# Textural Classification of Mammographic Parenchymal Patterns with the SONNET Selforganizing Neural Network

Authors: Daniel Howard; Simon C. Roberts; Conor Ryan; Adrian Brezulianu
Journal: Journal of Biomedicine and Biotechnology
 (2008)

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## Abstract

In nationwide mammography screening, thousands of mammography examinations must be processed. Each consists of two standard views of each breast, and each mammogram must be visually examined by an experienced radiologist to assess it for any anomalies. The ability to detect an anomaly in mammographic texture is important to successful outcomes in mammography screening and, in this study, a large number of mammograms were digitized with a highly accurate scanner; and textural features were derived from the mammograms as input data to a SONNET selforganizing neural network. The paper discusses how SONNET was used to produce a taxonomic organization of the mammography archive in an unsupervised manner. This process is subject to certain choices of SONNET parameters, in these numerical experiments using the craniocaudal view, and typically produced O(10), for example, 39 mammogram classes, by analysis of features from O(103) mammogram images. The mammogram taxonomy captured typical subtleties to discriminate mammograms, and it is submitted that this may be exploited to aid the detection of mammographic anomalies, for example, by acting as a preprocessing stage to simplify the task for a computational detection scheme, or by ordering mammography examinations by mammogram taxonomic class prior to screening in order to encourage more successful visual examination during screening. The resulting taxonomy may help train screening radiologists and conceivably help to settle legal cases concerning a mammography screening examination because the taxonomy can reveal the frequency of mammographic patterns in a population.


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## Body

## 1. Introduction

Nationwide mammography screening (NMS) is the most
successful method for the early detection of breast cancer [1]. There exist differing opinions concerning the details of an ideal NMS programme, with a body of opinion arguing that it should involve women over the age of
40 attending an annual mammography examination that
obtains X-ray of each breast (for the two standard views), with technicians ensuring that the subject is imaged consistently each year to allow a comparison of the images over time, which is essential to mammography screening. Longitudinal comparisons of mammograms are quite revealing.  Consider Figure 1, which pertains to a woman who assisted frequent screening for over 20 years. This longitudinal comparison llustrates the involution of the parenchyma with age of
the subject as it is replaced by adipose tissue. Exceptions relate to extensive fibrosis or adenosis for which
this involution to all intent and purposes cannot be observed [2]. Also, mammograms of subjects starting
hormone replacement therapy appeared to us to restore an earlier appearance. By
comparing images longitudinally, it may be possible to detect a lesion as an abnormality
that grows in time in contrast to the gradual but perceivable retraction of the
parenchyma.Figure 1
Longitudinal study showing the process of involution of the parenchyma with age of subject
(digitized from L. Tabár archive). The CC view is shown from examinations in
1980, 1989, 1997, and 2002 (left to right).An NMS programme also requires an integrated clinical
team involving a pathologist, radiologist, oncologist and surgeon. Ideally, when a patient undergoes an invasive procedure then the radiologist should obtain X-ray images of sections of the biopsy specimen to visually compare these with the original mammogram so as to improve his or her abilities at detecting lesions.If the NMS programme were to encourage the same radiologist to screen the same women for a number of years, it is possible that fewer women would be recalled without good reason.  When fewer women are recalled without good reason, higher levels of compliance and participation of women usually follow, and if so, then the benefits of screening: early detection and arguably lower cancer mortality rates should follow.To date, computer-aided detection (CAD) of cancer does not appear to have achieved significant penetration in NMS services. A challenge of CAD is to help with difficult-to-perceive and subtle lesions also known as distortions, which are strong indications of breast cancer.  Calcifications are not as significant because up to 80% of calcification occurrences in screening are benign [3].Architectural distortions are variable in shape and size and difficult to pick-up in early detection even by an experienced radiologist. Figures2, 3, and 4 illustrate this typical
progression for consecutive examinations over time, the X-ray images can be
seen to differ most significantly with an impression of a “pulling”
effect at the site of the distortion. These examples are very obvious but it is
necessary to detect very subtle distortions early on. By observing the foremost
radiologists at work it became apparent that anomalies in image texture (angles
in the orientation of textural patterns) accounted for their intuitions about
the presence of a lesion. Radiologists have used emotive terms to explain how
they pick-up on subtle anomalies and the detection of mammographic lesions has
been described as “visual art” [3]. This together with the
variability and elusiveness of architectural distortions motivated us to
develop machine vision algorithms to construct a taxonomy of mammography
textural patterns rather than to produce a more standard CAD tool.
It was observed that unusual angular orientations of texture
alerted the experienced radiologist to a subtle distortion. This
observation, however, is an oversimplification for the purpose of
this discussion, as clinical knowledge is essential for the
detection of the lesion.Figure 2
Left to right: longitudinal progression of a distortion (digitized from L. Tabár
archive).Figure 3
Left to right: longitudinal progression of a distortion (digitized from L. Tabár archive).Figure 4
Left to right: longitudinal progression of a distortion (digitized from L. Tabár archive).


## 2. A Computational Tool for  Mammogram Classification

How to best assist an NMS programme using a computational tool for image analysis? This is
the research question that we set out to answer. In cancer screening, the
number of normal cases far exceeds the number of suspected lesions (perhaps to
a ratio of 50 to 1). This can lead to fatigue in
human-facilitated screening and a lack of lesion
examples with which radiologists are trained.
Furthermore, the high variability of normal cases has led it to be said that a
mammogram can equate to a fingerprint in its subject identification ability.Our aim was to apply artificial intelligence (AI) and
image analysis techniques to answer the aforementioned research question. In
order to study the problem quantitatively, we deployed an accurate Lumysis
scanner to digitize a large number of pristine film mammograms from a
long-established archive that contains arguably the greatest density of
high-quality mammograms in the world [4].
Leading radiologists of the breast such as Wolf and Tabár considered
“parenchymal types” [3, 5] to establish a subjective classification of mammograms
into a few categories. This paper addresses the automation of this
classification process by using an unsupervised, selforganizing method of AI
known as SONNET (described in Section 3). The automated classification scheme
is based on image textural analysis because, as previously mentioned, we
surmised that textural patterns and orientations (the angles that can be
perceived in this texture) are the important criteria of visual inspection for
radiologists; they constitute a type of visual “algedonic alert”
[6] to the presence of
a subtle distortion in the mammogram.A categorized organization of a mammogram archive by
texture could have many potential uses. Learning and training are obvious but
for example with the objective of higher accuracy in screening, the mammograms
could be sorted by taxonomic pattern to enable the organized viewing that gives
time for radiologists to become accustomed to the background texture. This
normal texture could then more easily be compared against the anomalous texture
of architectural distortions and lesions. Also, patients could be tracked
longitudinally based on their progression through the taxonomy of parenchymal
types [4, 5, 7]. This could provide
additional information for a mammographic examination by allowing comparison to
other patients who experienced a similar progression. The aberrations of normal
breast development may be studied with this taxonomy. They could offer clues to
reasons for a higher incidence of breast cancer in a population, for instance,
according to lifestyle or genetic profile. Conceivably, a taxonomy could help
to settle a legal case as it quantifies how common is the parenchymal pattern,
to help settle a dispute concerning an early breast cancer warning that was
missed.


