Logo Design Analysis by Ranking
Takuro Karamatsu∗ , Daiki Suehiro∗† , and Seiichi Uchida∗∗ Kyushu University † RIKEN

Keywords-Logo design; Graphic design analysis; Top-ranklearning; TopPush algorithm; Machine learning

negative

most
positive?

positive(logo samples fromthe target industry)(a)true positive rate

ROC by TopPush
absolute
top (ATP)
most

I. I NTRODUCTION
Our daily life is surrounded by many graphic designs.
Typical graphic designs are poster and advertisement, signboard, logo and icon, book cover, the label of goods,
web page, and so on. Graphic designs often give us somespecial impression that affects our reaction to them, suchas decision, behavior, and feeling. For example, we often
make our decision on buying a commercial product justby watching its label design. In other words, professional
designers always try to give a certain impression to thecustomers through their graphic design.
The relationship between graphic design and its impression is still an interesting open problem. Of course, there
are many graphic design textbooks and they show various
examples and use-cases. However, most textbooks just give
subjective and intuitive explanations to the examples andthus give neither objective nor quantified facts revealed
through scientific analysis with enough amount of data.
Graphic design analysis is not only meaningful as ascientific exploration of the relationship between graphic
designs and their impression but also useful for various
application. Clearly, the results will help the process ofcreating various graphic designs. In addition, the relationshipbetween graphic designs and their use-cases will be usefulfor image understanding. An example is Jolly et al. [1] wherebook cover designs are utilized to understand book genres.
An example in more general image understanding research isMovshovitz et al. [2], where that visual design of storefront
is used for recognizing the store class.
In this paper, we analyze logo designs objectively andautomatically by using machine learning, as a promising
trial of graphic design analysis. Especially, we will focus
on favicon images, instead of dealing with arbitrary logo
images. Each favicon image is a tiny square logo and used as

standard SVM(b) (for classification)

positive
TopPush(for top-rank learning)

absolute top

Abstract—In this paper, we analyze logo designs by using
machine learning, as a promising trial of graphic design
analysis. Specifically, we will focus on favicon images, which
are tiny logos used as company icons on web browsers, andanalyze them to understand their trends in individual industry
classes. For example, if we can catch the subtle trends infavicons of financial companies, they will suggest to us how
professional designers express the atmosphere of financial
companies graphically. For the purpose, we will use top-ranklearning, which is one of the recent machine learning methods
for ranking and very suitable for revealing the subtle trends
in graphic designs.

ROC by standard SVM
false positive rate(c)(d)
Figure 1.
Overview of top-rank learning for logo (favicon) analysis.
(a) Logo sample distribution. Samples from the target industry are shownby orange dots. (b) Standard SVM for classification. Its result is not suitableto rank the samples. (c) Top-rank learning by the TopPush algorithm. It cangive “absolute top” samples that contain the most positive sample and other“very positive” samples. (d) Relationship to ROC. Absolute top samples by
top-rank learning form the vertical-rise of ROC.

