東海大学紀要情報通信学部
Vol.10,No.2,2017,pp.1-8
東海大学紀要情報通信学部
Vol. 11, No.02 ,2017, pp.xx -xx

Paper
Paper

Performance Evaluation of Combined Approach of Topic Modeland LMS Estimation for Multi-label Classification
by

ALAMRI Salah Aziz *1 and Iwao FUJINO *2(received on Sep. 4, 2017 & accepted on Jan. 11, 2018)

Abstract
In this paper, we will give a performance evaluation to a two-stage approach for multi-label classification. At first, we will provide
a simple description to our two-stage approach combining topic model and LMS estimation for providing multiple labels to text
documents and other kinds of feature data. The first stage of the approach applies unsupervised learning with topic model to obtain a
topic distribution for given instances, while the second stage performs supervised learning using the results of the first stage as features.
Then we will show some experiment results to evaluate the performance of this combined approach using several typical evaluation
open data set for multi-label classification. The results of these experiments confirm that our approach works effectively as expected.
Keywords: multi-label classification, topic model, latent Dirichlet allocation, least mean square estimation, MLKNN (multi-label knearest neighbor).

1. Introduction

within the range can be considered as lazy learning approach, inwhich the classifier will not learn from training data set until the test

In recent years, because of the great advancement of digital

instance is given. In order to derive a label vector for each new

and internet technology, tremendous text documents, digital images

given instance, the distances between the new given instance and all

and various evaluations of products and services can be widelytraining instances must be recalculated and resorted from theaccumulated from the general public. In order to manage such

beginning. In the case of a large number of training instances ordigital information and provide them on web search engines, itfeatures, this leads to a very expensive calculation cost. There are

becomes necessary to classify them into specific categories or

two key points that should be improved. The first key point is theassociate them with specific tags. However and for practicallazy approach, i.e., one cannot make any preparation in advanceproblems, each instance could belong to several different classes

even if the training data set is available. The second key point is thesimultaneously. In contrast with single label classification, this kindfeature dimensionality of the instance. In order to speed up theof multi-label classification has not reached, to the best of ourclassification processing, it might be necessary to introduce aknowledge, efficient solution so far, not only in the meaning ofdimensionality reducing stage, which can provide new features

theoretical viewpoint but also in the meaning of practical method ofwithutilization.

dimensionality is very small comparing with that of the original

efficientinformationforclassification

whereas

its

data.

Over the past few years, the multi-label classification problem
has attracted increasing attention of researchers involved in machine

Following the considerations mentioned above, we developed alearning. While early approaches were specially designed fortwo-stage approach for multi-label classification. The first stage ofmulti-label classification, McCallum proposed an approach using a

the approach applies unsupervised learning with topic model as a

mixture-based model [1], Schapire and Singer suggested an

preparation stage. Here topic model is implemented by the LDA

approach so-called Boostexter [2], while Elisseeff and Weston(Latent Dirichlet Allocation) [6] method, which gives a topic

introduced a ranking algorithm based on a Support Vector Machine

distribution expression for each document. The second stage(SVM) [3]. Designed as extensions of the k nearest neighbor (kNN)

performs supervised learning using the results of the first stage as

method, multi-label classification algorithms have been also

features, while supervised learning we used is least mean square

proposed [4] and [5]. However, these kNN based methods are

estimation. Our research is based on the following assumption. A*1 Graduate School of Information and Telecommunication
Engineering, Course of Information and Telecommunication
Engineering, Master’s Program*2 School of Information and Telecommunication Engineering,
Department of Communication and Network Engineering, Professor

topic should be independent from all others under ideal conditions,

―
―
−1
1−

so that the topic distribution can be a feature vector for each
instance. This gives the advantage of offering a great reduction of
the feature dimensionality. Furthermore, the label vector is derived

Performance Evaluation of Combined Approach of Topic Model and LMS Estimation for Multi-label Classiﬁcation

