Abstract

   Disease-related protein-coding genes have been widely studied, but
   disease-related non-coding genes remain largely unknown. This work
   introduces a new vector to represent diseases, and applies the newly
   vectorized data for a positive-unlabeled learning algorithm to predict
   and rank disease-related long non-coding RNA (lncRNA) genes. This novel
   vector representation for diseases consists of two sub-vectors, one is
   composed of 45 elements, characterizing the information entropies of
   the disease genes distribution over 45 chromosome substructures. This
   idea is supported by our observation that some substructures (e.g., the
   chromosome 6 p-arm) are highly preferred by disease-related protein
   coding genes, while some (e.g., the 21 p-arm) are not favored at all.
   The second sub-vector is 30-dimensional, characterizing the
   distribution of disease gene enriched KEGG pathways in comparison with
   our manually created pathway groups. The second sub-vector complements
   with the first one to differentiate between various diseases. Our
   prediction method outperforms the state-of-the-art methods on benchmark
   datasets for prioritizing disease related lncRNA genes. The method also
   works well when only the sequence information of an lncRNA gene is
   known, or even when a given disease has no currently recognized long
   non-coding genes.

   Keywords: chromosome preference, vectorization, long noncoding RNA

INTRODUCTION

   Benefiting from the breakthroughs of the next generation sequencing
   (NGS) technologies [[34]1], disease related protein coding genes have
   been widely studied during the last decades. Non-coding genes have been
   also found involved in human disease development by functioning as
   regulators of their target protein coding genes [[35]2]. Especially,
   long non-coding RNAs (lncRNAs), a kind of RNA that do not encode
   proteins and are longer than 200nt, have been found to contain
   significant genetic information and functions [[36]3]. The
   dysregulation of lncRNAs can result in the dysfunction of their target
   protein coding genes or their participated cellular processes, causing
   the development of diseases. For example, the lncRNA NEAT1 was reported
   to be a potential target of ERα and is an important mediator for
   maintenance of prostate cancer [[37]4]. Loc285194, another lncRNA, is
   also a tumor suppressor that regulates p53 [[38]5]. Increasing number
   of studies have been focusing on the application of disease-lncRNA
   associations including disease diagnosis [[39]6], survival prediction
   [[40]7] and RNA therapeutics [[41]8]. However, the function annotation
   of lncRNA genes such as their roles in disease development is remaining
   largely unknown.

   Genomic locus inferring methods [[42]9–[43]10], computational methods
   including gene-lncRNA co-expression methods [[44]11–[45]12], network
   analysis methods [[46]13], similarities analysis or semi-supervised
   learning methods [[47]14], supervised learning methods [[48]15] and
   others [[49]16] can speed up this area of research for disease gene
   prediction. The network analysis heavily relies on the topology
   properties of the constructed networks. The semi-supervised learning
   methods depend on accurate similarity measurements between diseases and
   lncRNAs. The supervised learning approach has not been extensively
   explored because of lack of reliable negative samples of disease
   related lncRNA genes.

   We propose to use a positive-unlabeled learning (PU-learning) method to
   predict disease related lncRNA genes. PU learning can well address the
   problem of lacking reliable negative samples to gain high prediction
   performance. In this work, we also introduce a novel vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mi>d</mi></msub><mo>></mo></mrow>
   :MATH]
   to represent a disease d, and a novel vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi></m
   row></msub><mo>></mo></mrow> :MATH]
   to represent an lncRNA gene Lnc. We merge these two vectors as
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mi>d</mi></msub><mo>,</mo><msub><mi>V<
   /mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi></mrow></msub><mo>></mo></mrow>
   :MATH]
   to represent the pair of disease d and the lncRNA gene Lnc. The
   prediction problem is: whether this merged vector can be mapped to 1 or
   0 with a certain level of probability. If it is mapped to 1 with a high
   probability (e.g., 90%), then it means that the disease d is related to
   the lncRNA gene Lnc under a high probability. Otherwise, the disease d
   has little relationship with lncRNA gene Lnc.