## 3. The Sonnet Classifier

The artificial neural network known as SONNET [8] consists of an
array of classifiers connected to an input field as shown in Figure 5. Input
patterns are presented in turn to the input field and typical patterns are gradually encoded as
follows. The constituent classifiers compete to encode each pattern such that
the classifier with the best match to the current input tends to adapt itself
more than the other classifiers. This winning classifier adapts itself by
partially encoding the current input pattern on weighted excitatory connections from the
input field. Furthermore, the classifier adapts weighted inhibitory connections
to the other competing classifiers, thus allowing the winning classifier to
suppress its competitors. The classifiers consequently diverge so that each
responds only to input patterns which are similar to the pattern encoded on its
excitatory connections.Figure 5
SONNET architecture.SONNET is a selforganizing neural network based on
adaptive resonance theory [2] that encodes classifications using unsupervised
learning. The SONNET architecture is shown in Figure 5 where a field of input
neurons is connected to a field of classification neurons via weighted
connections. An input pattern is a pattern of relative neural activity in the
input field at any given moment, and a set of input patterns is presented to
SONNET by setting the activity of the input neurons to each pattern in turn for
a fixed duration.Each input neuron is connected to each classification
neuron by an excitatory weighted connection, and the weight on each connection
is continually adapted via a learning rule (this is similar to Hebbian learning
[9, 10] which postulates that
memory is stored in the synaptic weights and learning is the process that
changes those weights) such that the connection becomes stronger when the two
corresponding neurons are simultaneously active. Furthermore, higher activity
on the two neurons causes the connection to become stronger more rapidly. The
maximum rate at which the weights can change governs the network's learning
speed and this is regulated by controlling parameters that are set prior to a
SONNET run.The relative pattern of excitatory weights on
connections to a single-classification neuron represents the so-calledprototype for that classifier. The
excitatory input to a classification neuron is based on two measures. The first
measure is based on the size of the excitatory weights so that a large
excitatory input can be achieved when strong weights gate high-input
activations. The second measure quantifies how well the prototype matches the
current input pattern such that a large excitatory input can be achieved for a
good match even when the prototype is represented by small excitatory weights.
A large excitatory input to a classification neuron allows the neuron to gain a
high activation in response to the current input pattern. This activation
represents the confidence with which the neuron classifies the input pattern.
The learning speed can be set to allow the prototype to form gradually from
repeated exposure to input patterns, such that the prototype encodes a generalization for multiple similar input
patterns. The classification neuron can then obtain a high activation when any
one of these input patterns occurs and thus it classifies these patterns
together.The classifiers compete to encode each input pattern
such that the classifier with the best match to the current input tends to
adapt itself more than the other classifiers, thus further improving its
competitive advantage. Each classifier is connected to all other classifiers by
an inhibitory weighted connection that is again adapted via a learning rule
such that a connection becomes stronger (i.e., more inhibitory) when the
corresponding neurons are simultaneously active. Classifiers that have
partially encoded similar patterns thus compete strongly against each other,
causing one classifier to eventually suppress its competitors. The classifiers
consequently diverge to encode different input patterns so that only one
classification neuron achieves a high activation in response to each input
pattern. When the input pattern changes, the activation of a previously excited
classifier can decrease due to both passive decay and inhibition from competing
classifiers that better represent the new input pattern.SONNET performs real-time learning by continually
adapting its weights in the selforganizing manner described above. The learning
algorithm is unsupervised and there is no reinforcement of any kind from an
external source to judge the emergent classifications against expected
classifications. The network is initialized with random small weights and the
classifiers compete such that the most common input patterns are encoded first
and the less common patterns are encoded more gradually.The selforganizing behaviour causes SONNET to be
susceptible to the so-calledstability-plasticity dilemma [2], which states that a network
should always remain adaptive to learn new patterns (i.e., have plasticity)
without degrading well-formed encodings for previously learned patterns (i.e.,
have stability). SONNET achieves plasticity due to the aforementioned learning
algorithm but it also achieves stability by reducing the learning speed at a
single classifier when the size of the classifier's
excitatory weights become large. A classifier can only gain large excitatory
weights after it has encoded a good representation for one or more input
patterns, and a stable classifier is said to be committed with excitatory weights that
constitute a long-term memory of the encoding.For the current application, each input pattern
represented features extracted from a mammogram. A set of mammograms was
selected with which totrain SONNET, and each presentation of the full mammogram set is known as an epoch.
SONNET typically learned by adapting itself over many epochs until a stable set of classifiers could classify
each mammogram with a significant degree of confidence. The order of mammogram
presentation was randomized on each epoch. This reduced the likelihood of an
unstable classifier from oscillating between similar yet significantly
different potential classes.SONNET is a highly dynamic system which is controlled
by many parameters as discussed in other recent research presentations in
[11–13]. It is a fully unsupervised
system which encodes classes via selforganization in response to the input
patterns. However, the manual specification of SONNET's controlling parameters
allows a degree of supervision. For example, a number of parameters govern
SONNET's learning speed which in turn influences the number of classes encoded.
The greatest learning speed produces one-shot learning where SONNET simply
memorizes each input pattern. Slower learning produces broader classes, where a
single classifier can represent multiple similar patterns by forming encodings
that generalize the characteristic features of the class.Multiple SONNET runs were conducted using different
randomized initial weights on the connections within the network. This allowed
different encodings to form on each run. SONNET's controlling parameters were
also varied on different runs to change the learning speed. SONNET comprised at
most 80 classifiers though the actual number was set in accordance with the
learning speed. Each run terminated after 100 epochs but the final epoch did
not necessarily represent the optimum SONNET state. Section4.5 explains how
the optimum SONNET runs and epochs were identified.