ヘッダー

by a linear transform from its topic distribution. This leads us todesigned by adapting single label Naive Bayesian classifier tocalculate the optimum solution under the least mean squaremulti-label classification. A two-step feature selection strategy iscondition. Therefore, the optimum solution of label vector

first applied, and aims to satisfy the assumption of conditional

estimation under the least mean square condition is finally derived.

independency given by Naive Bayes classification theory. While

Lastly, we introduced a method for deriving the most appropriate

first deriving the posteriori probability for each label, the averagedecisions from the LMS estimation results. In order to evaluate thevalue of posteriori probability of all labels is used as a threshold toproposed methods, we conducted several experiments using typicaldetermine which label the instance belongs to. This paper showedevaluation data sets of multi-label classification. The results of thesesome experimental results on Yahoo data set, which gives highly

experiments confirm that our approach works effectively ascompetitive performance with several famous algorithms.

expected.
The remainder of this paper is organized as follows. Section 2

3. Basic Considerations and Methodology

surveys a series of related works on multi-label classification.
Section 3 describes the basic considerations and methodologies

This

sectiondescribes

the

basic

considerations

andapplied by our study. We also derive the optimum solution of themethodology of our study. At first the basic main principles of our

LMS estimation of the label vector from topic distributions of LDA

two-stage approach are introduced. Next the principles behind theand a training label data. Last, the paper describes a ranking-based

derivation of an optimum solution for LMS estimation ofdecision rule for determining the proper labels from estimation

multi-label classification are developed. Finally, concrete decision

results. In section 4, the suggested method is applied to several

rules for determining the label from the result of LMS estimation

typical data sets and gives some discussions while comparing theare presented.

experiment results of this data set. Finally section 5 concludes thepaper and describes a few directions for future research.

3.1 Basic Considerations
As mentioned above, in the case of massive training instances

2. Related Works

and a large number of features contained in each instance, MLKNN
and other kNN based methods cause very expensive calculation cost.

MLKNN is a binary relevance learner initially proposed by

As opposed to lazy learning, we adopt eager learning in our study,

Zhang and Zhou [4]. It learns to build a classifier according to eachi.e. we invest our effort on training the classifier. We think alabel taken separately.

It inferences each label according to a

two-stage structure of unsupervised learning and supervised

maximum a posteriori principle and calculates the posteriori

learning will benefit to solve this problem. For details, our study is

probability by counting the number of instance with specific label in

performed based on the following basic considerations.

the k-nearest neighbors. For each given instance, at first identify its(1) Introducing unsupervised learning LDA algorithm as a

k-nearest neighbors in the training set. Then, the conditional
probability is applied by counting the instances with similar labels.
Next, according to the Bayes theorem, the posteriori probability isderived. This paper showed some experimental results on Yeast data

preprocessing procedure, so that we can obtain mutuallyindependent features and reduce the feature dimensionality
from the number words (which is several ten thousands inset, nature scene data set and Yahoo data set, which confirmed theirusual) to the number of topics (which is a few dozen or about

method outperformed conventional algorithms.

one hundred in usual).

The IBLR (Instance-Based Logistic Regression) algorithm,
introduced by Cheng and Hüllermeier [7], combines instance-based(2) After the preprocessing procedure, because the topic islearning and logistic regression techniques, where they include theindependent from each other under ideal condition, i.e., topics

statistics of k-nearest neighbors as features in the logistic regression.

will make a vector space and a multi-label of an instance canConsidering label information of neighbored examples as features

be thought a vector of this vector space or subspace. Therefore,of a query instance, the idea of IBLR is to reduce instance-basedlearning formally to logistic regression. This approach allows one tocapture interdependencies between class labels for multi-label
classification. According to the reported experimental results, theproposed approach improves predictive accuracy in terms of several
evaluation criteria.
The NBML algorithm proposed by Wei and colleagues [8] is――− 22 −

the LMS estimation is applied to get the optimum solution for
the transform matrix.
(3) In order to deride the appropriate labels from the estimatedlabel probability of a given instance, we identify a series
decision rules with regards with the average and standard

ALAMRI Salah Aziz and Iwao FUJINO

ヘッダー

deviation of the label length in training data set, maximum

�value, mean value and standard deviation of estimated� � � �� ��� � � ���� ��

probability.

