Data reduction techniques for high dimensional biological data

IJRET: International Journal of Research in Engineering and Technology eISSN: 2319-1163 | pISSN: 2321-7308
_______________________________________________________________________________________
Volume: 05 Issue: 02 | Feb-2016, Available @ http://www.ijret.org 319
DATA REDUCTION TECHNIQUES FOR HIGH DIMENSIONAL
BIOLOGICAL DATA
Shyam Mohan J S1
, P.Shanmugapriya2
, N.Kumaran3
1
Research Scholar, Department of CSE, SCSVMV University, Enathur, Kanchipuram - 631 561
2
Associate Professor, Department of IT, SCSVMV University, Enathur, Kanchipuram - 631 561
3
Assistant Professor, Department of IT, SCSVMV University, Enathur, Kanchipuram - 631 561
Abstract
High dimensional biological datasets in recent years has been growing rapidly. Extracting the knowledge and analyzing high-
dimensional biological data is one the key challenges in which variety and veracity are the two distinct characteristics. The
question that arises now is, how to perform dimensionality reduction for this heterogeneous data and how to develop a high
performance platform to efficiently analyze high dimensional biological data and how to find the useful things from this data. To
deeply discuss this issue, this paper begins with a brief introduction to data analytics available for biological data, followed by
the discussions of big data analytics and then a survey on various data reduction methods for biological data. We propose a dense
clustering algorithm for standard high dimensional biological data.
Keywords: Big Data Analytics, Dimensionality Reduction.
---------------------------------------------------------------------***---------------------------------------------------------------------
1. INTRODUCTION
Data Reduction is a part of the analysis where the data is
shortened, focused and organizing in such a way that
Researchers take effective decisions based on the data
pulled out. Dataset reduction can be done in many ways
.First, data coded in an exploratory analysis. Second, data
partitioning for theoretical or hypothesis testing. Third, by
eliminating the irrelevant data which is not used for
analysis.[1]. High Dimensional data sets in biology arise in
many ways. With the widespread utilization of DNA
microarrays and high throughput, parallel analysis of
thousands of genes for gene expression data has been done
easily. [2].One of the common technique is feature
extraction and dimensionality reduction.[3].Datasets
collaborate with each other (also called Big data) have a
large number of dimensions (attributes) .[4, 5].Each dataset
represents a point in a multidimensional space. Clustering is
an unsupervised learning method which do not require any
supervision, i.e., it groups similar data points into clusters
(dense regions).[6]. As the dimensionality of data increases,
it is difficult to form clusters. Traditional clustering
algorithms like DBSCAN [7] generate clusters in the full-
dimensional space by measuring the proximity and
dimensions of a dataset and therefore these classical
clustering algorithms are ineffective as well as inefficient
for the high-dimensional datasets. [8]. In data mining, data
reduction for low dimension datasets can be done using
principal component analysis [9], singular value
decomposition[10], and dynamic tensor analysis[11].but
however the above techniques fail for high dimension
datasets. Generally, high-dimensional data [12] has two
main implications: (1) Finding the relative contrast between
similar and dissimilar points is difficult as the
dimensionality of data grows.[13]. (2) Grouping of different
data sets with each other.[14].
2. MOTIVATING EXAMPLES
High dimensional Data sets in biology: In biology, high
dimensional data sets are obtained from microarray chips,
which forms a matrix [15].Each cell in the matrix contains
rows and columns , rows contain the expression level of a
gene and columns contain experimental condition. Rows
and columns can be clustered to form meaningful biological
inferences. But, only a subset of genes are considered for
experiments.[16].Forming clusters for biological data is
called as bi clustering for microarray datasets.[17].
Bioinformatics: In bioinformatics, large genomes are
represented using Expressed Sequence Tag (EST) that
contain portions of genes ( mature mRNA) of length at least
500–800 nucleotides long. Finding locations of genes can be
performed by searching.[18]. The task of identifying related
or different genes or protein domains by sequence search
techniques is a complex task. A highly beneficial search for
proteins is Remote homology.[19,20].
3. BACKGROUND AND LITERATURE WORK
Many data reduction techniques have been proposed in the
literature. Data reduction techniques can be divided into two
categories: global alignment and local alignment methods.
Global alignment or full-sequence matching is used in
global optimization, and local alignment method is used in
identifying the local regions that are globally divergent.
Table 1 shows various alignment methods available with
their description.