   The novel disease vector representation
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mi>d</mi></msub><mo>></mo></mrow>
   :MATH]
   consists of two sub-vectors. The elements of the first sub-vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   represent the chromosome substructures’ distribution information
   entropies of the genes related to the disease d. We consider 45
   chromosome substructures in this work (details presented later).

   This idea for disease representation is inspired by a chromosome
   substructure enrichment analysis of the disease related protein coding
   genes. It is similar to gene pathway enrichment analysis that the
   protein gene set of a disease can be enriched at each chromosome
   substructure containing the protein gene set. We have observed that
   about 16.2% of 2802 diseases' genes can be enriched to chromosome 6
   p-arm (with Fisher's exact test, p-value<0.05), implying a strong
   chromosome preference of disease genes. This preference is
   significantly higher than the second most enriched chromosome 2 q-arm
   (containing just 5.92% of the 2802 diseases). Furthermore, no disease
   gene set can be enriched to the chromosome 21 p-arm. Our hypothesis is
   that genes are located at various positions on chromosomes and
   mitochondrion, and the distribution of disease related protein coding
   genes on the chromosomes can be used to characterize the differences
   between diseases.

   The second sub-vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   represents the KEGG pathway groups’ distribution information entropies
   of disease d related genes enriched KEGG pathways. Human KEGG pathways
   [[50]17] can be divided into 30 groups. By the disease gene KEGG
   pathway enrichment analysis on the 2802 diseases, we have observed that
   almost all these KEGG pathways are involved in disease developments.
   The distribution of disease gene sets on KEGG pathway groups is also
   uneven. For example, more than 30% of the 2802 diseases are associated
   with 6 pathways including hsa04933: AGE-RAGE signaling pathway in
   diabetic complications and hsa05321: Inflammatory bowel disease (IBD).
   In comparison, as many as 61 kinds of pathways are related to less than
   1% of these diseases.

   Comparing with existing disease characterization methods through
   computing similarities of disease related coding or non-coding genes
   [[51]18], semantics [[52]19], phenotypes [[53]20, [54]21], symptoms
   [[55]22] and ontology [[56]23], our disease vectorization
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>,</mo><msubsup><mi>V</mi><mi>d</mi><mrow
   ><mi>p</mi><mi>a</mi><mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></m
   row> :MATH]
   is much simpler. It does not need repeated set operations such as union
   and intersection or large scale of text mining. Our disease vectors are
   also effective to capture unique disease characteristics. The disease
   similarity can reach to the average area under ROC curve (AUC) of
   0.9458 when the diseases are represented by our vectors. However,
   FunSim [[57]18] and a disease symptom representation method [[58]22]
   have only 0.9202 and 0.7674 AUC respectively on the same set of
   diseases.

   The vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi></m
   row></msub><mo>></mo></mrow> :MATH]
   representing an lncRNA gene Lnc consists of two sub-vectors
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   and
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   as well.The first one represents its sequence’s k-mer frequencies, and
   the second one represents its expression profiles. Merging the two
   disease sub-vectors
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   and
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   , the two lncRNA sub-vectors
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   and
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   , we can represent a disease-lncRNA gene pair (denoted d-Lnc) as
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mi>d</mi></msub><mo>,</mo><msub><mi>V<
   /mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi></mrow></msub><mo>></mo></mrow>
   :MATH]
   Procedures for constructing the main sub-vectors are shown in Figure
   [59]1.

Figure 1. The flowchart for the vectorization representation of a
disease-lncRNA gene pair.

   [60]Figure 1
   [61]Open in a new tab

   A disease-lncRNA gene pair can be represented by the integration of
   four sub-vectors including disease gene chromosome substructures’
   distribution information entropy vector (disease gene distribution
   vector), the disease gene enriched pathway groups’ distribution
   information entropy vector (disease pathway distribution vector), the
   lncRNA gene sequence’s k-mer frequency vector and the lncRNA gene
   expression profile.