���

3.2 Optimum Solution of the Estimated Label Vector
Topic model is a probabilistic generative model applied to text
document. An implementation of the topic model called LDA has
been proposed by Blei et al. [6]. A graphical model representationof LDA is shown in Fig.1, where � is a topic proportion on
documents, and � is a word distribution on words. Also α is a
hyper parameter for generating � and � is a hyper parameter for

generating �. Furthermore z is a topic matrix and w is a word countmatrix for each document and each word.

α

θ

z

w

φ

β

(1)

number of topics. Here let us suppose that we can transform the
topic proportion vector �� to label probability vector �� by

(2)

…
…
⋱
�

���
���
⋮ �
���

�, the following expression is obtained.

��� ������ ��� � � ������ ��� ���� ����� � �����
��

��

(7)

� �, we can get the optimum solution for the(8)

vector and label probability vector will not change with time, so fora given topic proportion vector �� from test set, we can estimate
label vector � � according to the following expression.

�� � ������������� � �|�� � ��� � �|�����������

(9)

(10)

3.3 Label Decision Rule from the Optimum Solutionof Estimated Label Vector
In the case of bipartition decision, the result for each label isdecided according to the following decision rule.

where � � and � can be expressed as follows.

��� ������ ������ ⋮ ⋮
��� ���

(6)

Then by differentiating this evaluation function � by weight matrix���� � ��� �����where M denotes the number of documents and K denotes the����� � � � �� ����� � ���� … � ��⋮���� � ����� �� � � ������ ��� � � ����� �� ��� �

Finally, we assume that this transform relation topic proportion

The results of the LDA processing give a topic
proportion vector for each document as follows.

�� � ��� ���� � ���� … � ��

expression.

���∗ � ��� ���

Fig. 1 Graphical model representation of LDA

introducing a weight matrix � as follows.

equation, let us derive the evaluation function to the following

weight matrix �∗ as follows.

M

���
�
�� � � �� ����� � ���� … � ��⋮���where � � �� � � � is the error vector between true label vector
�� and estimated label vector �� . After derivation of the matrix

Then from

K

N

(5)

However, in practical cases, it may be assumed that there is one
label at least for each instance, but sometimes bipartition decision(3)

rule gives no True label in the result at all. To deal with this problem,a method using the mean value of all labels as a threshold has beenreported [8]. By extending this method, we define a few rules to(4)take a final decision for each label. From an optimum solution of
estimated label vector � , we can sort its elements in descendingorder shown as follows.

where L denotes the number of labels. In order to determine theweight matrix, from least mean square (LMS) criterion, theevaluation function can be defined as follows.

��� � ��� � � � ��� � � � ���and then select the label �� ��� as true label if the following two

rules are satisfied.

――− 33 −

Performance Evaluation of Combined Approach of Topic Model and LMS Estimation for Multi-label Classiﬁcation

ヘッダー(1) Suppose �� mean value of label length and �� is thestandard deviation of label length in training data set. The firstrule is given as follows.

regards to �� . Also suppose the data set has T instances and L labels.
To describe the basic conditions of the data set for experiments, we
use these parameters and defined as follows.

(1) Label cardinality [11]: label cardinality is the average� � ������ � ��� �

number of labels for each document. Its definition is shown(11)(2) Suppose ρ is the maximum value, μ is the mean value andas follows.

σ is the standard deviation of probability ��� ��� � 1��� � ��.

The second rule is given as follows.
������� � ��������� � ����� � ��� μ����������

�� �

�

1
�|���� �|
�

(13)

���

(2) Label density [11]: label density is the average number of(12)average labels for each document. Its definition is shown as
follows.