## 4. Developing a Mammogram Taxonomy Using Unsupervised Classification

The development of an unsupervised classification scheme to produce a mammogram taxonomy had to
address the following issues: input feature extraction; input feature selection
to produce a minimal set of features which best characterize the input cases;
input feature preprocessing prior to presentation to the classification system;
classifier development; and the definition of classification performance
measures in order to compare the classifiers resulting from different SONNET
runs. These issues are discussed in the following subsections.


### 4.1. Mammogram Feature Extraction

450 mammograms were chosen for the current study. These mammograms represented the CC left and
right views for 225 different patients. The mammograms were X-rayed between
1990 and 2002; and they were of a highly consistent
top quality. Most mammograms displayed normal breast tissue but 49 of the
patients had been diagnosed as having breast cancer. Subtle cancerous lesions
were evident in the mammograms corresponding to these patients.The breast tissue in a mammogram must be segmented
from the background before mammogram features can be extracted. This was
achieved by locating maximal brightness gradients to produce multiple
hypotheses for the actual breast margin. The best hypothesis was identified by
optimizing contour shape and smoothness. The location of the nipple was also
estimated to ascertain three different regions within the breast as shown in Figure6. These regions are the retroareolar region (behind the nipple), an axillar
region (outer) and a medial region (inner). The identification of the breast
margin allowed equivalent regions to be defined on different mammograms by
specifying positions relative to the nipple location.Figure 6
Mammogram regions.Standard image processing techniques were used to
extract the following information from each of the three regions: brightness
distribution, contrast distribution, and textural measures. Brightness was calculated
in a 10 mm square (as depicted in Figure6) which was swept over each region to
give the brightness distribution as represented by minimum, maximum, average,
and standard deviation values. The same procedure was used to calculate the
contrast distribution.Textural measures were calculated by accumulating
co-occurrence matrices over each region. The following 9 textural features were
calculated from each matrix: angular second moment, inverse difference moment,
contrast, entropy, sum entropy, difference entropy, and three correlation
measures. Furthermore, co-occurrence matrices were generated for each of four
orientations: 0, 45, 90, and 135 degrees. Hence 12 matrices were generated;
four orientations for the three regions.The above processing resulted in 132 image features
for each mammogram. Note that the mammogram for the left breast was flipped
horizontally before processing to map the axillar and medial regions onto those
for the right breast, and to give the appropriate orientations for the textural
features.


### 4.2. Mammogram Feature Preprocessing

The extracted image features constitute an input
feature vector that can be presented to SONNET's input field. However, each
dimension of the input feature vector must be normalized so that each feature varies
over the same range. This prevents individual dimensions from dominating the
input feature space. For example, suppose dimensionX ranged from 0 to 255 and
dimension Y ranged from 0 to 1, then without normalization X would dominate Y
in the input vector so that Y would effectively be negligible. Furthermore, the
normalization improves the discrimination between input cases. In the above
example, without normalization each input case would typically be represented
by a vector where X is two orders of magnitude greater than Y. Consequently,
the input cases would appear more similar to each other than if each input
dimension was normalized.The mammogram features were linearly scaled to range
from 0 to 1 by analyzing the mammogram set for each input dimension
independently. For a single input dimension, the minimum and maximum values
across the mammogram set were discovered and these were used to normalize each
input case.


### 4.3. Mammogram Feature Selection

The 132 features extracted from each of the 450 mammograms
were analyzed to produce a minimal set of features which best characterized the
mammograms. The procedure for this was as follows:(i)
calculate the correlation between each pair of
features across the set of mammograms,(ii)
identify the most correlated pair of features;
featuresX and Y,(iii)
omit featureX if it has the least deviation
across the set of mammograms, else omit feature Y,(iv)
repeat from step 2 whilst the highest
correlation is above a prescribed threshold.This procedure produced the correlations shown in
Figure7. It can be seen from the maximum correlations that many of the
features were highly correlated. These correlations corresponded to the same
type of textural features taken from the same mammogram regions, but where the
features pertained to different textural orientations. For example, the
entropies in the retroareolar region at 45 degrees and 135 degrees were highly
correlated. The maximum correlation between nontextural features was 0.87.Figure 7
Average and maximum correlations between mammogram features against the number of features omitted.The figure shows that the omission of highly
correlated features tended to reduce the average correlation between features
after an initial increase in this average. The discrimination between
mammograms improves as the average correlation between the features is
minimized. However, as the average correlation tends to continually decrease a
correlation threshold must be set to terminate feature omission. This threshold
was set by considering the distance between mammograms in feature space.Section4.1 explained that each feature was scaled to
range from 0 to 1, hence the maximum distance between two mammograms in feature
space was the square root of the number of features used. For example, the
maximum distance for the original 132 features was 11.5. Therefore, for a given
number of features, the distance between mammograms can be calculated and then
normalized by the maximum potential distance.Figure8 displays the variation in the average
normalized distance between mammograms as highly correlated features were
omitted. Similarly, Figure 9 displays the variation in the maximum normalized
distance between mammograms. The normalized distance between mammograms should
be maximized to improve the discrimination between mammograms. The figures show
that the normalized distances increase slightly as more features were omitted.
However, excessively omitting features would restrict the information captured
from the mammograms. Consequently, a correlation threshold of 0.98 was set to
terminate feature omission. This caused 79 features to be omitted which
approximately corresponds to local maxima in Figures 8 and 9.Figure 8
Average normalized distance between mammograms against the number of features
omitted.Figure 9
Maximum normalized distance between mammograms against the number of features omitted.In summary, mammogram features were omitted from the
input vector in order to minimize the correlation between the remaining
features, whilst maximizing the normalized distance between the mammograms in
feature space. A correlation threshold of 0.98 was set to limit the highest
correlation between mammogram features. This caused 79 features to be omitted
and thus retained 53 features. SONNET's input field therefore consisted of 53
input neurons where each neuron represented a specific type of mammogram
feature.


### 4.4. Classification Performance Measures

This section defines performance measures to compare
different mammogram classifications. The measures in the first subsection are
general to any classification task whereas those in the second subsection are
specific to mammogram classification.