   Disease related lncRNA genes should also prefer to co-expressing with
   other genes that are associated with this disease (such as those lncRNA
   genes which regulate some of the disease related protein coding genes).
   With this hypothesis, we add these co-expression features as the fifth
   sub-vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><mi
   >exp</mi></mrow></msub><mo>></mo></mrow> :MATH]
   to the merged vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mi>d</mi></msub><mo>,</mo><msub><mi>V<
   /mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi></mrow></msub><mo>></mo></mrow>
   :MATH]
   . From our baseline classifier selection experiments, we have proved
   that this new sub-vector can further improve the prediction
   performance.

   A bagging SVM for PU learning algorithm [[62]24] is adopted to
   prioritize disease related lncRNA genes. This model was trained on a
   set of disease-lncRNA vectors. On three data sets retrieved from three
   disease-lncRNA association databases: LncRNADisease [[63]9], Lnc2Cancer
   [[64]25] and MNDR [[65]26], the overall AUC scores of leave-one-out
   cross validation (LOOCV) by our method are 0.8016, 0.8335 and 0.7527
   respectively. This performance is significantly superior to two
   state-of-the-art methods: LRLSLDA [[66]14] (0.6882, 0.7308 and 0.6346)
   and LRLSLDA-ILNCSIM [[67]27] (0.6949, 0.7390 and 0.6435). Especially
   when only the sequence information of the lncRNA genes is available,
   our method can still work well for the prediction. The overall LOOCV
   AUC scores for the three datasets are 0.7889, 0.8266 and 0.7216. The
   results of the following leave-one-disease-out cross-validation
   (LODOCV) experiments show the ability of our method to predict without
   known disease related lncRNA genes for a given disease as the average
   AUC value is 0.7356 for the LncRNADisease dataset. There are 68 out of
   162 diseases can achieve the AUC values bigger than 0.9.

RESULTS

Chromosome preference and disfavor of disease genes

   In the understanding of unique characteristics of disease genes on the
   chromosomes, we constructed chromosome enrichment analysis of disease
   genes. The process is similar to the implementation of Fisher’s exact
   test for pathway enrichment analysis which we have described in
   Algorithm [68]1. The main difference is that the pathway genes are
   replaced with the chromosome involved genes. We note that only protein
   coding genes are considered for the chromosome preference analysis of
   disease genes as the non-coding disease genes are under prediction.

Algorithm 1. Disease vectorization.

