clusters
they participate in: There are 21 meta-clusters that include cell
populations from at least 20% of the AML samples. Some of the
meta-clusters common to a large number of AML samples represent
non-AML specific cell populations. For example, Fig. 3(e) shows
the average marker expressions of the meta-cluster shown in the blue
bar in Fig. 3(d). This meta-cluster has low to medium side scatter
and high CD45 expression, and therefore represents lymphocytes
(Fig. 2). Since lymphocytes are not affected by AML, this metacluster does not express any AML-related markers, and hence can
be described as HLA-DR− CD117− CD34− CD38− , as expected.
Fig. 3(f) shows the expression profile of another meta-cluster shown
in the red bar in Fig. 3(d). This meta-cluster consists of five cell
populations from five AML samples (with subject ids 37, 58, 67,
89, and 117) and exhibits medium side scatter and CD45 expression
and therefore, represents myeloid blast cells. Furthermore, this
meta-cluster is HLA-DR− CD117+ CD34− CD38+ , and represents
a profile known to be that of Acute Promyelocytic Leukemia
(APL) (Paietta, 2003). APL is subtype M3 in the FAB classification
of AML (Bennett et al., 1985)) and is characterized by chromosomal
translocation of retinoic acid receptor-alpha (RARα) gene on
chromosome 17 with the promyelocytic leukemia gene (PML) on
chromosome 15, a translocation denoted as t(15;17). In the feature
space of Tube 6, these APL samples are similar to each other while
significantly different from the other AML samples. Our templatebased classification algorithm groups these samples together in the
subtree colored red in the AML template tree shown in Fig. 3(b).

3.3

Identifying meta-clusters symptomatic of AML

In each tube, we register meta-clusters across the AML and
healthy templates using the mixed edge cover (MEC) algorithm.
Meta-clusters in the AML template that are not matched to any

6

Table 2. Some of the meta-clusters characteristic of AML for the 23 AML
samples in the training set. In the second column, ‘−’, ‘low’, and ‘+’ denote
very low, low and high, abundance of a marker, respectively, and ± denotes a
marker that is positively expressed by some samples and negatively expressed
by others. The number of samples participating in a meta-cluster is shown in
the third column. The average fraction of cells in a sample participating in a
meta-cluster, and the standard deviation, are shown in the fourth column.
Tube

Marker expression

#Samples

Fraction of cells

2
3
4
4
5
5
5
6
6
6
7
7
7

Kappalow Lambdalow CD19+ CD20−

5
4
17
8
10
18
6
11
13
5
3
3
1

6.3%(±6.8)
18.0%(±4.8)
16.6%(±6.9)
11.1%(±5.7)
13.5%(±5.2)
10.8%(±3.8)
13.8%(±4.3)
13.3%(±2.6)
17.3%(±6.6)
12.9%(±4.7)
12.3%(±2.4)
10.0%(±8.5)
9.9%

CD7+ CD4− CD8− CD2−
CD15− CD13+ CD16− CD56−
CD15− CD13+ CD16− CD56+
CD14− CD11c− CD64− CD33+
CD14− CD11c+ CD64− CD33+
CD14low CD11c+ CD64low CD33+
HLA-DR+ CD117+ CD34+ CD38+
HLA-DR+ CD117± CD34+ CD38+
HLA-DR− CD117± CD34− CD38+
CD5− CD19+ CD3− CD10−
CD5+ CD19− CD3− CD10−
CD5− CD19− CD3− CD10+