4. Experiments

In this section, at first we describe the data sets, several

�� �

performance measures and computer environment for our
experiment. Then we show the statistics summary of each data set,
At last we report the experimental results of the MLKNN algorithm
as a baseline and the experimental results of our proposed approachwith the number of topics as a parameter. About the number of
topics, we think it should be bigger than the number of labels andmuch smaller than the number of features.

4.1 Data Set for Confirmation Experiments

baseline for these experiments is MLKNN algorithm [4]. Firstly, asa confirmation experiment, we selected the Genbase data set andYeast data set. The Genbase dataset is provided by S. Diplaris, G.
Tsoumakas, P. Mitkas and I. Vlahavas [9], which is formed forclassifying proteins to structural families according to its functions.
The Yeast dataset is provided by A. Elisseeff and J. Weston, which
is formed for classifying gene to functional classes [3]. However

(14)

���

(3) ��� : ��� denotes the mean of maximum value in crosscorrelation coefficient between the labels of different
document. Its definition is shown as follows.

��� � ���� �������������� �� ���� �� �� � 1� � �� �(15)

� ���� �� � 1� � ���

In order to evaluate our proposed approach, several
experiments have been conducted using typical data sets. The�|���� �|1��
�

4.3 Performance Evaluation Measures
In order to evaluate a given multi-label classification test set
with T instances and L labels, the evaluation metrics used are shownas follows.
(1) To focus on the performance with regard to each label, we use
the F-measure to evaluate the results. The definition of
precision [11], recall [11] and F-measure are given as follows.

Genbase is a kind of easy level data set and Yeast is a kind ofdifficult level data set for multi-label classification problem. Afterthat as a confirmation experiment for practical use, we selected theYahoo data set. This data set is provided by N. Ueda, K. Saito [10],which is formed for classifying Web page to a number of different
categories. All these data sets are downloaded from the Mulan
website+1.

�|���� � � ���� �|1��������� � �|���� �|
�

(16)

���

�

|���� � � ���� �|1������ � �|���� �|
�

(17)

���

4.2 Measures Retained for Describing the Data Set
Suppose that the data set we used for experiments is���� � ���� ���, �� denotes a feature and ���� � is a label with

+1 http://mulan.sourceforge.net/datasets-mlc.html――− 44 −��� � ��������� � ������
��������� � ������

(18)(2) To focus the performance with regard to each instance, we use
hamming loss to evaluate the results. For a binary multi-label

ALAMRI Salah Aziz and Iwao FUJINO

ヘッダー

classifier h, hamming loss is an average value of how many

calculation time, although the value of our approach changes withtimes an instance-label pair is misclassified, which definition

the number of topics, it is still very small compared to that ofis shown as follows [5], where ∆ stands for the symmetric

The results of multi-label classification experiment for thedifference of two sets.

�11�������������� � � |���� �∆���� �|��

MLKNN.
Yeast data set are shown in Table 3, where the number of topics forour approach is from 5 to 25. From the results for the MLKNN
algorithm, we can confirm that the results of hamming-loss and(19)

one-error show almost same value as reported in [4], [5] and [7].

���(3) To focus the performance with regards to ranking approach,
we use one error to evaluate the results. For a ranking basedclassifier h, one error is an average value of how many times

The results show that the value of the performance measures of the
proposed method is slightly poor comparing with that of MLKNN.
For this data set, because the number of features is 103 and thenumber of labels is 14, so there is no proper value for topic number

the top-ranked is not in the set of true labels of the instances,

for our proposed method according to the rule to choose the topic

which definition is shown as follows [5].

number mentioned above. The improper topic number assigned may
affect the independence between topics and this causes the slightly����������� �poor result. Also, as seen in the results of Genbase data set,

�1
� � ���������� ���� � �� � ���� ������

MLKNN tends to give smaller label cardinality whereas ourapproach tends to give higher label cardinality compared to the oneof the original data set. With respect to calculation time, our(20)

approaches show from 21.1% to 36.6% increased than MLKNN.

