An Interactive Self-Supervised Learning Framework for Classifying Microarray Gene Expression Data

Presenter: Yijuan Lu

Outline Background Discriminant-EM (DEM) Kernel Discriminant-EM (KDEM) Experiments Relevance Feedback in Microarray Analysis Interactive self-supervised learning system

for gene classification and retrieval Conclusion and Discussion

Background Microarray technology enables us to

simultaneously observe the expression levels of many thousands of genes on the transcription level. These expression data shows distinct patterns.

Microarray: chip with a matrix of thousands of spots printed on to it Each spot binds to a specific gene

Gene ValueD26528_at 193D26561_cds1_at -70D26561_cds2_at 144D26561_cds3_at 33D26579_at 318D26598_at 1764D26599_at 1537D26600_at 1204D28114_at 707

Microarray chips Images scanned by laser

Background Two Major Characters : (1) high dimension (usually from tens to hundreds) Features: different genes expression measurements (2) small sample size (insufficient labeled training data) In general, most of genes’ function are not known.

For example: a simple leukemia microarray dataset Training set: 38 acute leukemia samples two types: ALL and AML Feature: 50 informative genes expression measurements

Background Based on the premise that genes of correlated functions tend to

exhibit similar expression patterns. Various machine learning methods have been applied to

capture these specific patterns in microarray data.

Two major characters become two challenges: High dimension: the machine learning is affected by the “curse

of dimensionality” as the search space grows exponentially with the dimension.

Small sample size: pure machine learning methods, such as SVM cannot give stable or meaningful results with small sample size.

Therefore, an approach that is relatively unaffected by these problems will allow us to get more from less.

Discriminant-EM (DEM) [1] is a self-supervised learning algorithm proposed for such a purpose.

Discriminant-EM (DEM) DEM algorithm [1] is a self-supervised learning algorithm and it has

been successfully used in content-based image retrieval (CBIR). DEM alleviates small sample size problem by compensating a small

set of labeled data with a large set of unlabeled data. The hybrid data set , Assume the hybrid data set is drawn from a mixture density

distribution of C components (each component corresponds to one class), which are parameterized by

The mixture model can be represented as:

The parameters can be estimated by maximizing a posteriori probability , which can be calculated by EM algorithm.

Predict the label of unlabeled data by

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Discriminant-EM (DEM) Find a mapping such that the data are clustered in the mapped

data space, in which the probabilistic structure could be simplified and captured by simpler Gaussian mixtures.

MDA is a traditional multi-class discriminant analysis which helps to find a mapping such that the data are better clustered in the reduced feature space. The goal is to maximize the ratio of (1).

(1)

Here, W denotes the weight vector of a linear feature extractor (i.e., for a sample x, the feature is given by the projections (WT·x). Between-class variance measures the separability of class centers and within-class variance measures the separability of class centers and samples within that class.

However, when the available labeled data are not enough, it is difficult to expect MDA to output good results.

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Discriminant-EM (DEM) By combining MDA with the EM framework, DEM

supplies MDA enough labeled data by identifying some “similar” samples in the unlabeled data set to enlarge the labeled data set.

And DEM can provide EM a projected space, which makes it easier to select the structure of Gaussian mixture models.

Kernel Discriminant-EM (KDEM)

Since the discriminating step is linear, it is difficult for DEM to handle nonlinearly separable data.

We extend the linear algorithm in DEM to a nonlinear kernel one and generalize the Kernel Discriminant-EM algorithm (KDEM) [2], in which the data are first projected nonlinearly into a high dimensional feature space F:

where the data are better linearly separated. After that, the original MDA algorithm is applied in a kernel feature space F.

Using superscript to denote quantities in the new space, we have the objective function in the following form:

with and as between-class and within-class scatter matrices respectively,

, , and N is the total number of samples.