meta-clusters in the healthy template represent the abnormal,
AML-specific immunophenotypes while the matched meta-clusters
represent healthy or non-AML-relevant cell populations. Table 2
lists several unmatched meta-clusters indicative of AML from
different tubes. As expected, every unmatched meta-cluster displays
medium side scatter and CD45 expression characteristic of myeloid
blast cells, and therefore we omit FS, SS, and CD45 values in
Table 2. We briefly discuss the immunophenotypes represented by
each AML-specific meta-cluster in each tube, omitting the isotype
control Tube 1 and unstained Tube 8.
Tube 6 is the most important panel for diagnosing AML since
it includes several markers expressed by AML blasts. HLA-DR is
an MHC class II cell surface receptor complex that is expressed on
antigen-presenting cells, e.g., B cells, dendritic cells, macrophages,
and activated T cells. It is expressed by myeloblasts in most
subtypes of AML except M3 and M7 (Campana and Behm, 2000).
CD117 is a tyrosine kinase receptor (c-KIT) expressed in blasts of
some cases (30 − 100%) of AML (Campana and Behm, 2000).
CD34 is a cell adhesion molecule expressed on different stem
cells and on the blast cells of many cases of AML (40%) (Mason
et al., 2006). CD38 is a glycoprotein found on the surface of
blasts of several subtypes of AML but usually not expressed in
the M3 subtypes of AML (Keyhani et al., 2000). In Tube 6, we
have identified two meta-clusters with high expressions of HLADR and CD34. One of them also expresses CD117 and CD34, and
Fig. 4(c) shows the bivariate contour plots of the cell populations
contained in this meta-cluster. The second meta-cluster expresses
positive but low levels of CD117 and CD34. These two HLADR+ CD34+ meta-clusters together are present in 18 out of the
23 training AML samples. The remaining five samples (subject id:
5, 7, 103, 165, 174) express HLA-DR− CD117± CD34− CD38+
myeloblasts, which is an immunophenotype of APL (Paietta, 2003)
as was discussed earlier. Fig. 4(d) shows the bivariate contour plots
of this APL-specific meta-cluster.
Tube 5 contains several antigens typically expressed by AML
blasts, of which CD33 is the most important. CD33 is a

transmembrane receptor protein usually expressed on immature
myeloid cells of the majority of cases of AML (91% reported
in (Legrand et al., 2000)). The AML specific meta-clusters
identified from markers in Tube 5 (see Table 2) include CD33+
myeloblasts from every sample in the training set. Several
of the CD33+ populations also express CD11c, a type I
transmembrane protein found on monocytes, macrophages and
neutrophils. CD11c is usually expressed by blast cells in acute
myelomonocytic leukemia (M4 subclass of AML), and acute
monocytic leukemia (M5 subclass of AML) (Campana and
Behm, 2000). Therefore CD14− CD11c+ CD64− CD33+ metacluster could represent patients with M4 and M5 subclasses of
AML. We show the bivariate contour plots of this meta-cluster in
Fig. 4(b) .
Tube 4 includes several markers usually expressed by AML
blasts, of which CD13 is the most important. CD13 is a zincmetalloproteinase enzyme that binds to the cell membrane and
degrades regulatory peptides (Mason et al., 2006). CD13 is
expressed on the blast cells of the majority of cases of AML (95%
as reported in (Legrand et al., 2000)). Table 2 shows two AMLspecific meta-clusters detected from the blast cells in Tube 4. In
addition to CD13, eight AML samples express CD56 glycoprotein
that is naturally expressed on NK cells, a subset of CD4+ T cells
and a subset of CD8+ T cells. Raspadori et al. (Raspadori et al.,
2001) reported that CD56 was more often expressed by myeloblasts
in FAB subclasses M2 and M5, which covers about 42% of AML
cases in a study by Legrand et al. (Legrand et al., 2000). In this
dataset, we observe more AML samples expressing CD13+ CD56−
blasts than expressing CD13+ CD56+ blasts, which conforms to the
findings of Raspadori et al. (Raspadori et al., 2001). Fig. 4(a) shows
the bivariate contour plots of the CD13+ CD56− meta-cluster.
Tube 2 is a B cell panel measuring B cell markers CD19
and CD20, and Kappa (κ) and Lambda (λ), immunoglobulin
light chains present on the surface of antibodies produced by B
lymphocytes. B-cell specific markers are occasionally co-expressed
with myeloid antigens especially in FAB M2 subtype of AML (with
chromosomal translocation t(8;21)) (Campana and Behm, 2000;
Walter et al., 2010). In Tube 2, we have identified a meta-cluster in
the myeloblasts that expresses high levels of CD19 and low levels
of Kappa and Lambda. The five samples with subject ids 5, 7, 103,
165, and 174 participating in this meta-cluster possibly belong to
the FAB-M2 subtype of AML. Tube 3 is a T cell panel measuring
T cell specific markers CD4, CD8, CD2, and CD7. Tube 7 is
a lymphocyte panel with several markers expressed on T and B
lymphocytes and is less important in detecting AML since they are
infrequently expressed by AML blasts.