4.4 Computer Environment
The computer environment of our experiment is shown as
follows:
Hardware: HP ZBook 17 Mobile Workstation (CPU: Intel

4.6 Confirmation Experiments with Yahoo Web Page
Categorization Data Sets
For confirmation experiments to classify a practical multilabel text, a Yahoo web page data set has been selected. We

Core i7-4800MQ, Memory: 32GB, HDD: 480GB)
Software: OS: Ubuntu 14.04 LTS (64bit), Programing

retained a data set for automatic web page categorization

language: Python 2.7, Software package: numpy 1.9.1, scipy 0.13.3.

introduced by Ueda and Saito in 2003 [10]. The statistics for eachcategory for the Yahoo data set is shown in Table 4. From a bagof-words description of documents, topic model can give a topic

4.5 Confirmation Experiments
In order to evaluate our approach, we made a computer

distribution for each document and a word distribution for eachprogram according to our proposed method and we also made a

topic. Because the number of topics is quite lower than the number

computer program according to the MLKNN algorithm [4] as aof words, by introducing the topic model at the preprocessing stage,baseline of evaluation. These experiments aim to confirm ourwe can reduce the dimensionality of feature significantly. For

computer programs for the experiments. The datasets we used are

implementing MLKNN algorithm for Yahoo data set, weGenbase and Yeast. The statistics of both data sets are shown in

preprocessed each data set to extract words with highest 2%

Table 1.

document frequency based on the report of Yang and Pedersen

The results of the multi-label classification experiment for the[12], although we think this may lead to some all zero feature

Genbase data set are shown in Table 2, where the number of topics

instances. But as the MLKNN binary bipartition algorithm does notfor our approach is from 20 to 120. From the results for thealways give label results, i.e., the results for all labels are possible

MLKNN algorithm, we can confirm that the results of hamming-

False for some instances, we introduced a ranking-based decision

loss and one-error show almost same value as reported in [5] andrule as mentioned in section 3.3, which is denoted as[7]. The results show that both MLKNN and our proposed method

MLKNN+Ranking in the tables of the experimental results. Also,

achieved satisfactory figures for each performance measure. Alsoand for all of experiments, we used all instances in the training set

our proposed method shows best value of F-measure where theto train the classifier and all instances in the test set to evaluate thenumber of topics t=100. About the value of label cardinality,

performance of the trained classifier. The experimental results of

MLKNN is 1.15 which is smaller than the one of the original data

F-measure, hamming-loss and one-error are shown in Table 5, 6, 7,

set, whereas the label cardinality of our approaches are 1.23~1.27,

respectively, where the number of topics for our approach is fromwhich is close to the value of the original data set. With respect to

10 to 90. From these results, one can see that, for each performance――− 55 −

Performance Evaluation of Combined Approach of Topic Model and LMS Estimation for Multi-label Classiﬁcation

ヘッダー

measure, as an average of all individual data set, our proposed

practical problems, an important factor for improving performance

approachthanis the correlation between labels. In future work, we would like to

MLKNN+Ranking. For details, as shown in Table 5, all the 11 data

explore a method to remove the cross correlation between labels by

sets using our proposed approach show better F-measure

introducing matrix factorization. By its result we expect to adopt

performance, with 68.2% improvement on maximum and 25.7%

Naive Bayesian approach to multi-label classification under ideal

improvement on average. Then as shown in Table 6, 10 out of 11

condition and this will bring us more performance improvements

data sets using our proposed approach show better hamming-loss

with relatively small calculation cost.