_______________________________________________________________________________________
Table 1: Existing Data Reduction Techniques
SI.
No.
Name References Description
1. BLAST 21 Uses heuristic search for computing long biological sequences.
2. BLAST2 22
Performs limited number of insertions and deletions to increase the speed of
computation.
3. MegaBLAST 23 Uses greedy search algorithm for detecting a variety of sequences.
4.
MPBLAST and
miBLAST
24 Provide results for queries done in parallel.
5. BLAT 25 Provides indexing and linear search for finding the best match in the index.
6. OASIS 26 Performs similarity measure using local alignment technique.
7. The Shift-Or algorithm 27 Used in searching large queries by following bit manipulation technique.
8. RBSA 28
Uses alphabetic reduction technique in which number 1 represents odd characters
and 0 represents even letters.
9.
short-read sequencing
methods
29
Performs near-exact subsequence matching comparison techniques by
assumption. Ex: SOAP
10. q-gram 30
Follows pigeon-hole principle i.e., two sequences share similar or distinguishing
sequences .
For parallel processing analytics, Principal Component
Analysis (PCA) is a well known model for dimensionality
reduction which requires few number of I/O and CPU
operations.[31,32, 33]. It can be applicable to any data set
with numeric dimensions. It is used in data mining for
dimensionality reduction.
EntityRel [34], is a entity correlation graph(biomedical
graph) constructed from unstructured data by computing the
differences between two heterogeneous entities .It extends
the scope of unstructured text data by finding the meta path
based relationship analysis [35] using data mining
techniques.
DRESS, a dimensionality reduction technique used in
finding efficient sequence search is capable of handling
large queries and provides accurate results in optimal time.
Applies mapping transformations for original strings toa
new strings for dimensionality reduction.[36]
IHOSVD is a tensor based dimensionality reduction method
which applies recursively the incremental matrix
decomposition algorithm and periodically updating the
orthogonal bases for computing the new or the core
tensor.[37].In tensor based dimensionality reduction
method, data is categorized into various modules like data:
collection, tensorization, dimensionality reduction, analysis
and service modules. We apply clustering techniques to one
of the module in the above model.
4. RELATED WORK
4.1 Data Tensorization Module
In this module, the collected data is not uniform i.e, it is
usually unstructured, semi-structured or structured data .In
a unified tensor model, the above data is represented in
various sub-tensors and finally combined to form a unified
heterogeneous tensor. Most of the unstructured data includes
video and audio data. Similarly XML documents,
ontological data, etc. are semi-structured data and structured
data is a combination of numbers and strings.[37].For
biological data, we consider semi-structured data in a
subspace cluster.
Definition: Clustering in Subspace
Detecting clusters in free space or subspace is clustering in
subspace. Points may be members belonging to any multiple
clusters existing in free space. [38].
Problem statement: For every different subspaces in
subspace clustering, it is given by the fact that there is a
space with dimensions.
Preliminary
For any point p, we define core or center points, nearby
points and outliers that are clustered together. For any point
p there exists three points as given below:
 Point p is a center point if any of the minimum points are
within distance x and which are nearby to p. No points
are nearby from a non-center point.
 A point q is nearby to p if there exists a path p1, ..., pn
where p1 = A and pn = B, such that for each pi+1 p is
nearby to pi i.e., all the points on the path must be center
points excluding B.
 Far away points which could not be reached are called
outliers.
As discussed in the above statement, any point p forms a
cluster consisting of center points joining other non-center
points that are nearby to the center point. Hence each cluster
consists of at least one center point.
XML Example 1:[39]
<Gene><genes><gene
id="361"><name>BNGT1</name><organism>Human</org
anism><annotations><protein_sequence>
BEPCKMHCNMDHNKG
</protein_sequence></annotations></gene><gene