a company icon on web browsers. This property of favicons
is useful to limit the variation of logo images since thedefinition of logo is wide [3] and thus their variation is toolarge to analyze.
Our main purpose of analyzing favicon designs is to catchtheir trends in individual industry classes, such as financeand transportation. For example, we want to analyze whatkind of favicons are distinctive to financial companies andhow their trend is different from the other industries. If we
can find any trend specific to finance, it will reveal how
professional designers express the impression of financial
companies through their favicon design.
Since we anticipate that difference of the favicon design
trends among industries is very subtle, we will employ amachine-learning strategy to pick up the most distinctive
favicon samples for each industry. More specifically, we
will use TopPush algorithm [4], which is a top-rank learningalgorithm that can give a ranking (i.e., an order) of samples
according to their distinctiveness.
Fig. 1 illustrates our favicon analysis formulated as a
top-rank learning problem. Fig. 1 (a) is an example of the
distribution of favicon image samples; they are comprisedof positive samples from the target industry and negative
samples from the others. One naive strategy to find themost distinctive samples (i.e., the most positive samples)is to use the classification boundary between positive andnegative sample sets by, for example, a standard SVM. The
furthest positive samples from the boundary are expected tobe the most distinctive samples for the target class. However,as shown in Fig. 1 (b), this strategy fails to find the mostpositive samples; this is simply because the standard SVM
is designed not for finding them but for higher classification
accuracy of all samples.
In contrast, as shown in Fig. 1 (c), top-rank learning by
TopPush provides a function to rank the samples so that themost positive samples achieve the top ranks and the negative
samples result in lower ranks. As an advantage of TopPush
over other top-rank learning algorithms, it is theoreticallyguaranteed that TopPush maximizes the number of absolute
top positives, which are positive samples distinguished fromall negative samples in their ranking. Consequently, TopPush
will be powerful for our favicon analysis task, by finding themost distinctive positive samples as absolute top positives,
even when the difference between positive and negative
samples is very subtle.
The main contributions of this paper are summarized asfollows.
• To the authors’ best knowledge, this is the first trial of
the objective and automatic analysis of the trends ofgraphic design in individual industry classes.
• We formulate the problem of selecting the most distinctive favicon images to each industry class as a
top-rank learning problem and applied the TopPush
algorithm to the favicon images as a solution to the
problem. Fortunately, we could catch their trends incolor and shape successfully, even though there arehuge variations in the favicon designs and thus theirtrends are too subtle and unclear.
II. R ELATED W ORK
A. Logo analysis
In [3], logo is defined as “a symbol, a graphic and visualsign which plays an important role into the communication
structure of a company” and has three types: “Iconic orsymbolic logo”, “text-based logo”, and “mixed logo.” Thesame paper also defines seven conditions (such as legibility)
and seven functions. Several functions are related to theimpression of the logo; for example, its signification function
will appeal some emotion to the observer and its aesthetics
function will inspire pleasure.
The recent progress of neural network technologies enables us to generate graphic designs. For example, automatic
font generation is a hot topic [5]–[8]. However, to theauthors’ best knowledge, automatic logo generation has notbeen tried except for Sage et al. [9]. They use generative
adversarial networks (GAN) and a public logo dataset called
Large Logo Dataset (LLD), for generating logo images andfavicon images. LLD contains more than 600 thousand logos
and thus larger than WebLogo-2M [10] which contains 194
different logos shown in 1,867,177 images.

Research for correlating graphic designs and their impressions has been analyzed for 100 years and always reliedon subjective and small-scale experiments. For example,
an old study [11] has made a subjective experiment tounderstand the impression of typefaces (i.e., fonts). Even
recent trials still rely on subjective impressions. For example,
Fontmatcher [12] for correlating typefaces and images uses
a font dataset with subjective impression [13]. In this paper,
we, therefore, try to reveal the correlation objectively andautomatically.
B. Learning-to-rank
Learning-to-rank is an important machine learning task,
especially in the field of information retrieval [14], [15]. The
bipartite ranking problem is a basic problem in learningto-rank, which assumes binary-labeled (i.e., positive andnegative) training data [15], [16]. Many algorithms to solve
the bipartite ranking problem have been proposed, and theapplied to the ranking tasks for various domains such asrecommendation, search engines, and financial risk analysis [15]–[18], in addition to classification tasks for maximizing AUC such as [19], [20].
Top-rank learning we apply in this paper has been theoretically and practically developed in the last decade or so [4],[21], [22]. TopPush [4] is one of the novel learning algorithms for top-rank learning, which maximizes the numberof absolute top positives rather than standard classification
algorithm, as shown in Fig. 1 (d).
Our key idea is that we can discover the distinctive
samples for an industry class from a large number of favicon
image data by only observing samples that are highly ranked
by TopPush. Although the design trends of the favicons
in the class is very subtle, we can still catch the trends
by observing highly-ranked images because these images(including absolute top positives) are very distinctive to theclass. To the best of our knowledge, top-rank learning, as
well as learning-to-rank, has not been applied to graphic
design analysis so far.
III. T OP - RANK LEARNING
We employ a learning-to-rank approach to discover distinctive samples and some trends for each industry class. In
this section, we first introduce the bipartite ranking problem
and then its extension, i.e., the top-rank learning problem.
TopPush, an algorithm to solve the top-rank learning problem, is also explained briefly. Note that we assume linear
classifiers throughout this paper for making the analysis
results more understandable.
A. Bipartite ranking problem
The bipartite ranking problem is one of the basic problems
in the learning-to-rank task. We briefly described the standard setting of the bipartite ranking problem as below: We
assume a training sample set that consists of p positive data

−
+
−
x+
1 , . . . , xp and n negative data x1 , . . . , xn . The goal of
the bipartite ranking problem is to find a ranking function fthat gives positive data higher values than negative data. Thatis, we want to find f that maximizes the number of pairs
−
+
−
(x+
i , xj ) which satisfies f (xi ) > f (xj ). Consequently,
the optimization of f is the maximization of AUC because
AUC is given as follows:

AUC =

p X
n
−
X
I(f (x+i ) > f (xj ))i=1 j=1pn,

where I denotes the indicator function. Since AUC is a wellknown performance measure for tasks with imbalanced data,
the ranking function f is robust to those tasks.
Among many algorithms for solving the problem,
RankSVM (or Ranking SVM) [15] is well-known and has
been applied to many imbalanced-classification tasks. The
key idea of RankSVM is to reformulate the AUC maximization to the minimization problem of the following loss:
LRankSVM =

p X
n
X

+
ℓ(f (x−j ) − f (xi )),(1)

i=1 j=1

where ℓ is the hinge-loss for given samples.
It should be emphasized that the above AUC maximization evaluates the overall ranking accuracy from the bottom
to top. In our graphic design analysis, we need to focus
only on top-ranked samples; this is because only top-ranked
samples will show the subtle trends and low-ranked samples
will not. Therefore, we do not need to push such low-ranked
samples to upper ranks.
B. Top-rank learning
The top-rank learning problem is an extension of the
bipartite ranking problem. Given binary labeled training
samples, its goal is to find a top-ranking function that maximizes the ranking accuracy at the top [21]. Specifically, wewant to maximize the rate of absolute top positives (hereafter
called ATP, shown in Fig. 1(c)) in whole positives [23]. ATP
is formulated as follows:


p
1X
+
−
I f (xi ) − max f (xj ) > 0 .
(2)
ATP =
j=1,...,np i=1
ATP evaluates the number of positive data which is ranked
higher than the highest negative data.
TopPush [4] is an efficient algorithm for maximizing ATP
for a linear ranking function (i.e., f (x) = w · x). TopPush
attempts to minimize the following loss which is a relaxedversion of ATP:


p
1X
+
LTopPush =, (3)ℓ max w · x−
−
w
·
x
j
i
p i=1 j=1,...,nwhere ℓ is a convex and non-decreasing loss function and weused the truncated quadratic loss ℓ(z) = [1 + z]2+ . Finally,
the optimization problem of TopPush is formulated as theminimization problem of (3) with a regularization term forw, namely:


p
λ
1X
−
+
2
min kwk +ℓmax w · xj − w · xi ,w 2
j=1,...,np i=1
where λ is a regularization parameter. If λ becomes smaller,
positive samples are more pushed to be top-ranked; if λ is set
at a very small positive value, it may give a result strongly
overfitted to the training samples.
IV. E XPERIMENTS
In order to understand the correlation between favicon
images and individual industry classes, an experiment was
conducted with 3,100 favicon images and TopPush.
A. Data collection
For the experiment, we collected 3,100 favicon images
using web scraping technique since Large Log Dataset(LLD) [9] does not have industry class information. Specifically, we searched for the official website of each company
on the list by NASDAQ1 . After finding the official website,
we extract its favicon image analyzing HTML of the website.
Some group companies share the same favicons and we do
not unify them. Each favicon image is resized to 32 × 32
pixels2 .
As industry classes, we follow the definition in the NASDAQ list. In the list, all companies are classified into 12
industry classes, such as “Basic Industry” and “Transportation,” as shown in Fig. 2. In other words, each of 3,100
favicons is classified into one of 12 classes.
B. The detailed procedure for ranking favicons by TopPush
In order to rank the favicon images of a certain industry
class, we use the implementation3 of TopPush. TopPush
is applied to all 3,100 favicons by considering a certain
target industry class as the positive class and the other 11classes as the (big) negative class. Then we can expect thatfavicon images with the most distinctive designs to the target
class will be ranked at the top. We perform this one-vsothers ranking task for each of 12 industry classes. Although
this one-vs-others task is an imbalance problem, top-ranklearning is theoretically robust for imbalanced tasks and we
do not need to give any weight to the positive samples.
In order to understand our analysis result easily,
we use the bitmap feature to represent each favicon
image. Since each favicon is a 32 × 32 RGB image,its feature becomes a 3,072-dimensional vector. We
also conducted other experiments using different feature
vectors, such as an RGB histogram and a Histogramof-gradient (HOG) feature. Those results are given athttps://github.com/karamatsutakuro/logo_
TopPush_supplementary.
1 https://www.nasdaq.com/
2 The dataset will be published upon the paper acceptance.
3 http://lamda.nju.edu.cn/files/TopPush.zipIndustry
Basic
Industries(215)