shows

at

least

25%

improvement

performance, with 40.6% improvement on maximum and 25.3% on

References

average. Also as shown in Table 7, all the 11 data sets using our
proposed approach show better one-error performance, with 46.6%
improvement on maximum and 30.7% on average. Also from the[1] A. K. McCallum: Multi-label Text Classification with a Mixture

data of Table 5, a line graph of F-measure vs. the number of topics

Model Trained by EM, Proceedings of AAAI’99 Workshop on

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Allocation, Journal of Machine Learning Research, vol.3,

Fig. 2 F-measure vs. the number of topics

pp.993-1022 (2003)[7] W. Cheng and E. Hüllermeier: Combining Instance-based

5. Conclusions

Learning and Logistic Regression for Multilabel Classification,

This paper presents a two-stage approach for multi-label
classification. The first stage is an unsupervised learning stage toimplement mutually independent features and also dimensionality
reducing by introducing topic model, while the second stage issupervised learning to perform a topic-label transform according toa least mean square estimation. The experimental results on public
evaluation data set show that our proposed approach is suitable forthe case with big amount training instances and a large number offeatures. However the experimental results also show that our
proposed approach is not suitable for the case with a small numberof features like Yeast data set. For Yahoo web page categorization
data set, we achieved remarkable performance improvementcomparing with MLKNN algorithm in all of F-measure, hammingloss and one-error measures. It also appears that calculation time
can be decreased for the case of a large number of features.
Although we have achieved many progresses, the current
performances are still not good enough for practical use. For――− 66 −

Machine Learning, vol.76(2-3), pp.211-225 (2009)[8] Z. Wei, H. Zhang, Z. Zhang, W. Li and D. Miao: A Naive
Bayesian

Multi-label

Classification

Algorithm

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Classification

with

Multiple

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ALAMRI Salah Aziz and Iwao FUJINO

ヘッダー[12] Y. Yang and J. O. Pedersen: A Comparative Study on Feature
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in

Text

Categorization,

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Table 1 Statistics of Genbase and Yeast data setsin training set

Instances

Instancesin test set

FeaturesLabelsLabel
Cardinality

Label
Density

Mean of max.
crosscorr.

genbase

463

199

1186

27

1.252

0.04630.4436

yeast

1500

917

103

14

4.237

0.3026

0.6149

Data set

T a b l e 2 E x p e r i m e n t a l r e s u l t s f or t h e G e n b a s e d a t a s e t s
Precision

RecallF-measureHamming
Loss

One
Error

MLKNN(k=10)0.98990.96690.97820.00350.01001.15

148

LDA(t=20)+LMS

0.94970.96180.95570.00800.0301

1.23

12

LDA(t=40)+LMS

0.95470.95850.95660.00850.0201

1.22

18

LDA(t=60)+LMS

0.9581

0.98190.96990.00570.0050

1.27

25
30

Algorithm

Cardinality Time(s)LDA(t=80)+LMS

0.96480.97690.97080.00590.0201

1.23

LDA(t=100)+LMS

0.97900.97780.97840.00460.0251

1.23

40

LDA(t=120)+LMS

0.9526

0.96980.97460.00480.01501.23

45

Table 3 Experimental results for the Yeast data sets
Algorithm

Precision

MLKNN(k=10)
LDA(t=5)+LMS

Hamming
Loss

One
Error

RecallF-measure

Cardinality Time(s)0.73220.54910.6275

0.19800.28463.14

0.49320.76310.59920.31000.2497

6.42

172

LDA(t=10)+LMS

0.49200.75810.59670.31270.2508

6.37

178

LDA(t=15)+LMS

0.49300.74150.59260.31270.2617

6.24

193

LDA(t=20)+LMS

0.49110.75170.59400.31410.2595

6.34

189

LDA(t=25)+LMS

0.49730.73140.59200.30840.2671

6.13

194

142

Table 4 Statistics of the Yahoo data set
Data set

Instancesin training set

Instancesin test set

FeaturesLabelsLabelcardinalityLabeldensity

Mean of max.
cross-corr.