#### 4.4.1. Distance in Input Feature Space

A set of input cases can be conceived as a set of
points in input feature space. Thus the performance of a classification scheme
can be quantified by considering the distances between input cases in input
feature space. These distances give rise to the following rule.Input cases which receive the same
classification should be proximate in feature space, whereas cases which are
classified differently should be distant from each other. Hence, the
classification task becomes a multiobjective optimization problem which is
required to minimize the average within-class distance between case-pairs,
whilst maximizing the average between-class distance.Performance measures can be formulated for the current
task by considering two mammogramsi and j which are a distance dij apart in input feature space. Suppose that
these mammograms are classified as being of type χi and χj respectively, and that the corresponding
classification confidences are ci and cj. It is more important for mammograms which are
classified with a high confidence to be consistent with the above rule, than it
is for mammograms classified with a lower confidence. Hence, the distance dij should be weighted by the confidences ci and cj.The average distance over a set of mammograms can now
be calculated. The average within-class distance,Dw, would be calculated over the set of mammograms which received the same
classification (i.e., χi=χj), whereas the average between-class distance, Db, would be calculated over the set of mammograms which received different
classifications (i.e., χi≠χj). These average distances are calculated as follows:
(1)Dw=∑χi=χjcicjdij∑χi=χjcicj,(2)Db=∑χi≠χjcicjdij∑χi≠χjcicj.


#### 4.4.2. Patient-Wise Mammogram Comparison

A patient should receive the same classification for their left and right CC mammograms,
and this notion was confirmed by casual subjective observation. This notion can
be tested by analyzing the distances between pairs of mammograms in feature
space. Figure10 shows the distances between mammogram-pairs in the reduced
feature space of 53 feature types. Comparison between the left and right mammograms
for the same patient produced the lower line, where each point corresponded to
a single patient and the points were ranked according to increasing distance.Figure 10
Comparing the distances between mammograms using 53 features: (a)same, the left and right views within
patients, (b) diff D1, the right views between patients, and (c) diff
S1, the left views between patients.Each “diff D1” point was produced by comparing the
right views between two different patients, and this comparison was repeated
for all combinations of patient-pairs. Similarly, the “diff S1” points were
produced by comparing pairs of left views of different patients. The points
were again ranked according to increasing distance. There was no significance
in comparing the left or right views individually and so the corresponding
points overlap to appear as the upper line in Figure10.The figure shows that within-patient distances were
typically less than between-patient distances. Approximately 70% of the
within-patient comparisons gave distances less than 1, and all these
comparisons gave distances less than 2. Conversely, only 5% and 50% of the
between-patient comparisons gave distances less than 1 and 2 respectively.The results in this section justify the use of
patient-wise performance measures for the mammogram classifiers. However,
because the two mammograms for a particular patient can differ significantly,
patient-wise performance measures should be used only as secondary measures.
For example, patient-wise performance measures could be used to compare
classifiers which are indistinguishable when using the measures based on
distances in mammogram feature space. Note that patient-wise performance
measures did not actively drive SONNET's development, but instead the measures were
used to assess classification performance after development.


### 4.5. Discovering Optimum Classifications

Section3 stated that multiple SONNET runs were
conducted for 100 epochs. Any of these epochs could represent the optimum
SONNET state, where many stable classifiers separate the mammogram set into
clearly distinguishable classes. Every epoch was assessed according to various
performance measures and this posed a multiobjective optimization problem. The
number of candidate optimum SONNET epochs was reduced by discovering the Pareto front across the performance
measures. Consequently, none of these candidate epochs could be dominated by
another epoch on every performance measure. The Pareto front was discovered across the following
dimensions:(i)
average within-class distanceDw (1),(ii)
average between-class distanceDb (2),(iii)
the number of classes encoded,(iv)
the classification confidences,(v)
the fraction of patients which received the same
classification for their two mammograms.Dw was minimized whereas all of the other
performance measures were maximized.


## 4.1. Mammogram Feature Extraction

450 mammograms were chosen for the current study. These mammograms represented the CC left and
right views for 225 different patients. The mammograms were X-rayed between
1990 and 2002; and they were of a highly consistent
top quality. Most mammograms displayed normal breast tissue but 49 of the
patients had been diagnosed as having breast cancer. Subtle cancerous lesions
were evident in the mammograms corresponding to these patients.The breast tissue in a mammogram must be segmented
from the background before mammogram features can be extracted. This was
achieved by locating maximal brightness gradients to produce multiple
hypotheses for the actual breast margin. The best hypothesis was identified by
optimizing contour shape and smoothness. The location of the nipple was also
estimated to ascertain three different regions within the breast as shown in Figure6. These regions are the retroareolar region (behind the nipple), an axillar
region (outer) and a medial region (inner). The identification of the breast
margin allowed equivalent regions to be defined on different mammograms by
specifying positions relative to the nipple location.Figure 6
Mammogram regions.Standard image processing techniques were used to
extract the following information from each of the three regions: brightness
distribution, contrast distribution, and textural measures. Brightness was calculated
in a 10 mm square (as depicted in Figure6) which was swept over each region to
give the brightness distribution as represented by minimum, maximum, average,
and standard deviation values. The same procedure was used to calculate the
contrast distribution.Textural measures were calculated by accumulating
co-occurrence matrices over each region. The following 9 textural features were
calculated from each matrix: angular second moment, inverse difference moment,
contrast, entropy, sum entropy, difference entropy, and three correlation
measures. Furthermore, co-occurrence matrices were generated for each of four
orientations: 0, 45, 90, and 135 degrees. Hence 12 matrices were generated;
four orientations for the three regions.The above processing resulted in 132 image features
for each mammogram. Note that the mammogram for the left breast was flipped
horizontally before processing to map the axillar and medial regions onto those
for the right breast, and to give the appropriate orientations for the textural
features.


## 4.2. Mammogram Feature Preprocessing

The extracted image features constitute an input
feature vector that can be presented to SONNET's input field. However, each
dimension of the input feature vector must be normalized so that each feature varies
over the same range. This prevents individual dimensions from dominating the
input feature space. For example, suppose dimensionX ranged from 0 to 255 and
dimension Y ranged from 0 to 1, then without normalization X would dominate Y
in the input vector so that Y would effectively be negligible. Furthermore, the
normalization improves the discrimination between input cases. In the above
example, without normalization each input case would typically be represented
by a vector where X is two orders of magnitude greater than Y. Consequently,
the input cases would appear more similar to each other than if each input
dimension was normalized.The mammogram features were linearly scaled to range
from 0 to 1 by analyzing the mammogram set for each input dimension
independently. For a single input dimension, the minimum and maximum values
across the mammogram set were discovered and these were used to normalize each
input case.