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the span of all training samples in F, i.e., . Thus, for some expansion coefficients

where . We can therefore project a data point onto one coordinate of

the linear subspace of F as follows:

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Kernel Discriminant-EM (KDEM) Similarly, we can project each of the class means onto an

axis of the subspace of feature space F using only products:

Hence, where and where The goal has been changed to find

where , and are matrices which require only

kernel computations on the training samples.

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Kernel Discriminant-EM (KDEM) KDEM can be initialized by selecting all labeled

data as kernel vectors and by training a weak classifier based on only labeled samples. Then, the three steps of KDEM are iterated until some appropriate criterion is satisfied:

E-step: set D-step: set , and project a data

point x to a linear subspace of feature space F. M-Step: set Here, Z={label, weight}.

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KDEM on yeast cell cycle regulation dataset The sequencing and the functional annotation of the

whole S. cerevisiae genome has been complete, and thus it serves as an ideal test bed to estimate the accuracy of proposed methods.

We focused on five representative functional classes (Table I) that have been previously analyzed and demonstrated to be learnable by [4].

TABLE I

Functional classes and distribution of member genes used in our evaluation. Class

ID Functional Class number

of genes

1 TCA Cycle 18 2 Respiration 68 3 Cytoplasmic ribsome 171 4 Proteasome 77 5 Histone/Chromosome 51 6 Other classes 1939

Total 2324

KDEM on yeast cell cycle regulation dataset

In a well-cited study [4], the use of SVM, two decision tree learners (C4.5 and MOC1) and Parzen windows etc. have been investigated in gene classification to the same dataset.

Results: SVM with kernel functions significantly outperformed the other algorithms.

We focused on the comparison of KDEM with SVM using the same polynomial and radial basis kernel (RBF) functions.

Polynomial kernel functions: , RBF functions: . was set to

be a widely used value, distances from each positive example to the nearest negative example [4].

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KDEM on yeast cell cycle regulation dataset

We performed a two-class classification with positive genes from one functional class and the negative genes from the remaining classes.

The yeast gene dataset is an imbalanced dataset, in which the number of negative genes is much larger than the number of positive genes.

In this case, accuracy and single precision are not good evaluation metrics because FN is more important than FP [4]. Thus, we chose to use f_measure.

For each class, we randomly selected 2/3 positive genes and 2/3 negative genes as training set and the remaining gene data as testing set to do classification. This procedure was repeated for 100 times.

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Experiment One parameter for KDEM: the number of kernel vectors

used. There was no good way on how to choose it until now. In

our experiments, we tested KDEM under different number of kernel vectors as an example and the best one is the one which showed the highest f_measure for most classes.

Fig. 1 shows the average f_measure in percentage of KDEM with RBF under varying number of kernel vectors used on yeast data. (could be deleted)

0

20

40

60

80

1 5 10 20 40 60 80 100 150 200

N umber of K ernel Vectors

f_m

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class1

class2

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KDEM on yeast cell cycle regulation dataset

Table II Comparison of precision, recall, f_measure for various

classification methods on yeast cell cycle regulation data set. SVM (%) KDEM (%)

Class method D-p 1 D-p 2 D-p 3 D-p 4 RBF

DEM

(%) D-p 1 D-p 2 D-p 3 D-p 4 RBF

Precision 0.0 60.56 65 28.89 3.33 35.52 28.66 16.57 11.45 4.30 33.6

Recall 0.0 13.33 16.67 5.56 0.56 47.78 45 30.56 27.22 10.56 59.44 TCA Cycle

f_measure 0.0 21.15 25.64 9.10 0.95 40.22 34.12 20.38 15.72 6.01 42.44

Precision 0.0 71.21 61.64 47.31 90.17 44.94 43.84 31.49 22.6 16.95 45.29

Recall 0.0 20.28 22.22 11.39 11.94 32.64 35.56 27.22 18.89 13.61 45.83 Respiration

f_measure 0.0 31.13 32.26 17.84 20.68 37.44 38.67 28.81 20.24 14.94 44.97

Precision 88.27 89.06 86.12 85.97 96.28 69.82 70.13 60.21 57.06 54.29 66.04

Recall 47.84 46.55 45.85 43.27 45.67 56.55 58.25 55.67 52.11 46.02 70.12 Cytoplasmic

ribsome f_measure 61.8 60.89 59.6 57.31 61.72 62.38 63.43 57.74 54.15 49.48 67.85