   Input disease d related gene set d[g], Approved genes G, human pathway
   set P, each pathway p[j] contained gene set g[pj], parameter k1, k2, T;
   1: Sort G according to the chromosome location of g[i], sort P
   according to the ids of p[j];
   2: Separate G according to the natural chromosome structure such as
   chr1 p-arm, chr1 q-arm,…. There are totally S chromosome substructures,
   i.e. chr[1], chr[2], …, chr[u], …, chr[S];
   3: Divide P into T groups, i.e. p[g1], p[g2], …, p[gw], …, p[gT];
   4: Generate the initial status series of each S_chr[u] = (0,0, …, 0)
   and S_p[gw] = (0, 0, …, 0);
   5: Map d[g] to chr[u] according to its location and change the
   corresponding status in S_chr[u] as 1;
   6: Set k = k1
   7: for u = 1 to S do
   8: Scan S_chr[u] with window size of k and step size 1;
   9: Compute the frequency of qth k-mer sub-status series as f[q];
   10: Compute the information entropy of the k-mer sub-status series for
   S_chr[u] as
   [MATH: <mrow><mi mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">c</mi><mi
   mathvariant="bold-italic">h</mi><msub><mi
   mathvariant="bold-italic">r</mi><mi
   mathvariant="bold-italic">u</mi></msub></mrow></msub><mo>=</mo><mo
   mathvariant="bold">−</mo><msub><mi mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">q</mi></msub><mo>×</mo><mstyle
   displaystyle="true"><munderover><mo>∑</mo><mrow><mi
   mathvariant="bold-italic">q</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup>
   <mn>2</mn><mi
   mathvariant="bold-italic">k</mi></msup></mrow></munderover><mrow><mi>lo
   g</mi><mrow><mo>(</mo><mrow><msub><mi
   mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">q</mi></msub></mrow><mo>)</mo></mrow><mo>;</m
   o></mrow></mstyle></mrow> :MATH]
   11: end for
   12: for j = 1 to M do
   13: Count genes in g[pj] as L = Length (g[pj]);
   14: Count genes mapped into p[j] as
   [MATH:
   <mrow><mi>B</mi><mo>=</mo><mi>L</mi><mi>e</mi><mi>n</mi><mi>g</mi><mi>t
   </mi><mi>h</mi><mrow><mo>(</mo><mrow><msub><mi
   mathvariant="bold-italic">d</mi><mi
   mathvariant="bold-italic">g</mi></msub><mo>∩</mo><msub><mi
   mathvariant="bold-italic">g</mi><mrow><mi
   mathvariant="bold-italic">p</mi><mi
   mathvariant="bold-italic">j</mi></mrow></msub></mrow><mo>)</mo></mrow><
   mo>;</mo></mrow> :MATH]
   15: Do the fisher’s exact test:
   16: [h, p, stats] = fishertest ([L- B, B;A - L - n + B; n - B]), where
   p is the p-value;
   17: if p <= 0.05 then
   18: Change the status of p[j] in S_p[gw] as 1;
   19: end if
   20: end for
   21: Set k = k2
   22: for w = 1 to T do
   23: Scan S_p[gw] with window size of k and step size 1;
   24: Compute the frequency of vth k-mer sub-status series as f[v]
   25: Compute the information entropy of the k- mer sub-status series for
   S_p[gw] as
   [MATH: <mrow><mi mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mi
   mathvariant="bold-italic">P</mi></msub><msub><mi
   mathvariant="bold-italic">g</mi><mi
   mathvariant="bold-italic">w</mi></msub><mo>=</mo><mo>−</mo><msub><mi
   mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">v</mi></msub><mo>×</mo><mstyle
   displaystyle="true"><munderover><mo>∑</mo><mrow><mi
   mathvariant="bold-italic">v</mi><mo>=</mo><mn>1</mn></mrow><mrow><msup>
   <mn>2</mn><mi
   mathvariant="bold-italic">k</mi></msup></mrow></munderover><mrow><mi
   mathvariant="bold-italic">l</mi><mi mathvariant="bold-italic">o</mi><mi
   mathvariant="bold-italic">g</mi><mrow><mo>(</mo><mrow><msub><mi
   mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">v</mi></msub></mrow><mo>)</mo></mrow><mo>;</m
   o></mrow></mstyle></mrow> :MATH]
   26: end for
   Output The disease gene distribution entropy vector:
   [MATH: <mrow><mrow><mo><</mo><mrow><msubsup><mtext
   mathvariant="bold">V</mtext><mi
   mathvariant="bold-italic">d</mi><mrow><mi
   mathvariant="bold-italic">c</mi><mi mathvariant="bold-italic">h</mi><mi
   mathvariant="bold-italic">r</mi></mrow></msubsup></mrow><mo>></mo></mro
   w><mo>=</mo><mrow><mo><</mo><mrow><mi
   mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">c</mi><mi
   mathvariant="bold-italic">h</mi><msub><mi
   mathvariant="bold-italic">r</mi><mn
   mathvariant="bold">1</mn></msub></mrow></msub><mo>,</mo><mi
   mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">c</mi><mi
   mathvariant="bold-italic">h</mi><msub><mi
   mathvariant="bold-italic">r</mi><mn>2</mn></msub></mrow></msub><mo>,</m
   o><mo>…</mo><mo>,</mo><mi mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">c</mi><mi
   mathvariant="bold-italic">h</mi><msub><mi
   mathvariant="bold-italic">r</mi><mi
   mathvariant="bold-italic">S</mi></msub></mrow></msub></mrow><mo>></mo><
   /mrow></mrow> :MATH]
   Output The disease pathway distribution entropy vector:
   [MATH: <mrow><mrow><mo><</mo><mrow><msubsup><mi
   mathvariant="bold-italic">V</mi><mi
   mathvariant="bold-italic">d</mi><mrow><mi
   mathvariant="bold-italic">p</mi><mi mathvariant="bold-italic">a</mi><mi
   mathvariant="bold-italic">t</mi><mi
   mathvariant="bold-italic">h</mi></mrow></msubsup></mrow><mo>></mo></mro
   w><mo>=</mo><mrow><mo><</mo><mrow><mi
   mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">p</mi><msub><mi
   mathvariant="bold-italic">g</mi><mn>1</mn></msub></mrow></msub><mo>,</m
   o><mi mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">p</mi><msub><mi
   mathvariant="bold-italic">g</mi><mn>2</mn></msub></mrow></msub><mo>,</m
   o><mo>…</mo><mo>,</mo><mi mathvariant="bold-italic">I</mi><msub><mi
   mathvariant="bold-italic">E</mi><mrow><mi
   mathvariant="bold-italic">p</mi><msub><mi
   mathvariant="bold-italic">g</mi><mi
   mathvariant="bold-italic">r</mi></msub></mrow></msub></mrow><mo>></mo><
   /mrow></mrow> :MATH]
   [69]Open in a new tab