3.4

Impact of each tube in the classification

As discussed in the methods section, we build six independent
classifiers based on the healthy and AML templates created from
Tubes 2-7 of the AML dataset. A sample is classified as an AML
sample if the classification score is positive, and as a healthy sample
otherwise. Let true positives (TP) be the number of AML samples
correctly classified, true negatives (TN) be the number of healthy
samples correctly classified, false positives (FP) be the number of
healthy samples incorrectly classified as AML, and false negatives
(FN) be the number of AML samples incorrectly classified as
healthy. Then, we evaluate the performance of each template-based
classifier with the well-known four statistical measures: Precision,

Recall(Sensitivity), Specificity, and F-value, defined as Precision =
TP
TP
TN
TP+FP , Recall(Sensitivity) = TP+FN , Specificity = FP+TN , and
Precision×Recall)
. These four measures take values in the
F-value = 2(Precision
+Recall
interval [0,1], and the higher the values the better the classifier.
First, we evaluate the impact of each tube in the classification
of the training samples. For a training sample X, the classification
score is computed by comparing it with the healthy and AML
templates created from the training set after removing X. The
predicted status of X is then compared against true status to
evaluate the classification accuracy. Table 3 (left panel) shows
various statistical measures for the classifiers defined in Tubes 27 of the training set. The classifiers based on Tubes 4, 5, and
6 have the highest sensitivity because these tubes include several
markers relevant to AML diagnosis (Campana and Behm, 2000;
Paietta, 2003). The number of true negatives TN is high in every
tube since the identification of healthy samples does not depend
on the detection of AML-specific markers. Hence specificity is
close to one for all tubes. Analogously, FP is low for most tubes,
and we observe high precision for most tubes. The F-value is a
harmonic mean of precision and recall, and denotes the superior
classification ability of markers in Tubes 4-6. Averaging scores from
all tubes does not improve the sensitivity and F-value dramatically.
However, combining Tubes 4-6 gives almost perfect classification
with one misclassification for the training set. We plot the average
classification scores from Tubes 4-6 for the training samples in
Fig. 5(a). The class labels of samples are also shown (blue circles
for healthy and red triangles for AML samples).
In Fig. 5(a), we observe an AML sample (subject id 116)
with score below the classification boundary. In this subject, the
proportion of myeloid blasts is 4.4%, which is lower than the
minimum 20% AML blasts necessary to recognize a patient to be
AML-positive according to the WHO guidelines (Estey and Döhner,
2006) (the FAB threshold is even higher, at 30%). Hence this is
either a rare case of AML, or one with minimal residual disease
after therapy, or perhaps it was incorrectly labeled as AML in the
training set. Subject 116 was classified with the healthy samples by
methods in other published work (Biehl et al., 2013).

3.5

Classifying test samples

Now we turn to the test samples. For each tube, we compute the
classification score for each sample in the test set using templates
created from the training set and applying Eq. 3. Since the average
classification score from Tubes 4-6 performs best for the training set,
we use it as a classifier for the test set as well. Since the status of
test samples was released after the DREAM6/FlowCAP2 challenge,
we can determine the classification accuracy of the test samples.
Fig. 5(b) shows the classification scores of the test samples, where
samples are placed in ascending order of classification scores. In
Fig. 5(b), we observe perfect classification in the test set. Similar to
the training set, we tabulate statistical measures for the classifiers in
Table 3.
When classifying a sample X, we assume the null hypothesis: X
is healthy (non-leukemic). The sample X receives a positive score
if it contains AML-specific immunophenotypes, and the higher
the score, the stronger the evidence against the null hypothesis.
Since Tube 1 (isotype control) does not include any AMLspecific markers, it can provide a background distribution for the
classification scores. In Tube 1, 174 out of 179 training samples