Precision 0.0 1.667 0.0 0.83 72.5 42.96 44.39 25.09 11.46 6.775 49.44

Recall 0.0 0.123 0.0 0.12 5.56 15.19 12.35 13.58 7.778 6.173 34.44 Proteasome

f_measure 0.0 0.23 0.0 0.22 10.17 21.94 18.91 17.09 9.206 6.366 40.25

Precision 10 90.28 65.29 52.93 86.67 26.07 23.17 18.86 11.51 8.982 27.93

Recall 0.59 11.57 11.18 8.824 9.02 14.90 14.51 15.88 13.14 9.608 19.8 Histone/

Chromosome f_measure 1.11 20.2 18.52 14.66 16.16 18.64 17.57 17 12.09 9.103 22.18

KDEM on yeast cell cycle regulation dataset Given a small sample size, SVM could hardly find sufficient

labeled data to train classifiers well. By contrast, DEM and KDEM released the pain of small sample size problem by incorporating a large number of unlabeled data.

Figure 2 proves our expectation by showing the performance of KDEM, DEM, and SVM on class Histone/Chromosome as the size of training samples drops from 2/3 to 1/7 of the total samples.

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5

10

15

20

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2/3 1/3 1/5 1/7

portion of training set

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SVM_rbf

DEM

KDEM_rbf

KDEM on yeast cell cycle regulation dataset Compared to DEM, KDEM has a better capacity to

separate linearly non-separable data. Fig. 3. Data distribution in the projected subspace: the

left is DEM and the right is KDEM. Different samples are more separated and clustered in the nonlinear subspace by KDEM. (*: Cytoplasmic ribsome class; o: Proteasome class

KDEM on Malaria Plasmodium falciparum microarray dataset

Malaria is one of the most devastating infectious diseases. Approximately 500 million cases present annually and about 2 million people die. The causative agent of the most burdensome form of human malaria is a protozoan parasite Plasmodium falciparum.

The whole genome sequencing of P. falciparum predicted over 5,400 genes [5], of which, about 60% functions unknown.

Table III. Functional classes and number of member genes.Group_ID Name Number

1 Transcription machinery 23

2 Cytoplasmic Translation machinery 159

3 Glycolytic pathway and TCA cycle 25

4 Ribonucleotide synthesis and

Deoxynucleotide synthesis 25

5 DNA replication 40

6 Proteasome 35

7 Plastid genome 20

8 Merozoite Invasion 87

9 Actin myosin motors 17

10 Early ring transcripts 34

11 Mitochondrial 19

12 Organellar Translation machinery 39

Total 523

KDEM on Malaria Plasmodium falciparum microarray dataset For each class, we randomly selected 2/3 positive genes and

2/3 negative genes as training set and the remaining gene data as testing set to do classification. This procedure was repeated for 100 times.

Table IV Comparision of f_measure for various classification methods on P. falciparum data set SVM (%) KDEM (%)