   The 24 chromosomes of human genome can be naturally divided into 48
   substructures with the p-arm and the q-arm as two substructures for
   each chromosome. However, for chromosome 13 (chr13), there is only one
   protein gene on the centromere and there is no approved protein gene
   located at its p-arm; for chromosome 14, only one gene is located at
   its p-arm; and there is no gene located at the p-arm of chr15 or chr22.
   Thus, these four chromosomes were not divided. We consider the
   mitochondrion as a special chromosome which cannot be divided into two
   substructures. In total, we have 45 chromosome substructures, namely
   S=45 in Algorithm [70]1. Figure [71]2 and Figure [72]3 show the
   statistics of the chromosome substructure enrichment analysis for the
   disease genes of each of the 2802 diseases.

Figure 2. The disease chromosome enrichment analysis pie graph.

   [73]Figure 2
   [74]Open in a new tab

   Subchr means chromosome substructure. We did the statistics of how many
   chromosomes a disease gene set enriches. More than a half (53%) of the
   2802 diseases are just enriched to only one chromosome substructure,
   while just 3% of these diseases can be enriched to more than 4
   chromosome substructures.

Figure 3. The disease chromosome enrichment analysis results.

   [75]Figure 3
   [76]Open in a new tab

   The y-axis are percentages of diseases that enriched to each of the
   chromosome substructures. The x-axis are the indexes of the chromosome
   substructures. The bar graph at the top right shows the statistics of
   the numbers of chromosome substructures that contained by diseases with
   given percentages scopes.

   There are about 75% of the diseases whose related gene sets can be
   enriched to no more than 1 chromosome substructure (Figure [77]2).
   There are just 3% of the diseases whose related gene sets can be
   enriched to more than 4 chromosome substructures. This distribution of
   disease genes on the chromosome substructures reveals that the disease
   genes of a given disease are very likely located at a neighborhood
   region. As indicated by Figure [78]3, the p-arm of chromosome 6 is the
   most preferred substructure of disease genes - about 16.2% of the
   disease related gene sets can be enriched here. This percentage is
   significantly higher than the other substructures (all no more than
   6%). Interestingly, there is no disease related gene set that can be
   enriched to the p-arm of chromosome 21. From the top-right bar graph of
   Figure [79]3, we can also see that 16 out of the 45 chromosome
   substructures are enriched by only 1% -2% of the 2802 gene sets. There
   are 10 and 8 substructures can be enriched by 2%-3% and 3%-4% of the
   2802 gene sets. Thus, most of the chromosome substructures (38 out of
   45) can be enriched by no more than 3% of the 2802 gene sets. These
   observations suggest a phenomenon that disease genes are unevenly
   distributed in the 45 chromosome substructures. The genes related to a
   disease are preferred at a physical neighborhood close to each other in
   the chromosomes. This observation of chromosome preference lays down
   the foundation for our disease vector representation.

   We also conducted pathway enrichment analysis to understand the
   distribution of disease genes in human KEGG pathways. We found that
   disease genes are also unevenly enriched in these pathways. More than
   30% of the 2802 diseases are associated with one of the top 6 pathways
   such as hsa04933: AGE-RAGE signaling pathway in diabetic complications,
   and hsa05321: Inflammatory bowel disease (IBD). In contrast, 61 out of
   303 pathways are related to less than 1% of these diseases. More
   details are reported in [80]Supplementary File 1.