Industry example

Favicon example

・Agricultural Chemicals
・Major Chemicals
・Precious Metals
・Steel/Iron Ore

・Auto Manufacturing
Capital Goods ・Electrical Products
・Industrial Machinery/Components(231)
・Metal Fabrications
Consumer
Durables(92)

・Automotive Aftermarket
・Home Furnishings
・Specialty Chemicals
・Telecommunications Equipment

・ApparelConsumer・Beverages (Production/Distribution)
Non-Durables
・Electronic Components(136)
・Packaged Foods

Figure 2.

Industry

Industry example

Finance(521)

・Business Services
・Investment Bankers/Brokers/Service
・Major Banks
・Savings Institutions

Health Care
(532)

Favicon example

・Hospital/Nursing Management
・Industrial Specialties
・Major Pharmaceuticals
・Medical/Dental Instruments

・Business Services
Miscellaneous ・Industrial Machinery/Components
・Multi-Sector Companies(95)
・Publishing・Electric Utilities: Central
Public Utilities ・Natural Gas Distribution
・Power Generation(131)
・Telecommunications Equipment
・Computer Software:
Prepackaged Software
・Diversified Commercial Services
・EDP Services
・Semiconductors

Consumer
Services(467)

・Broadcasting・Hotels/Resorts
・Real Estate Investment Trusts
・Restaurants

Technology(427)

Energy(179)

・Industrial Machinery/Components
・Integrated oil Companies
・Natural Gas Distribution
・Oil & Gas Production

・Air Freight/Delivery Services
Transportation ・Marine Transportation
・Oil Refining/Marketing(74)
・Trucking Freight/Courier Services

Twelve industry classes defined by NASDAQ. The parenthesized number represents the number of favicon images of each industry class.

C. Qualitative evaluation
Fig. 3 shows six ranking results. In each result, all
3,100 favicon images are ranked in the order from topleft to bottom-right. The ranking orders are different inthose results because of the difference in the target industry
class and the parameter value of λ. Among 12 classes,
we picked up three classes, “Energy”, “Technology” and“Transportation” in Fig. 3 because the top-ranked samples
have smaller variances than the other classes. In other words,
each of these three classes has more similar top-ranked
samples. The parameter λ is set at 0.1 or 10. In the figure,top-10 images of the target class are also shown along with
their average image. Fig. 4 shows the top-10 ranked favicons
and their average for all 12 classes (at λ = 10).
In Fig. 3, a pair of images w+ and w− are also shown tovisualize the learned w = w+ − w− . In w+ , brighter pixels
correspond to larger positive-valued elements of w. Black
pixels correspond to negative-valued elements. Similarly, in
w− , brighter pixels correspond to larger negative-valued
elements. If a favicon image x has an RGB value similar
to w+ (i.e., if x · w+ is large), the favicon will be ranked
higher. If x · w− is large, it will be ranked lower.
From those figures, the following facts can be observed:• The favicons of the target class are ranked around the
top as expected since the black boxes indicating therank distribution of the target favicons gather aroundthe top. Especially when λ = 0.1, most favicons belong
to ATP. (This implies the rank result is overfitted to thesamples with λ = 0.1.)+• Since w
and w− become a random dot-like patternand does not show any structure, there is no common
structure or part in the favicon images in any class. Thissuggests that favicon images have huge variations evenif we consider only a single industry class.
• In spite of the huge variations, TopPush still could catch
subtle color trends in their design, as shown by theaverage of top-10 images. Specifically, the top-ranked“Energy” favicons have more yellow and blue pixels
whereas “Technology” favicons have more orange andgreen and “Transportation” have more blue and red.
• A similar observation of the average images suggeststhat TopPush also catches a subtle shape trend for eachclass. As shown in Fig. 4, several classes have an average image capturing a roundish structure. For example,“Transportation”, “Consumer Services” and “HealthCare” have such a roundish structure. In contrast, theaverage images of “Finance”, “Public Utilities”, and“Technology” are much less roundish.
About the last two facts, it should be emphasized again thatthey are not just an average image. They are an average image of top-ranked favicons, which are the distinctive favicons
to the class. (There are many favicons which show different
designs from the average images but they are ranked lower.)
TopPush could catch the subtle trends specific to the classand make the favicons showing the trends distinctively to be
ranked higher.
D. Quantitative evaluation by comparing TopPush to thestandard SVM
Finally, as a quantitative evaluation of TopPush for our
favicon image ranking task, we compare TopPush to thestandard SVM. Although TopPush is robust to class imbalanced tasks, the standard SVM is not. We, therefore, use a
simple remedy by Akibani et al. [24] to deal with the classtop-10 favicons from the target class and their averagerank #1