_______________________________________________________________________________________
id="362"><name>BNGT2</name><organism>Human</org
anism><family>angiopoietin</family><annotations><protei
n_sequence>
KQWJIHFTLHCILM
</protein_sequence></annotations></gene></genes><intera
ctions><sequence_similarity id="10001" gene1="361"
gene2="362"><score> 70
</score></sequence_similarity></interactions><relationship
s/></Gene>
Attribute<Protein
Sequence>
Attribute<Id> Gene<Id>
Text Text
Root
Element<Organism>
Element<Human Being>
Figure 1: Parsed tree For the example 1
5. METHOD
Without loss of generosity, we assume that for each
individual cluster we have one data point in step 1. In step 2,
the two neighboring clusters are merged to form a new
cluster leaving one cluster behind and therefore forming a
hierarchical clustering structure. STREAM algorithm is used
for constructing hierarchical clustering structure.[40] In
STREAM, the original data is divided [41]into clusters and
then the small sized clusters are merged with bigger clusters
using agglomerative algorithm.
5.1 Clustering Algorithm
Input: Initialize cluster size say D=30, distance x , minimum
points
Output: All P' x-nearby points and P.
1. Assign C to 0
2. Begin
3. Move For each point in dataset D
4. If(P=visited)
5. Proceed to next point which is nearby
6. mark P =visited
7. Nearbypoints1 = Compute Query(P, x)
8. If((size of NeighborPts1) < minimum points)
9. Then
10. Mark P =Outlier
11. else
12. Move C to next cluster
Expanding Cluster
Input: Initialize cluster size say D=30, distance x , minimum
points
Output: All P' x-nearby points and P.
1. Read Cluster C, Nearby points, P, x, minimum points
2. Move P to cluster C
3. For each point P' in Nearby points1 and
4. If P' is not visited Then
5. Mark P'=visited
6. Nearby points2 = Compute Query(P', x)
7. If((size of Nearby points2) >= minimum points) Then
8. Nearby points = Nearby points1 joined with Nearby
points2
9. If P Cluster C
10. Add P' to cluster C
11. Computed values(P, x)
Human Being Organism
Protein Sequence
(Gene Id, Attribute Id)
Figure 2: Clusters for the sample dataset
Table 2: Keywords and their Description
Keywords Description
ProbeID Unique identifier for each probe sequence
Annotation miRNAs recognized by the probe
miRNA h Human
miRNA m Mouse
miRNA r Rat
Sequence sequence of probe
6. RESULTS
6.1 Datasets
In this paper, we apply clustering techniques for
dimensionality reduction for biological data. The miRNA
sequences can be downloaded from [42].The statistical
results for 30 samples of miRNA sequences is shown in
table 3. For evaluation, we took 30 sample datasets from
table 3.The Iris dataset[43] which can be downloaded from
the UCI machine learning repository[44] and the Rat Central
Nervous System (CNS) dataset can be downloaded from
[45].The Iris dataset contains 50 samples with four features
measured from each sample .[46].The Rat CNS dataset
consists of 112 genes over 17 conditions during rat central
nervous system development.[47].We apply clustering
algorithm for miRNA data sets. Each datasets is provided
with a probe Id followed by annotation and the sequence.
For other datasets we just display the final number of
clusters in table 4.The final result is three clusters with their
sample datasets shown in figure.2.