Performance on the prediction of highly similar diseases using our disease
vector representation

   We tested the performance of our vectorization model for computing
   disease similarities on the dataset downloaded from the supplementary
   files of Cheng's paper [[81]18]. It contains a candidate disease set
   and a benchmark set of similar disease pairs. The disease set is
   composed of 2802 diseases and their related genes. There are 70 similar
   disease pairs in the benchmark set. Zhou et al. [[82]22] proposed a
   symptom representation method for measuring disease similarities. To
   compare this method with ours, we downloaded their similarity scores
   between 1596 diseases and mapped these diseases to the 2802- disease
   set. Totally 1012 diseases and 56 similar disease pairs in the
   benchmark set can be mapped. These two disease sets have been stored in
   [83]Supplementary File 2.

   Following cheng's method, we drew a ROC curve to display how our method
   can rank the similar pairs in the benchmark set comparing with those
   randomly selected unknown disease pairs. That means, for a given
   threshold, if the similarity of a pair in the benchmark set exceeds
   this threshold, it is defined as a true positive, otherwise, as a false
   negative. Inversely, an unknown disease pair exceeds the threshold is
   defined as a false positive. A total of 560 testing disease-disease
   pairs were randomly selected from the 1012 candidate diseases (but not
   overlapping with the benchmark set). This process was repeated 100
   times.

   There are three parameters, i.e. k1, k2 and T, for Algorithm [84]1 and
   one parameter θ for equation [85](3) need to be tuned. According to the
   HGNC database, there are 19025 approved protein coding genes. Because
   the minimum length of the chromosome substructure is 9 (only 9 protein
   coding genes on this substructure), thus the parameter k1 was changed
   from 1 to 9 with the step size of 1. There are 303 different human KEGG
   pathways. To simplify our model, we set T=30 with the first 29 groups
   containing 10 pathways while the last group has 13 pathways. Finally,
   the disease genes chromosome substructures’ distribution information
   entropy (disease gene distribution entropy) feature is represented as a
   45-dimensional vector while the disease gene enriched pathway groups’
   distribution information entropy (disease pathway distribution entropy)
   feature is a 30-dimensional vector. k2 was changed from 1 to 10 with
   the step size of 1. The integration parameter θ was in the range of [0,
   1].

   When k1=9, we can get the biggest average AUC=0.9429. Meanwhile, when
   k2=8, the AUC value with just pathway distribution entropy vectors can
   achieve 0.8872. Thus, we set k1=9 and k2=8 for the subsequent
   experiments.

   We also compared the performances of our methods (namely the entropy
   vector methods and the status series vector methods), the FunSim
   [[86]18] and symptom representation method [[87]22]. We implemented the
   FunSim according to the published paper. Then, the AUC values were
   computed according to the scores via different methods. During the
   comparison, θ was set to be 0 to 1 with the step size of 0.1. When
   θ=0.8, the integrated similarity method can work the best with average
   AUC=0.9458. We drew the corresponding overall ROC curves (all the 100
   times repeat experiments’ results are combined together to compute the
   False Positive Rate and True Positive Rate; thus, the overall AUC
   values are smaller than the average AUC values) of the 100 times
   experiments in Figure [88]4. More comparison results for the original
   2802 disease set can be found in the [89]Supplementary File 1.

Figure 4. The ROC curves of different methods for computing the disease
similarities.

   [90]Figure 4
   [91]Open in a new tab

   There are 7 ROC curves: the disease pathway distribution entropy vector
   method (θ=0, AUC=0.8555); the disease gene distribution entropy vector
   method (θ=1, AUC=0.9067); the integrated similarity method (θ=0.8,
   AUC=0.9094); the pathway status series vector method (AUC=0.7867); the
   disease gene status series vector method (AUC=0.5882); FunSim
   (AUC=0.8858) and Symptom representation method (AUC=0.7455).