## 4.3. Mammogram Feature Selection

The 132 features extracted from each of the 450 mammograms
were analyzed to produce a minimal set of features which best characterized the
mammograms. The procedure for this was as follows:(i)
calculate the correlation between each pair of
features across the set of mammograms,(ii)
identify the most correlated pair of features;
featuresX and Y,(iii)
omit featureX if it has the least deviation
across the set of mammograms, else omit feature Y,(iv)
repeat from step 2 whilst the highest
correlation is above a prescribed threshold.This procedure produced the correlations shown in
Figure7. It can be seen from the maximum correlations that many of the
features were highly correlated. These correlations corresponded to the same
type of textural features taken from the same mammogram regions, but where the
features pertained to different textural orientations. For example, the
entropies in the retroareolar region at 45 degrees and 135 degrees were highly
correlated. The maximum correlation between nontextural features was 0.87.Figure 7
Average and maximum correlations between mammogram features against the number of features omitted.The figure shows that the omission of highly
correlated features tended to reduce the average correlation between features
after an initial increase in this average. The discrimination between
mammograms improves as the average correlation between the features is
minimized. However, as the average correlation tends to continually decrease a
correlation threshold must be set to terminate feature omission. This threshold
was set by considering the distance between mammograms in feature space.Section4.1 explained that each feature was scaled to
range from 0 to 1, hence the maximum distance between two mammograms in feature
space was the square root of the number of features used. For example, the
maximum distance for the original 132 features was 11.5. Therefore, for a given
number of features, the distance between mammograms can be calculated and then
normalized by the maximum potential distance.Figure8 displays the variation in the average
normalized distance between mammograms as highly correlated features were
omitted. Similarly, Figure 9 displays the variation in the maximum normalized
distance between mammograms. The normalized distance between mammograms should
be maximized to improve the discrimination between mammograms. The figures show
that the normalized distances increase slightly as more features were omitted.
However, excessively omitting features would restrict the information captured
from the mammograms. Consequently, a correlation threshold of 0.98 was set to
terminate feature omission. This caused 79 features to be omitted which
approximately corresponds to local maxima in Figures 8 and 9.Figure 8
Average normalized distance between mammograms against the number of features
omitted.Figure 9
Maximum normalized distance between mammograms against the number of features omitted.In summary, mammogram features were omitted from the
input vector in order to minimize the correlation between the remaining
features, whilst maximizing the normalized distance between the mammograms in
feature space. A correlation threshold of 0.98 was set to limit the highest
correlation between mammogram features. This caused 79 features to be omitted
and thus retained 53 features. SONNET's input field therefore consisted of 53
input neurons where each neuron represented a specific type of mammogram
feature.


## 4.4. Classification Performance Measures

This section defines performance measures to compare
different mammogram classifications. The measures in the first subsection are
general to any classification task whereas those in the second subsection are
specific to mammogram classification.


### 4.4.1. Distance in Input Feature Space

A set of input cases can be conceived as a set of
points in input feature space. Thus the performance of a classification scheme
can be quantified by considering the distances between input cases in input
feature space. These distances give rise to the following rule.Input cases which receive the same
classification should be proximate in feature space, whereas cases which are
classified differently should be distant from each other. Hence, the
classification task becomes a multiobjective optimization problem which is
required to minimize the average within-class distance between case-pairs,
whilst maximizing the average between-class distance.Performance measures can be formulated for the current
task by considering two mammogramsi and j which are a distance dij apart in input feature space. Suppose that
these mammograms are classified as being of type χi and χj respectively, and that the corresponding
classification confidences are ci and cj. It is more important for mammograms which are
classified with a high confidence to be consistent with the above rule, than it
is for mammograms classified with a lower confidence. Hence, the distance dij should be weighted by the confidences ci and cj.The average distance over a set of mammograms can now
be calculated. The average within-class distance,Dw, would be calculated over the set of mammograms which received the same
classification (i.e., χi=χj), whereas the average between-class distance, Db, would be calculated over the set of mammograms which received different
classifications (i.e., χi≠χj). These average distances are calculated as follows:
(1)Dw=∑χi=χjcicjdij∑χi=χjcicj,(2)Db=∑χi≠χjcicjdij∑χi≠χjcicj.


### 4.4.2. Patient-Wise Mammogram Comparison

A patient should receive the same classification for their left and right CC mammograms,
and this notion was confirmed by casual subjective observation. This notion can
be tested by analyzing the distances between pairs of mammograms in feature
space. Figure10 shows the distances between mammogram-pairs in the reduced
feature space of 53 feature types. Comparison between the left and right mammograms
for the same patient produced the lower line, where each point corresponded to
a single patient and the points were ranked according to increasing distance.Figure 10
Comparing the distances between mammograms using 53 features: (a)same, the left and right views within
patients, (b) diff D1, the right views between patients, and (c) diff
S1, the left views between patients.Each “diff D1” point was produced by comparing the
right views between two different patients, and this comparison was repeated
for all combinations of patient-pairs. Similarly, the “diff S1” points were
produced by comparing pairs of left views of different patients. The points
were again ranked according to increasing distance. There was no significance
in comparing the left or right views individually and so the corresponding
points overlap to appear as the upper line in Figure10.The figure shows that within-patient distances were
typically less than between-patient distances. Approximately 70% of the
within-patient comparisons gave distances less than 1, and all these
comparisons gave distances less than 2. Conversely, only 5% and 50% of the
between-patient comparisons gave distances less than 1 and 2 respectively.The results in this section justify the use of
patient-wise performance measures for the mammogram classifiers. However,
because the two mammograms for a particular patient can differ significantly,
patient-wise performance measures should be used only as secondary measures.
For example, patient-wise performance measures could be used to compare
classifiers which are indistinguishable when using the measures based on
distances in mammogram feature space. Note that patient-wise performance
measures did not actively drive SONNET's development, but instead the measures were
used to assess classification performance after development.


## 4.4.1. Distance in Input Feature Space

A set of input cases can be conceived as a set of
points in input feature space. Thus the performance of a classification scheme
can be quantified by considering the distances between input cases in input
feature space. These distances give rise to the following rule.Input cases which receive the same
classification should be proximate in feature space, whereas cases which are
classified differently should be distant from each other. Hence, the
classification task becomes a multiobjective optimization problem which is
required to minimize the average within-class distance between case-pairs,
whilst maximizing the average between-class distance.Performance measures can be formulated for the current
task by considering two mammogramsi and j which are a distance dij apart in input feature space. Suppose that
these mammograms are classified as being of type χi and χj respectively, and that the corresponding
classification confidences are ci and cj. It is more important for mammograms which are
classified with a high confidence to be consistent with the above rule, than it
is for mammograms classified with a lower confidence. Hence, the distance dij should be weighted by the confidences ci and cj.The average distance over a set of mammograms can now
be calculated. The average within-class distance,Dw, would be calculated over the set of mammograms which received the same
classification (i.e., χi=χj), whereas the average between-class distance, Db, would be calculated over the set of mammograms which received different
classifications (i.e., χi≠χj). These average distances are calculated as follows:
(1)Dw=∑χi=χjcicjdij∑χi=χjcicj,(2)Db=∑χi≠χjcicjdij∑χi≠χjcicj.