Functional Class D-p 1 D-p 2 D-p 3 D-p 4 RBF

DEM

(%) D-p 1 D-p 2 D-p 3 D-p 4 RBF

Transcription 0.0 0.0 0.0 0.0 0.0 16 19.5 19 20.4 19.1 30.0

Cytoplasmic Translation 82.9 86.1 86.3 86 87.5 79.7 16.4 16.7 16.5 20.3 87.2

Glycolysis pathway and

TCA cycle 0.0 0.0 0.0 0.0 1.33 17.6 21.3 17.1 19.9 18.6 35.6

nucleotide synthesis 0.0 0.0 0.0 0.0 0.0 22.0 23.0 18.2 20.3 18.4 23.6

DNA replication 0.0 0.0 0.0 0.0 17.6 59.9 17.2 18.5 21.1 20.8 58.4

Proteasome 0.0 0.0 0.0 0.0 71 28.8 18.9 16.7 19.3 18.4 87.4

Plastid genome 0.0 0.0 0.0 0.0 57.9 67.3 21.3 18.5 19.7 20.1 81.3

Merozoite invasion 79 77.9 75.1 74.1 84.1 80.7 17.8 15.7 16.9 19.3 86.5

Actin myosin motors 0.0 0.0 2.06 7.98 0.0 32.7 20.3 20.2 21.7 19.9 35.3

Early ring transcripts 84.9 86 85.8 85.2 91.3 90.6 16.7 17.6 20.2 18.5 91.4

Mitochondrial 0.0 0.0 0.0 0.0 0.0 27.3 18.9 16.8 21.4 21.7 35.5

Organellar Translation 0.0 0.0 0.0 0.0 0.0 26.2 21.6 16.4 20.9 21.8 42.4

Putative genes of specific functional classes identified by KDEM

Functional Class Oligo_ID Gene_ID Annotation Prob. (%)

f22770_1 96.4 opfc0750

PFC0805w DNA-directed RNA pol II 77.9

m44300_14 PF13_0152 sir2 homologue 99.6 f21506_2 MAL8P1.131 Transcription factor Gas41 homologue 51.3

Transcription

M33088_1 MAL13P1.213 Putative transcription activator 98.2 c430 PFC0635c translation initiation factor E4 89.8 f26262_1 PF07_0117 eukaryotic translation initiation factor 2 alpha 55.4 j346_4 PF10_0103 eukaryotic translation initiation factor 2, beta 96.3 j353_17 76.9 ks142_1 92.1 popfj52810

PF10_0136 Initiation factor 2 subunit family 88.9

opfI0097 PFL2430c eukaryotic translation initiation factor 2b,subunit 2 63.5 a3310_7 PFA0495c selenocysteine-specific elongation factor selB 69.5 c578 PFC0870w elongation factor 1 (EF-1) 97.9 f64345_2 PFL1590c elongation factor g 85.0 f41218_2 MAL7P1.20 peptide chain release factor 50.9

Translation

opff72453 MAL6P1.210 nascent polypeptide associated complex alpha c 92.8 j21_14 PF10_0363 pyruvate kinase 89.7 ks152_12 PF11_0157 glycerol-3-phosphate dehydrogenase 89.7 L2_270 PFL0780w glycerol-3-phosphate dehydrogenase 81.7 Z_5_70 99.9 Z_5_80 99.2 Z_5_90

PF13_0141 L-lactate dehydrogenase 99.9

m16243_2 PF13_0269 glycerol kinase 99.9 N132_136 PF14_0341 glucose-6-phosphate isomerase 54.1 E714_14 PFE0225w 3-methyl-2-oxobutanoate dehydrogenase 97.5 J158_3 PF10_0218 citrate synthase, mitochondrial precursor 97.3

Glycolysis TCA

oPFBLOB0009 PF10_0334 flavoprotein subunit of succinate dehydrogenase 91.8 Nucleotide synthesis

m38941_10 PF13_0349 nucleoside diphosphate kinase b 67.2

D17715_47 PFD0475c replication factor a protein 99.9 D12635_36 PFD0950w ran binding protein 1 94.5 F64125_2 PFE0520c topoisomerase I 51.2 F16271_1 PF07_0105 exonuclease i 99.9 F16210_1 79.6 oPFG0045

MAL7P1.145 DNA mismatch repair protein pms1 homologue 95.1

DNA replication

F57777_1 MAL6P1.125 DNA polymerase epsilon, catalytic subunit a 99.9 D6287_29 PFD0165w ubiquitin-specific protease 74.6 D23156_23 PFD0680c ubiquitin carboxyl-terminal hydrolase a, putative 99.9 Z_7_90 MAL8P1.142 proteasome beta-subunit 93.3

Proteasome

oPFL0014 PFL2345c tat-binding protein homolog 99.9

Relevance Feedback (RF) RF was transformed and introduced into content-based

image retrieval (CBIR), during early and mid 1990’s [5].