�

+

�

−

rank #40

λ = 0.1

rank #1 is black =rank #1 is a favicon of
the target industry

all 3,100 favicons
ranked by TopPush
for the target industry class(from top-left to bottom-right)

rank distribution of favicons of thetarget industry class

λ = 10rank #3,100

EnergyTechnology

Transportation

Figure 3. Ranking results of three industry classes, “Energy”, “Technology” and “Transportation.” Those results are given by TopPush under two parametervalues λ = 0.1 and 10. For each result, top-10 favicon images from the target industry class, their average image, a bitmap representation of w+ and
w− , the rank of all 3,100 favicons from top-left to bottom-right, and the rank distribution of the favicons of the target industry class (indicated as blackboxes).

imbalance. With the remedy, the standard SVM formulated
as the following optimization problem:pn
X
1nC X +2minξj− ,ξi + Ckwk +p i=1
w,b,ξ+ ,ξ− 2
j=1

SVM. Note that several ROC curves of the standard SVM
show a short horizontal shift in their leftmost side. Thismeans that the very top-ranked samples come from nontarget classes like Fig. 1 (b). In contrast, the ROC curves of
TopPush do not have such a part.

++sub.to (w · x+
i + b ≥ 1 − ξi ) ∧ (ξi ≥ 0) for i = 1, . . . , p,

V. CONCLUSION−−(−(w · x−
j + b) ≥ 1 − ξj ) ∧ (ξj ≥ 0) for j = 1, . . . , n,where p and n are the number of positive and negative
samples and p ≪ n. Finally, we rank the samples {x}by the inner-product value between x and the classification
hypeArplane w for different values of C.
Figs. 5 (a) and (b) show the ROC curves by TopPush
and the standard SVM, respectively, for the class “Basic
Industries.” (We omit the plots for other classes because theyalso show similar ROC curves as those figures.) From theleftmost side of the ROC curves in (a), we can understandthat TopPush could find absolute top. We can see that the
ATP of TopPush is significantly larger than the standard

In this paper, we analyzed 3,100 favicon images to understand the trends in their design at individual industry classes
objectively and automatically. For the analysis, we used TopPush, which is an algorithm for a top-rank learning problem.
The analysis result shows that TopPush could catch very
suitable trends in favicon designs in spite of huge graphicalvariations in them. We also confirmed quantitatively that
TopPush shows better performance than the standard SVM
in the ranking task.
Future work will focus on further trend analysis in somedifferent feature space, which will show the trends more distinctively. Instead of the bitmap feature, color histogram andBasicIndustries

7525

Capital
Goods

7610

Consumer
Durables

8347

Consumer
Non-Dur.

7873

Consumer
Services

8020

Energy6683

Finance7525

HealthCare

7690

Miscellaneous

6195

PublicUtilities

6726

Technology

5616

Transportation

6297

Figure 4. Top-10 favicon images and their average image (at λ = 10).
The last value is the variance of pixel values of those 10 images.
1.0

1.0

0.8

0.8

C
1e-04

0.001
0.005

0.6
lambda
0.001
0.01
0.1
1
10
100
1000

0.4
0.2
0.0
0.0

0.2

0.4
0.6
False Positive Rate

0.8

1.0

True Positive Rate

True Positive Rate

5e-04

0.01
0.05

0.6

0.1
0.5
1

0.4

5
10
50
100

0.2

500
1000
5000

0.0

10000
0.0

0.4

0.6

0.8

1.0

False Positive Rate(a) TopPush
Figure 5.