7

0.8

0

0

0

0

0.6
0.4

SS
SS

0.0

0.2

(a) Tube 6
HLA-DR+CD117+
CD34+CD38+
blasts

0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0

0.2

0.4

0.6

0.2

0.4

0.6

CD117−
PE
CD117−PE

0.8 0.0

0.2

0.4

0.6

0.8 0.0

0.2

0.4

0.6

CD34−
PC5
CD34−PC5

0.8 0.0

0.2

0.4

0.6

0.8

0.8 0.0

0.2

0.4

0.6

0.8

CD38−
PC7
CD38−PC7

0

0

0

0

0.6
0.4

SS
SS

0.0

0.2

(b) Tube 6
HLA-DR-CD117±
CD34-CD38+
blasts

HLA−
DR−
FITC
HLA−
DR−FITC

0.8

CD45−
ECD
CD45−ECD

0.0 0.2 0.4 0.6 0.8 1.0 0.0

CD45−
ECD
CD45−ECD

0.2

0.4

0.6

HLA−
DR−
FITC
HLA−
DR−FITC

0.8 0.0

CD117−
PE
CD117−PE

CD34−
PC5
CD34−PC5

CD38−
PC7
CD38−PC7

Fig. 4. Bivariate contour plots (side scatter vs. individual marker) for two meta-clusters (one in each row) indicative of AML. The ellipses in a subplot denote
the 95th quantile contour lines of cell populations included in the corresponding meta-cluster. Myeloblast cells have medium side scatter (SS) and CD45
expressions. The red lines indicate approximate myeloblast boundaries (located on the left-most subfigures in each row and extended horizontally to the
subfigures on the right) and confirm that these meta-clusters represent immunophenotypes of myeloblast cells. Blue vertical lines denote the +/- boundaries
of a marker. Gray subplots show contour plots of dominant markers defining the meta-cluster in the same row. (a) HLA-DR+ CD117+ CD34+ CD38+ metacluster shared by 11 AML samples in Tube 6. (b) HLA-DR− CD117± CD34− CD38+ meta-cluster shared by 5 AML samples in Tube 6. This meta-cluster
is indicative of acute promyelocytic leukemia (APL). These bivariate plots are shown for illustration only, since the populations of specific cell types are
identified from seven-dimensional data.
Table 3. Four statistical measures evaluating the performance of the template-based classification in the training
set and test set of the AML data. The statistical measures are computed for each tube separately and two
combinations of tubes.
Tubes

Test set

Specificity

F-value

Precision

Recall

Specificity

F-value

0.74
0.91
0.70
0.74
0.96

0.99
0.96
1.00
1.00
1.00

0.83
0.82
0.82
0.85
0.98

1.00
0.65
1.00
1.00
1.00

0.75
0.85
0.80
0.85
1.00

1.00
0.94
1.00
1.00
1.00

0.86
0.74
0.89
0.92
1.00

0.5

AML

classification boundary

0

50

100

150

Training samples, ordered

(b) Test set

Actual class
Healthy
AML

0.5

1.0

Healthy

classification boundary

0.0

Actual class
Sam

1.0

Recall

0.94
0.75
1.00
1.00
1.00

Classification score

Precision

(a) Training set

0.0

Classification score

4
5
6
All (2-7)
4,5,6

Training set

0

50

100

150

Test samples, ordered

Fig. 5. Average classification score from Tubes 4,5,6 for each sample in the (a) training set and (b) test set. Samples with scores above the horizontal line are
classified as AML, and as healthy otherwise. The actual class of each sample is also shown. An AML sample (subject id 116) is always misclassified in the
training set, and this is discussed in the text.

have negative classification scores, but five samples have positive
scores, with values less than 0.2. In the best classifier designed
from Tubes 4, 5, 6, we observe that two AML-positive samples in
the training set and three AML-positive samples in the test set have
scores between 0 and 0.2. The classifier is relatively less confident
about these samples; nevertheless, the p-values of these five samples

8

(computed from the distribution in Tube 1) are still small (< 0.05),
so that they can be classified as AML-positive. The rest of the AML
samples in the training and test sets have scores greater than 0.2 and
the classifier is quite confident about their status (p-value zero).
Four AML samples in the test set (ids 239, 262, 285, and 326)
were subclassified as APL by comparing against distinct template

trees for APL and the other AML samples in the training set (cf.
Fig. 3 (b)).
Finally, we state the computational times required on an iMac
with four 2.7 GHz cores and 8 GB memory. Our code is in
R. Consider a single tube with 359 samples in it. The k-means
clustering of all samples took one hour, primarily because we need
to run the algorithm multiple times (about ten on the average) to find
the optimal value of the number of clusters. Creating the healthy
template from 156 samples in the training set required 10 seconds
(s) on one core, and the AML template for 23 AML samples took
0.5s on one core. Cross validation (leave one out) of the training set
took 30 minutes, and computing the classification score for the 180
test samples took 15s, both on four cores. We could have reduced
the running time by executing the code in parallel on more cores.
We have made the dominant step, the k-means clustering of all the
samples with an optimal number of clusters, faster using a GPU,
reducing the total time to a few minutes.

4

CONCLUSIONS

We have demonstrated that an algorithmic pipeline for templatebased classification can successfully identify immunophenotypes
of clinical interest in AML. These could be used to differentiate
the subtypes of AML, which is advantageous since prognosis and
treatment depends on the subtype. The templates enable us to
classify AML samples in spite of their heterogeneity. This was
accomplished by creating a scoring function that accounts for the
subtleties in cell populations within AML samples. We are currently
applying this approach to a larger AML data set, and intend to
analyze other heterogeneous data sets.

ACKNOWLEDGMENTS
This research was supported by NIH grant IR21EB015707-01, NSF
grant CCF-1218916, and DOE grant 13SC-003242.

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9