_______________________________________________________________________________________
6.2 Standard Biological Datasets
We applied our clustering algorithm for high dimensional
biological data. Each dataset consists [48]of 500
samples(apprx.) stored over each dataset. For evaluation, we
take the datasets in XML format which is also used in tensor
based dimensionality reduction technique.
Figure 3: Rapid growth of miRNA Sequences
Table 4: Total number of Clusters for Standard High
dimensional Biological Datasets.
Dataset Number of
Samples Taken
Number of
Clusters
Iris dataset 50 2
miRNA Dataset 130(apprx.) 3
Rat CNS dataset 112 genes over 17
conditions
6
cell phenotype
dataset
444 samples in
41dimensions with
4 centers
5
7. CONCLUSION
Forming Clusters for large biological datasets is a difficult
task which involves many algorithms. Real time video
streaming of biological datasets cannot be computed easily
as they contain highly sensitive information. In future we
hope to compute real time video analytics for biological
datasets.
Table 3: Statistical Results of miRNA Sequences
Protein Coding Sequence ID Annotation Protein Sequence of max. length 30
EamA190 h-miR-10b_rfam7.0 PKKMLECCTRCGEYIAMHSIYWQVLDWHAF
EamA187 hmr-miR-107_rfam7.0 AKKMLCKCTRCMEYIAMKSIYWQVLDWHE
EamA185 hmr-miR-103_rfam7.0 AKOMLECCHRCGEYIAMHSIYWQVLDWHA
EamA181 hmr-let-7f_rfam7.0 PBKMLECCTRIGEYIXMHSIYWZVLDWHAF
EamA179 hmr-let-7d_rfam7.0 MAMLECCTRCGEYIAMHSIYWQVLDWHAG
EamA177 mr-miR-101b_rfam7.0 MAHMLECCTRCGEYIAMHSIYWQVLDWHA
EamA175 hmr-miR-320_rfam7.0 KHGMLECCTRCGEYIAMHSIYWQVLDWHAF
EamA168 hmr-let-7e_rfam7.0 PKKMLECCTRFTHYIAMHSIYWQVLDWHAF
EamA161 hmr-miR-28_rfam7.0 SHYTLECCTRCGEYIAMHSIYWQVLDWHAF
EamA160 hmr-miR-26b_rfam7.0 HJYTREYUTRCGEYIAMHSIYWQVLDWHAF
EamA155 hmr-miR-136_rfam7.0 AKKMLCKCTRCMEYIAMKSIYWQVLDWHEF
EamA283 mr-miR-211_rfam7.0 AKOMLECCHRCGEYIAMHSIYWQVLDWHAF
EamA282 m-miR-199b_rfam7.0 PBKMLECCTRIGEYIXMHSIYWZVLDWHAFE
EamA281 mr-miR-217_rfam7.0 MAMLECCTRCGEYIAMHSIYWQVLDWHAG
EamA280 hmr-miR-30a-3p_rfam7.0 MAHMLECCTRCGEYIAMHSIYWQVLDWHAK
EamA279 hmr-miR-29c_rfam7.0 KHGMLECCTRCGEYIAMHSIYWQVLDWHAF
EamA278 hmr-miR-98_rfam7.0 PKKMLECCTRFTHYIAMHSIYWQVLDWHAF
EamA238 hm-miR-1_rfam7.0 SHYTLECCTRCGEYIAMHSIYWQVLDWHAF
EamA270 hmr-miR-30b_rfam7.0 HJYTREYUTRCGEYIAMHSIYWQVLDWHAF
EamA159 hmr-miR-130a_rfam7.0 MAHMLECCTRCGEYIAMHSIYWQVLDWHAK
EamA163 hmr-miR-142-3p_rfam7.0 KHGMLECCTRCGEYIAMHSIYWQVLDWHAF
EamA171 hmr-miR-137_rfam7.0 PKKMLECCTRFTHYIAMHSIYWQVLDWHAF
EamA306 m-miR-201_rfam7.0 SHYTLECCTRCGEYIAMHSIYWQVLDWHAF
EamA307 m-miR-202_rfam7.0 HJYTREYUTRCGEYIAMHSIYWQVLDWHAF
EamA308 hmr-miR-206_rfam7.0 AKKMLCKCTRCMEYIAMKSIYWQVLDWHEF
EamA309 m-miR-207_rfam7.0 AKOMLECCHRCGEYIAMHSIYWQVLDWHAF
EamA310 hmr-miR-208_rfam7.0 PBKMLECCTRIGEYIXMHSIYWZVLDWHAFE
EamA247 hmr-miR-212_rfam7.0 MAMLECCTRCGEYIAMHSIYWQVLDWHAG
EamA251 hmr-miR-216_rfam7.0 MAHMLECCTRCGEYIAMHSIYWQVLDWHAK
EamA253 hmr-miR-218_rfam7.0 KHGMLECCTRCGEYIAMHSIYWQVLDWHAF