0.2(b) standard SVM

ROC curves for favicons of “Basic Industries.”

bag-of-visual-words representation will be the first choices
as the feature space to be examined. Analysis of other graphic
designs is also a promising research direction.
ACKNOWLEDGEMENT
We appreciate all anonymous reviewer’s helpful comments.
This work was supported by JSPS KAKENHI Grant Number
JP17H06100 and JP18K18001.
R EFERENCES[1] S. Jolly, B. K. Iwana, R. Kuroki, and S. Uchida, “How do
convolutional neural networks learn design?” in Proc. ICPR,
2018.
[2] Y. Movshovitz-Attias, Q. Yu, M. C. Stumpe, V. Shet,
S. Arnoud, and L. Yatziv, “Ontological supervision for finegrained classification of street view storefronts,” in Proc.
CVPR, 2015.
[3] G. Adı̂r, V. Adı̂r, and N. E. Pascu, “Logo design and thecorporate identity,” Procedia-Social and Behavioral Sciences,vol. 51, pp. 650–654, 2012.
[4] N. Li, R. Jin, and Z.-H. Zhou, “Top rank optimization in
linear time,” in Proc. NIPS, 2014.

[5] P. Lyu, X. Bai, C. Yao, Z. Zhu, T. Huang, and W. Liu, “Autoencoder guided GAN for chinese calligraphy synthesis,” inProc. ICDAR, 2017.
[6] A. K. Bhunia, A. K. Bhunia, P. Banerjee, A. Konwer,
A. Bhowmick, P. P. Roy, and U. Pal, “Word level font-to-fontimage translation using convolutional recurrent generative
adversarial networks,” in Proc. ICPR, 2018.
[7] Y. Guo, Z. Lian, Y. Tang, and J. Xiao, “Creating new chinese
fonts based on manifold learning and adversarial networks,”
in Eurographics, 2018.
[8] S. Azadi, M. Fisher, V. G. Kim, Z. Wang, E. Shechtman,
and T. Darrell, “Multi-content GAN for few-shot font styletransfer,” in Proc. CVPR, 2018.
[9] A. Sage, E. Agustsson, R. Timofte, and L. Van Gool, “Logosynthesis and manipulation with clustered generative adversarial networks,” in Proc. CVPR, 2018.
[10] H. Su, S. Gong, and X. Zhu, “WebLogo-2M: Scalable logo
detection by deep learning from the web,” in Proc. ICCVW,
2017.
[11] A. T. Poffenberger and R. Franken, “A study of the appropriateness of type faces.” J. Applied Psychology, vol. 7, no. 4,
pp. 312–329, 1923.
[12] S. Choi, K. Aizawa, and N. Sebe, “Fontmatcher: font image
paring for harmonious digital graphic design,” in Proc. IUI,
2018.
[13] P. O’Donovan, J. Lı̄beks, A. Agarwala, and A. Hertzmann,“Exploratory font selection using crowdsourced attributes,”
ACM Trans. Graphics, vol. 33, no. 4, 2014.
[14] W. W. Cohen, R. E. Schapire, and Y. Singer, “Learning toorder things,” J. Artificial Intelligence Research, vol. 10, pp.
243–279, 1999.
[15] T. Joachims, “Optimizing search engines using clickthroughdata,” in Proc. SIGKDD, 2002.
[16] Y. Freund, R. Iyer, R. E. Shapire, and Y. Singer, “An efficient
boosting algorithm for combining preferences,” JMLR, vol. 4,
pp. 933–969, 2003.
[17] X. Zhao, G. Li, M. Wang, J. Yuan, Z.-J. Zha, Z. Li, and T.-S.
Chua, “Integrating rich information for video recommendation with multi-task rank aggregation,” in Proc. ACM MM,
2011.
[18] X. Xu, C. Zhou, and Z. Wang, “Credit scoring algorithm
based on link analysis ranking with support vector machine,”
Expert Systems with Applications, vol. 36, no. 2, pp. 2625–
2632, 2009.
[19] U. Brefeld and T. Scheffer, “AUC maximizing support vector
learning,” in Proceedings of ICML Workshop, 2005.
[20] R. Cruz, K. Fernandes, J. S. Cardoso, and J. F. P. Costa,“Tackling class imbalance with ranking,” in Proc. IJCNN,
2016.
[21] C. Rudin, “Ranking with a p-norm push,” in Proc. COLT,
2006.
[22] H. Narasimhan and S. Agarwal, “SVMpAUCtight: A new
support vector method for optimizing partial AUC based ona tight convex upper bound,” in Proc. SIGKDD, 2013.
[23] S. Agarwal, “The infinite push: A new support vector ranking
algorithm that directly optimizes accuracy at the absolute topof the list,” in Proc. SDM, 2011.
[24] R. Akbani, S. Kwek, and N. Japkowicz, “Applying support
vector machines to imbalanced datasets,” in Proc. ECML,
2004.