A challenge in content-based image retrieval is the semantic gap between the high-level semantics in human mind and the low-level features (such as color, texture, and shape) computed by the machine.

Users seek semantic similarity (e.g., airplane and bird are very similar in terms of high level features such as shape), but the machine can only provide similarity by data processing.

To bridge the gap, RF with human in the loop was introduced to Microarray analysis.

Relevance Feedback There is a gap between the low-level expression data and its

high-level function. In the analysis of microarray data, people are interested to

find genes which have some kind of function. Yet, machines can only search for genes that have similar patterns of expression.

Two main problems (gaps) in this challenge: (1) how can we produce gene expression pattern from

expression data? (2) how can we go from expression pattern to function?

To bridge this gap, we introduce RF to microarray analysis and propose an interactive self-supervised learning framework for gene classification.

Relevance Feedback in microarray analysis Step 1. Machine provides first classification

results with initial training set, through query class. Step 2. Users provide feedback on the

classification result as to whether, and to what degree, they belong to that class, based on their knowledge such as Gene Ontology classification and functional annotation.

Step 3. Machine updates the training set based on feedback and produces new classification results with the updated training set. Go to step 2.

Interactive self-supervised learning system for gene classification and

retrieval

Improved Learning by Relevance Feedback This system achieves an improved performance by RF. In our

experiments, after a simple trial of correcting four ambiguous training examples (PF14_0601, PF14_0104, PF13_0178, and PFI1020c) based on Gene Ontology predictions, the classification accuracy increases from 84.5% to 87.2%.

It offers a powerful means for an annotation feedback. For instance, two oligonucleotide probes, both were predicted

to correspond to the same gene; however, these two probes display apparently different developmental profiles: one is positively classified into Group 1, whereas the other is classified as negative.

This discrepancy is probably due to the error in gene model. In other words, these two probes may represent two different genes rather than one. Our system clearly pinpointed these errors.

Conclusion and Discussion KDEM extends the linear DEM to a nonlinear one,

such that nonlinear discriminating features could be identified and training data could be better classified in a nonlinear feature subspace.

KDEM is applied on gene classification on the yeast and P. falciparum dataset, and compared to the state-of-the-art algorithm SVM with polynomial and RBF kernel functions. KDEM outperforms SVM in the extensive tests.

Some unknown genes in the P. falciparum dataset are identified with the agreement from both gene ontology and KDEM.

Conclusion and Discussion In order to bridge the gap between gene

expressions and the associated functions, an interactive learning framework Relevance Feedback is also introduced for microarray analysis and a real-time demo system is constructed for gene classification and retrieval.

This system can pinpoint annotation errors and it appears to improve learning significantly after a few iterations in RF, which exhibits the advantage of human in the loop very well.

Reference1. Y. Wu, Q. Tian, and T. S. Huang, “Discriminant EM algorithm

with application to image retrieval,” Proc. of IEEE Conf. Computer Vision and Pattern Recognition, 2000.

2. Q. Tian, Y. Wu, J. Yu, and T.S. Huang, "Self-Supervised Learning Based on Discriminative Nonlinear Features for Image Classification,” Pattern Recognition, Vol. 38, No. 6, pp. 903-917, 2005

3. B. Schölkopf, and A. J. Smola, “Learning with Kernels,” Mass: MIT Press, 2002

4. M. P. Brown,  W. N. Grundy,  D. Lin,   et al. “Knowledge-based analysis of microarray gene expression data by using support vector machines,” Proc. Natl. Acad. Sci. USA, 97(1), pp. 262-267, 2000.

5. X. Zhou, and T.S. Huang, “Relevance feedback in image retrieval: a comprehensive review,” ACM Multimedia Systems Journal, special issue on CBIR, 2003, 8(6), pp: 536-544.