_______________________________________________________________________________________
REFERENCES
[1].“Handbook For Team-Based Qualitative Research”,
Greg Guest and Kathleen M. MacQueen, Altamira Press,
United Kingdom, 2008.
[2]. Schena M, Shalon D, Davis RW, Brown PO (1995)
Quantitative monitoring of gene expression patterns with a
complementary DNA microarray. Science 270(5235):467–
470.
[3]. Shendure J, Ji H (2008) Next-generation DNA
sequencing. Nat Biotech.26(10):1135–1145.
[4]. Fan J, Han F, Liu H (2014) Challenges of big data
analysis. National Science Review 1(2):293–314.
[5]. Steinbach M, Ertöz L, Kumar V (2004) The challenges
of clustering high dimensional data. In: New directions in
statistical physics. Springer, Berlin Heidelberg. pp 273–
309.
[6].Aggarwal CC, Reddy CK (2013) Data clustering:
algorithms and applications. Data Mining Knowledge and
Discovery Series 1st. CRC Press.
[7]. Ester M, Kriegel H, Sander J, Xu X (1996) A density-
based algorithm for discovering clusters in large spatial
databases with noise. Int Conf Knowl Discov Data Min
96(34):226–231.
[8]. Zhang T, Ramakrishnan R, Livny M (1996) BIRCH: an
efficient data clustering method for very large databases. In:
Proc. of the ACM SIGMOD international conference on
management of data, vol. 1. ACM Press, USA. pp 103–114.
[9].H. Abdi and L. J. Williams,``Principal component
analysis,'' Wiley Interdiscipl. Rev., Comput. Statist., vol. 2,
no. 4, pp. 433_459,Jul./Aug. 2010.
[10]. M. Brand, ``Incremental singular value decomposition
of uncertain data with missing values,'' in Proc. 7th Eur.
Conf. Comput. Vis. (ECCV), 2002, pp. 707_720.
[11]. J. Sun, D. Tao, and C. Faloutsos, ``Beyond streams and
graphs: Dynamic tensor analysis,'' in Proc. 12th ACM
SIGKDD Int. Conf. Knowl. Discovery Data Mining (KDD),
2006, pp. 374_383.
[12]. Bellman RE (1961) Adaptive control processes: a
guided tour. Princeton University Press, New Jersey
[13]. Beyer K, Goldstein J (1999) When is nearest neighbor
meaningful? Proc 7th Int Conf Database theory. In:
DatabaseTheory –ICDT’99. Lecture Notes in Computer
Science. Springer, Berlin Heidelberg Vol. 1540. pp 217-235.
[14]. Parsons L, Haque E, Liu H (2004) Subspace clustering
for high dimensional data: a review. ACM SIGKDD Explor
News l6(1):90–105.
[15]. Babu MM (2004) Introduction to microarray data
analysis. In: Grant RP (ed). Computational genomics:
Theory and application. Horizon Press, UK. pp 225–249
[16]. Jiang D, Tang C, Zhang A (2004) Cluster analysis for
gene expression data: a survey. IEEE Trans Knowl Data
Eng 16(11):1370–1386
[17].Cheng Y, Church GM (2000) Biclustering of
expression data. Proc Int Conf Intell Syst Mol Biol 8:93–
103
[18].Jongeneel CV (2000) Searching the expressed sequence
tag (est) databases: panning for genes. Bioinformatics 1:76–
92.
[19].Liu B, Wang X, Zou Q, Dong Q, Chen Q (2013)
Protein remote homology detection by combining chous
pseudo amino acid composition and profile-based protein
representation. Mol Inf 32(9–10):775–782.
[20]. Bhadra R, Sandhya S, Abhinandan KR, Chakrabarti S,
Sowdhamini R, Srinivasan N (2006) Cascade psiblast web
server: a remote homology search tool for relating protein
domains. Nucleic Acids Res 34(Web–Server–Issue):143–
146.
[21].Altschul SF, Gish W, Miller W, Myers EW, Lipman DJ
(1990) Basic local alignment search tool. J Mol Biol
215(3):403–410.
[22]. Altschul S, Madden T, Schffer R, Zhang J, Zhang Z,
MillerW, Lipman D (1997) Gapped blast and psi-blast: a
new generation of protein database search programs.
Nucleic Acids Res 25:3389–3402.
[23]. Zhang Z, Schwartz S,Wagner L,MillerW(2000) A
greedy algorithm for aligning dna sequences. J Comput Biol
7:203–214.
[24].Korf I, Gish W (2000) Mpblast : improved blast
performance with multiplexed queries. Bioinformatics
16:1052–1053.
[25].Kent WJ (2002) Resource BLAT-The BLAST-like
alignment tool. Genome Res.
[26].Meek C, Patel JM, Kasetty S (2003) Oasis: an online
and accurate technique for local-alignment searches on
biological sequences. In: Proceedings of very large database
endowment (PVLDB), vol 29, pp.910–921.
[27]. Baeza-Yates R, Gonnet GH (1992) A new approach to
text searching. Commun ACM 35(10):74–82.
[28]. Papapetrou P, Athitsos V, Kollios G, Gunopulos D
(2009) Reference-based alignment in large sequence
databases. Proc Very Large Database Endow (PVLDB)
2(1):205–216.
[29]. Li R, Li Y, Kristiansen K, Wang J (2008c) Soap: short
oligonucleotide alignment program. Bioinformatics
24(5):713–714.
[30].Yang X, Wang B, Li C (2008) Cost-based variable-
length-gram selection for string collections to support
approximate queries efficiently. In: Proceedings of the 2008
ACMSIGMOD international conference on Management of
data, ACM, pp 353–364.
[31].Carlos Ordonez Et.Al.” PCA for large data sets with
parallel data summarization” Distrib Parallel Databases
(2014) 32:377–403,Springer, DOI 10.1007/s10619-013-
7134-6.
[32].Halko, N.H., Martinsson, P.-G., Shkolnisky, Y., Tygert,
M.: An algorithm for the principal component analysis of
large data sets. SIAM J. Sci. Comput. 33(5), 2580–2594
(2011).
[33].Hastie, T., Tibshirani, R., Friedman, J.H.: The Elements
of Statistical Learning, 1st edn. Springer, New York (2001).
[34].Ming Ji Et.al,” Mining strong relevance between
heterogeneous entities from unstructured biomedical data”,
Data Min Knowl Disc (2015) ,Springer,29:976–998. DOI
10.1007/s10618-014-0396-4.
[35].SunY,Han J,YanX,Yu PS,Wu T (2011) Pathsim: meta
path-based top-k similarity search in heterogeneous
information networks. PVLDB 4(11):992–1003.
[36].Alexios Kotsifakos et.al.” DRESS: dimensionality
reduction for efficient sequence search”, Data Min Knowl