## 4.4.2. Patient-Wise Mammogram Comparison

A patient should receive the same classification for their left and right CC mammograms,
and this notion was confirmed by casual subjective observation. This notion can
be tested by analyzing the distances between pairs of mammograms in feature
space. Figure10 shows the distances between mammogram-pairs in the reduced
feature space of 53 feature types. Comparison between the left and right mammograms
for the same patient produced the lower line, where each point corresponded to
a single patient and the points were ranked according to increasing distance.Figure 10
Comparing the distances between mammograms using 53 features: (a)same, the left and right views within
patients, (b) diff D1, the right views between patients, and (c) diff
S1, the left views between patients.Each “diff D1” point was produced by comparing the
right views between two different patients, and this comparison was repeated
for all combinations of patient-pairs. Similarly, the “diff S1” points were
produced by comparing pairs of left views of different patients. The points
were again ranked according to increasing distance. There was no significance
in comparing the left or right views individually and so the corresponding
points overlap to appear as the upper line in Figure10.The figure shows that within-patient distances were
typically less than between-patient distances. Approximately 70% of the
within-patient comparisons gave distances less than 1, and all these
comparisons gave distances less than 2. Conversely, only 5% and 50% of the
between-patient comparisons gave distances less than 1 and 2 respectively.The results in this section justify the use of
patient-wise performance measures for the mammogram classifiers. However,
because the two mammograms for a particular patient can differ significantly,
patient-wise performance measures should be used only as secondary measures.
For example, patient-wise performance measures could be used to compare
classifiers which are indistinguishable when using the measures based on
distances in mammogram feature space. Note that patient-wise performance
measures did not actively drive SONNET's development, but instead the measures were
used to assess classification performance after development.


## 4.5. Discovering Optimum Classifications

Section3 stated that multiple SONNET runs were
conducted for 100 epochs. Any of these epochs could represent the optimum
SONNET state, where many stable classifiers separate the mammogram set into
clearly distinguishable classes. Every epoch was assessed according to various
performance measures and this posed a multiobjective optimization problem. The
number of candidate optimum SONNET epochs was reduced by discovering the Pareto front across the performance
measures. Consequently, none of these candidate epochs could be dominated by
another epoch on every performance measure. The Pareto front was discovered across the following
dimensions:(i)
average within-class distanceDw (1),(ii)
average between-class distanceDb (2),(iii)
the number of classes encoded,(iv)
the classification confidences,(v)
the fraction of patients which received the same
classification for their two mammograms.Dw was minimized whereas all of the other
performance measures were maximized.


## 5. Mammogram Classification Performance

This section discusses the performance of SONNET in
establishing a mammogram taxonomy. The optimum classifications from multiple
SONNET runs were judged using the performance measures described in Section4.5.


### 5.1. Number of Mammogram Classes

Casual observation of the mammogram set can roughly
indicate the number of taxonomic classes involved but it is difficult to
precisely specify the number of required classes. However, the current study
focused on developing a maximal number of classes to discover the typical
subtleties which discriminate mammogram classes. Various SONNET parameters
control the number of classes encoded. These parameters were varied to analyze
the number of classes which most commonly formed, and this number was deemed to
correspond to the most natural taxonomic decomposition of the mammograms.Figure11 displays the number of classes formed on the
best SONNET epochs. These epochs relate to many different SONNET runs but a
single run could also produce multiple best epochs. The epochs were ranked
according to the number of classes formed and the number of these which were stable. The resulting rank numbers are
used to identify the best epochs in the subsequent discussion.Figure 11
The number of classes formed on the best SONNET epochs.nClass is the total number of classes
formed and nStable is the number
of stable classes. The epochs are ranked according to descending nClass and then descending nStable.Classes became stable in SONNET after their encoding
had been refined by sufficient past experience. Unstable classes were always
present however, to enable SONNET to adapt to changes in the input patterns.
Therefore, the proportion of SONNET's classes which were stable represents the
maturity of the overall network and the quality of the encodings. Hence, the
best results in Figure11 are those with the maximum number of stable classes.Figure11 shows that it was difficult for more than 40
stable classes to form. SONNET parameters were investigated to produce more
classes but this resulted in SONNET memorizing individual mammograms instead of
clustering them with other mammograms. SONNET commonly produced between 20 and
30 classes suggesting that this represents the most natural taxonomic
breakdown. SONNET parameters could be set to form fewer, broader classes but
these classifications obscure the subtleties which discriminate mammogram
classes.


### 5.2. Class Tightness

Figure12 shows the average distance in input feature
space for mammograms classified differently (between-class, Db given by (2)) and for mammograms classified
the same (within-class, Dw given by (1)). These distances were plotted
for each of the best SONNET epochs which were ranked in Figure 11.Figure 12
Average distance in input feature space for between-class mammograms and within-class
mammograms for the best SONNET epochs. The ratio of between-class distance over
within-class distance is also shown. The epoch ranking corresponds to Figure11.The SONNET epochs with low-rank numbers produced many narrow classes and thus yielded(i)
a low average within-class distance because
mammograms had to be highly proximate in feature space to be clustered
together,(ii)
a low average between-class distance because
the class tightness allowed similar mammograms to be classified differently. Conversely, SONNET epochs with high-rank numbers formed fewer, broader classes, and thus
yielded higher within-class and between-class distances.Reference distances were calculated to create a
context within which to consider the between-class and within-class distances.
The average distance between all the mammograms,Dav,
was 2.00 and the maximum distance, Dmax, was 4.66. (These reference distances can be seen in Figure 10.) Figure 12 shows
that the between-class distances for low-rank numbers approximately equalled Dav and that the maximum between-class distance
was approximately half Dmax.A further reference distance can be calculated by
considering a classification where each patient is distinct, such that their
two mammograms are classified the same with a confidence of 1. This would yieldDw=0.90 and Db≈Dav. Figure 12 shows that the within-class distances for low-rank numbers were
slightly greater than 0.9, which was expected as each class clustered
approximately 10 mammograms together.The best classifications minimized the within-class
distance yet maximized the between-class distance, therefore the ratio of
between-class distance over within-class distance should be maximized. Figure12 includes this ratio for each ranked epoch, and shows that the best epochs
produced a ratio of almost 2 by developing relatively tight classes (Dw≈1), whilst retaining typical between-class
distances (Db≈Dav).