Arts1

3712

3772

23146

26

1.65390.06361

Business1

5710

5504

21924

30

1.59890.05329

0.4028Computers1

6270

6174

34096

33

1.50720.04567

0.3085

Education1

6030

6000

27534

33

1.4631

0.04433

0.1419Entertainment1

6556

6374

32001

21

1.41370.06732

0.1998

Health1

4557

4648

30605

32

1.6441

0.05137

0.2915

Recreation1

6471

6357

30324

22

1.42890.06495

0.2214

Reference1

4027

4000

39679

33

1.17440.03558

0.1102

Science1

3214

3214

37187

40

1.4497

0.036240.2875Social1

6037

6074

52350

39

1.27920.03280.2729Society1

7273

7239

31802

27

1.67040.06186

0.1929――− 77 −

0.2159Performance Evaluation of Combined Approach of Topic Model and LMS Estimation for Multi-label Classiﬁcation

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Table 5 F-measure results for the Yahoo multi-label data set
MLKNN(k=10)+Ranking

LDA+LMS
t=30

LDA+LMS
t=50

LDA+LMS
t=70

LDA+LMS
t=90

Arts1

0.3908LDA+LMS
t=10

Business1

0.79050.77530.80120.81490.81540.8219Computers1

0.58450.60560.62700.64470.65620.6602

Data Set

0.45500.51800.54030.55200.5650

Education10.45050.41780.51330.53230.56160.5709Entertainment1

0.49970.53430.63320.66500.66650.6668

Health10.5782

0.61390.70060.73080.74450.7432

Recreation1

0.36380.40560.54500.57350.58990.6121

Reference1

0.5346

0.52950.58380.61590.61330.6441

Science10.36580.37870.49230.5181

0.54970.5656Social10.64050.64670.66980.69280.70620.7188Society1

0.51940.51460.56080.58830.60370.6214average0.51980.53430.60410.62880.64170.6536

Table 6 Hamming-loss results for the Yahoo multi-label data set
MLKNN(k=10)+Ranking

LDA+LMS
t=30

LDA+LMS
t=50

LDA+LMS
t=70

LDA+LMS
t=90

Arts1

0.1283

LDA+LMS
t=10

Business1

0.02930.02940.02740.02600.02640.0256

Computers1

0.0501

0.05880.05570.05230.05180.0518

Education1

0.07230.07580.06240.06050.05680.0564Entertainment1

0.12680.11330.08990.08390.08590.0867

Health1

0.06330.05850.04530.04150.03930.0398

Recreation1

0.15650.14400.10600.10180.09580.0929Reference1

0.03730.04440.03850.0357

0.03640.0339Science1

0.06490.06390.05030.04990.04700.0456

Data Set

0.10580.0996

0.09540.0922

0.0910Social1

0.03170.03340.03220.03050.02930.0286Society1

0.07520.08770.08480.07940.07820.0717average

0.07600.0741

0.06290.05970.0581

0.0567

Table 7 One-error results for Yahoo multi-label data set
MLKNN(k=10)+Ranking

LDA+LMS
t=30

LDA+LMS
t=50

LDA+LMS
t=70

LDA+LMS
t=90

Arts1

0.6219LDA+LMS
t=10

Data Set

0.5501

0.48440.45090.43370.4072Business1

0.12260.13370.11820.11210.11150.1099Computers1

0.39940.38090.37350.3506

0.3436

0.3346

Education1

0.55750.62180.49450.47330.44060.4256Entertainment1

0.53810.50700.36520.32390.32640.3214

Health10.42250.37040.27470.24090.21810.2252

Recreation1

0.66830.61380.4366

0.4056

0.37950.3706

Reference1

0.45800.47670.42470.39050.38120.3655

Science1

0.65050.6552

0.5211

0.48630.45080.4306Social1

0.35470.3646

0.33790.30520.28920.2820Society1

0.44380.47720.42720.40320.37510.3548average

0.4761

0.46830.38710.35840.34090.3298――− 88 −