_______________________________________________________________________________________
Disc (2015) 29:1280–1311,Springer, DOI 10.1007/s10618-
015-0413-2.
[37]. LIWEI KUANG Et.Al.” A Tensor-Based Approach for
Big Data Representation and Dimensionality
Reduction”, IEEE Transactions on emerging Topics in
Computing, Volume 2,No.3, September 2014.
[38]. https://en.wikipedia.org/wiki/DBSCAN.
[39].http://authors.phptr.com/graves/book_examples/ch10/e
x10_2.xml.
[40].O’callaghan L, Meyerson A, Motwani R, Mishra N,
Guha S (2002) Streaming-data algorithms for
high-quality clustering. In: ICDE, p 0685
[41]. Karypis G, Han E, Kumar V (1999) Chameleon:
hierarchical clustering using dynamic modeling.
Computer 32:68–75.
[42].http://www.broadinstitute.org/cgi-
bin/cancer/datasets.cgi.
[43].Fisher, R. A. The use of multiple measurements in
taxonomic problems. Annals of Eugenics 7, 179–188
(1936).
[44].Bache,K. & Lichman, M. Uci machine learning
repository, 2013. URL http://archive. ics. uci. edu/ml
(1990).
[45].Wen, X. et al. Large-scale temporal gene expression
mapping of central nervous system development.
Proceedings of the National Academy of Sciences 95, 334–
339 (1998).
[46].Chenyue W. Hu Et.Al.,” Progeny Clustering: A Method
to Identify Biological Phenotypes”, Open Scientific Reports,
DOI: 10.1038/srep12894.
[47]. Giancarlo, R., Scaturro, D. & Utro, F. Computational
cluster validation for microarray data analysis: experimental
assessment of clest, consensus clustering, figure of merit,
gap statistics and model explorer. BMC Bioinformatics 9,
462 (2008).
[48].Linxia Wan Et. Al.” Automatically clustering large-
scale miRNA sequences: methods and experiments”,
International Conference on Intelligent Biology and
Medicine (ICIBM) Nashville, TN, USA. 22-24 April 2012,
http://www.biomedcentral.com/1471-2164/13/S8/S15.

Data reduction techniques for high dimensional biological data

Recommended

More Related Content

What's hot (19)

Viewers also liked (18)

Similar to Data reduction techniques for high dimensional biological data (20)

More from eSAT Journals (20)

Recently uploaded (20)

Data reduction techniques for high dimensional biological data