### 5.3. Patient-Wise Performance Measures

Section4.4.2 justified the use of patient-wise
performance measures to quantify the extent to which the two mammograms for
each patient received the same classification. This patient-wise performance
measure was used as a secondary measure to discriminate classifiers which were
similar when judged using other performance measures.Figure13 displays the fraction of patients whose
mammograms were classified the same for the best SONNET epochs. This fraction
was approximately 40% for the epochs with narrow classes (low-rank numbers), as
these encodings captured the subtleties which differentiate the mammograms for
a single patient. Conversely, the epochs with broad classes (high-rank numbers)
classified approximately 75% of the patients as being the same for their two
mammograms.Figure 13
The fraction of
patients whose two mammograms received the same classification for the best
SONNET epochs. The epoch ranking corresponds to Figure11.


### 5.4. Mammogram Taxonomy

The best result was deemed to be the SONNET epoch with
rank number 6 in the previous discussion. This result produced 39 stable
classes, where the first was formed on the 2nd epoch of the run and the last
was formed on the 84th epoch.This result produced relatively narrow classes with an
average within-class distance of 1.01 whilst retaining a typical average
between-class distance of 2.00. Consequently, this result yielded a relatively
high ratio in Figure12 of 1.98. Approximately 37% of the patients had their
two mammograms classified the same.The chief features that discriminated class encodings
were two textural features, namely angular second moment and contrast. Figures14 to 19 are examples of the mammogram classes that were encoded by SONNET.Figure 14
Example of a taxonomic class.Figure 15
Example of a taxonomic class.Figure 16
Example of a taxonomic class.Figure 17
Example of a taxonomic class.Figure 18
Example of a taxonomic class.Figure 19
Example of a taxonomic class.


## 5.1. Number of Mammogram Classes

Casual observation of the mammogram set can roughly
indicate the number of taxonomic classes involved but it is difficult to
precisely specify the number of required classes. However, the current study
focused on developing a maximal number of classes to discover the typical
subtleties which discriminate mammogram classes. Various SONNET parameters
control the number of classes encoded. These parameters were varied to analyze
the number of classes which most commonly formed, and this number was deemed to
correspond to the most natural taxonomic decomposition of the mammograms.Figure11 displays the number of classes formed on the
best SONNET epochs. These epochs relate to many different SONNET runs but a
single run could also produce multiple best epochs. The epochs were ranked
according to the number of classes formed and the number of these which were stable. The resulting rank numbers are
used to identify the best epochs in the subsequent discussion.Figure 11
The number of classes formed on the best SONNET epochs.nClass is the total number of classes
formed and nStable is the number
of stable classes. The epochs are ranked according to descending nClass and then descending nStable.Classes became stable in SONNET after their encoding
had been refined by sufficient past experience. Unstable classes were always
present however, to enable SONNET to adapt to changes in the input patterns.
Therefore, the proportion of SONNET's classes which were stable represents the
maturity of the overall network and the quality of the encodings. Hence, the
best results in Figure11 are those with the maximum number of stable classes.Figure11 shows that it was difficult for more than 40
stable classes to form. SONNET parameters were investigated to produce more
classes but this resulted in SONNET memorizing individual mammograms instead of
clustering them with other mammograms. SONNET commonly produced between 20 and
30 classes suggesting that this represents the most natural taxonomic
breakdown. SONNET parameters could be set to form fewer, broader classes but
these classifications obscure the subtleties which discriminate mammogram
classes.


## 5.2. Class Tightness

Figure12 shows the average distance in input feature
space for mammograms classified differently (between-class, Db given by (2)) and for mammograms classified
the same (within-class, Dw given by (1)). These distances were plotted
for each of the best SONNET epochs which were ranked in Figure 11.Figure 12
Average distance in input feature space for between-class mammograms and within-class
mammograms for the best SONNET epochs. The ratio of between-class distance over
within-class distance is also shown. The epoch ranking corresponds to Figure11.The SONNET epochs with low-rank numbers produced many narrow classes and thus yielded(i)
a low average within-class distance because
mammograms had to be highly proximate in feature space to be clustered
together,(ii)
a low average between-class distance because
the class tightness allowed similar mammograms to be classified differently. Conversely, SONNET epochs with high-rank numbers formed fewer, broader classes, and thus
yielded higher within-class and between-class distances.Reference distances were calculated to create a
context within which to consider the between-class and within-class distances.
The average distance between all the mammograms,Dav,
was 2.00 and the maximum distance, Dmax, was 4.66. (These reference distances can be seen in Figure 10.) Figure 12 shows
that the between-class distances for low-rank numbers approximately equalled Dav and that the maximum between-class distance
was approximately half Dmax.A further reference distance can be calculated by
considering a classification where each patient is distinct, such that their
two mammograms are classified the same with a confidence of 1. This would yieldDw=0.90 and Db≈Dav. Figure 12 shows that the within-class distances for low-rank numbers were
slightly greater than 0.9, which was expected as each class clustered
approximately 10 mammograms together.The best classifications minimized the within-class
distance yet maximized the between-class distance, therefore the ratio of
between-class distance over within-class distance should be maximized. Figure12 includes this ratio for each ranked epoch, and shows that the best epochs
produced a ratio of almost 2 by developing relatively tight classes (Dw≈1), whilst retaining typical between-class
distances (Db≈Dav).


## 5.3. Patient-Wise Performance Measures

Section4.4.2 justified the use of patient-wise
performance measures to quantify the extent to which the two mammograms for
each patient received the same classification. This patient-wise performance
measure was used as a secondary measure to discriminate classifiers which were
similar when judged using other performance measures.Figure13 displays the fraction of patients whose
mammograms were classified the same for the best SONNET epochs. This fraction
was approximately 40% for the epochs with narrow classes (low-rank numbers), as
these encodings captured the subtleties which differentiate the mammograms for
a single patient. Conversely, the epochs with broad classes (high-rank numbers)
classified approximately 75% of the patients as being the same for their two
mammograms.Figure 13
The fraction of
patients whose two mammograms received the same classification for the best
SONNET epochs. The epoch ranking corresponds to Figure11.


## 5.4. Mammogram Taxonomy

The best result was deemed to be the SONNET epoch with
rank number 6 in the previous discussion. This result produced 39 stable
classes, where the first was formed on the 2nd epoch of the run and the last
was formed on the 84th epoch.This result produced relatively narrow classes with an
average within-class distance of 1.01 whilst retaining a typical average
between-class distance of 2.00. Consequently, this result yielded a relatively
high ratio in Figure12 of 1.98. Approximately 37% of the patients had their
two mammograms classified the same.The chief features that discriminated class encodings
were two textural features, namely angular second moment and contrast. Figures14 to 19 are examples of the mammogram classes that were encoded by SONNET.Figure 14
Example of a taxonomic class.Figure 15
Example of a taxonomic class.Figure 16
Example of a taxonomic class.Figure 17
Example of a taxonomic class.Figure 18
Example of a taxonomic class.Figure 19
Example of a taxonomic class.


## 6. Refining the Mammogram Taxonomy

### 6.1. Input Feature Selection

The main weakness with the current classification
scheme is considered to be the manual specification of the image features which
were extracted from the mammograms. The feature types and the regions from
which they were extracted were designed to capture a priori knowledge about mammography, for
instance, the importance of the retroareolar region. However, this manual
specification necessarily requires arbitrary decisions, for instance, the
quantitative position of the retroareolar region.The image features and their corresponding region
boundaries could beautomatically
evolved to produce an optimal input feature space. Two aspects of this
are(i)
capturinga priori mammographic knowledge, for
example, characteristic positions of lobular units, and(ii)
producing a high-quality feature space, for
example, a minimal set of features with maximal orthogonality.Other mammogram views could be used to extract input
features in addition to the craniocaudal projection, for example, the
mediolateral oblique view could be used.


### 6.2. Using Control Mammograms

Control mammograms could be exploited to refine the mammogram taxonomy. Control
mammograms should be selected to represent clearly distinguishable mammogram
classes. The classification scheme should initially be developed on these cases
alone to shape classifier encodings. More ambiguous mammograms could then be
introduced for subsequent classifier development. In order to achieve this, the
classification scheme must be capable ofincrehymental learning and it must also
address the so-called stability-plasticity dilemma [2]. SONNET satisfies these
requirements.


### 6.3. Alternative Classification Schemes

A supervised classification scheme could be used to
allow performance measures to actively drive classifier development in a manner
consistent with the passive discovery of optimal SONNET classifications, as
outlined in Section4.5.Anevolutionary computing (EC) technique
could form an alternative classification scheme. EC is a flexible and adaptable
technique and consequently it could combine a number of the processing stages
detailed in the above protocol for producing a mammogram taxonomy. For example,
EC could optimize its own subset of input feature types by processing raw image
features directly.


## 6.1. Input Feature Selection

The main weakness with the current classification
scheme is considered to be the manual specification of the image features which
were extracted from the mammograms. The feature types and the regions from
which they were extracted were designed to capture a priori knowledge about mammography, for
instance, the importance of the retroareolar region. However, this manual
specification necessarily requires arbitrary decisions, for instance, the
quantitative position of the retroareolar region.The image features and their corresponding region
boundaries could beautomatically
evolved to produce an optimal input feature space. Two aspects of this
are(i)
capturinga priori mammographic knowledge, for
example, characteristic positions of lobular units, and(ii)
producing a high-quality feature space, for
example, a minimal set of features with maximal orthogonality.Other mammogram views could be used to extract input
features in addition to the craniocaudal projection, for example, the
mediolateral oblique view could be used.


## 6.2. Using Control Mammograms

Control mammograms could be exploited to refine the mammogram taxonomy. Control
mammograms should be selected to represent clearly distinguishable mammogram
classes. The classification scheme should initially be developed on these cases
alone to shape classifier encodings. More ambiguous mammograms could then be
introduced for subsequent classifier development. In order to achieve this, the
classification scheme must be capable ofincrehymental learning and it must also
address the so-called stability-plasticity dilemma [2]. SONNET satisfies these
requirements.


## 6.3. Alternative Classification Schemes

A supervised classification scheme could be used to
allow performance measures to actively drive classifier development in a manner
consistent with the passive discovery of optimal SONNET classifications, as
outlined in Section4.5.Anevolutionary computing (EC) technique
could form an alternative classification scheme. EC is a flexible and adaptable
technique and consequently it could combine a number of the processing stages
detailed in the above protocol for producing a mammogram taxonomy. For example,
EC could optimize its own subset of input feature types by processing raw image
features directly.


## 7. Conclusions

This study has developed a mammogram taxonomy by using
an unsupervised classification scheme called SONNET. The encoded mammogram
classes captured typical subtleties which discriminate mammograms. SONNET's
controlling parameters were varied to govern the coarseness of the taxonomies.
The developed classification scheme is considered to be a successful prototype
but the scheme's efficacy is yet to be established.The study shows promise for researching automated
computational tools to assist with the detection of mammographic abnormalities.
A mammogram taxonomy can be exploited to aid the detection of cancerous lesions
via asymmetry identification [14], that is, by identifying anomalies between a
patient's left and right mammograms. The evidence for cancerous lesions within
the complex breast tissue can be very subtle, so mammogram features must
capture localized information in a contextual manner, that is, multiscale features are required.The authors have developed an evolutionary computation
approach to discover multiscale features in imagery for a target detection
application [15, 16].
This scheme used a data crawler which was evolved to gather evidence to discriminate target objects from
nontarget objects. The crawler focused on low-level features in its immediate
vicinity and processed these in the context of higher-level features collected
over the crawler's trail.As the data crawler has been developed for target
detection in imagery, it is highly transferable to the problem of lesion
detection in mammograms. The crawler could scrutinize mammogram areas which
possess the greatest asymmetry and thus focus on candidate lesions. The
evolutionary approach allows the crawler to discover its own multiscale
features which best locate lesions.The search for multiscale features over a diverse set
of mammograms represents a very challenging problem, due to the high
dimensionality of the potential search space. Hence, it is desirable to
segregate the problem into multiple subproblems with less diversity. This can
be achieved by exploiting the mammogram taxonomy as a preprocessing stage. This
stage would classify a patient's mammograms, and thus would allow a data
crawler to be evolved to specialize in only these taxonomic classes. Multiple
crawlers could then be evolved, each of which specializes on its own subset of
classes. Hence, the taxonomy would greatly constrain the search space in order
to optimize asymmetry identification, and consequently, lesion detection.



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*Source: 526343-2008-07-22.xml*