   Figure [92]4 shows that the integrated similarity method is better than
   the other methods. However, it just improves 0.0027 on the AUC value
   comparing with just disease gene distribution entropy vector method
   (k1=9, θ=1). It implies that there are not much complementary between
   the disease gene distribution entropy and disease pathway distribution
   entropy features as to compute the similarities of diseases. The
   integrated similarity method with θ=0.8 outperforms the FunSim and
   symptom representation method by improving AUC values of 0.0236 and
   0.1639 respectively. In comparison, the status series vector methods
   cannot work as well as the entropy vector methods. The entropy vector
   methods (disease gene distribution entropy vs. disease gene status
   series and disease pathway distribution entropy vs. pathway status
   series) improve the overall AUC values by 0.3185 and 0.0688. This
   proves our “part overcomes the whole” hypothesis that our dividing and
   information entropy strategy for representing diseases is more
   effective than the original status series.

Performance on the prediction and prioritization of disease related lncRNA
genes

   The performance of our disease vectorization method for predicting and
   prioritizing disease related lncRNA genes was tested and evaluated on
   three data sets: the lncRNADisease dataset (454 positive samples, i.e.,
   454 known associations between some diseases and some lncRNA genes),
   the lnc2cancer dataset (594 positive samples) and the MNDR dataset (176
   positive samples). See details of these data sets at the section
   Materials and Methods.

Classifier and parameter selection for final prediction model with the
lncRNADisease dataset

   We used both liner and RBF kernel for the SVM-based positive-unlabled
   learning method to conduct cross validation on the lncRNADisease data
   set. The number of positive samples is 454, and the number of unlabeled
   samples (i.e., the number of unknown associations) is 29840, derived by
   exhaustively pairing the 162 diseases and 187 lncRNAs in the
   lncRNADisease data set after the deduction of the number of 454
   positive samples. Recall that our vector representation for a pair of
   disease and lncRNA gene consists of five sub-vectors. Here, we choose
   different combination of these sub-vectors to understand that all of
   these sub-vectors are important for the prediction. The steps are
   presented in Algorithm [93]2.

Algorithm 2. A bagging SVM for prioritizing the disease related lncRNA genes.

   Input Positive dataset PO, unlabeled dataset UN, bootstrap sample size
   R, bootstrap number V, SVM parameters, feature type W;
   1: for a=1 to 100 do
   2: Randomly select |PO| of unlabeled samples as negative samples;
   3: Implement a 5-fold cross validation on the positive-negative dataset
   with feature type W and do grid search of SVM parameters;
   4: end for
   5: Use F1 score as the metric, determine the optimal SVM parameters
   opPara and the optimal feature type W[op];
   6:
   [MATH: <mrow><mo>∀</mo><mtext> </mtext><mi
   mathvariant="bold-italic">x</mi><mi>ϵ</mi><mi
   mathvariant="bold-italic">U</mi><mi
   mathvariant="bold-italic">N</mi><mo>,</mo><mi
   mathvariant="bold-italic">n</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>←</mo><mn>0</mn><m
   o>,</mo><mi mathvariant="bold-italic">f</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>←</mo><mn>0</mn><m
   o>;</mo></mrow> :MATH]
   7: for b=1 to V do
   8: Draw a bootstrap sample UN[b] of size R in UN;
   9: Train a classifier f[b] to discriminate PO against UN[b] with opPara
   and W[op];
   10: For any
   [MATH: <mrow><mi mathvariant="bold-italic">x</mi><mi
   mathvariant="bold-italic">ϵ</mi><mrow><mo>(</mo><mrow><mi
   mathvariant="bold-italic">U</mi><mi
   mathvariant="bold-italic">N</mi><mo>\</mo><mi
   mathvariant="bold-italic">U</mi><msub><mi
   mathvariant="bold-italic">N</mi><mi
   mathvariant="bold-italic">b</mi></msub></mrow><mo>)</mo></mrow></mrow>
   :MATH]
   , update:
   11:
   [MATH: <mrow><mi mathvariant="bold-italic">f</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>←</mo><mi
   mathvariant="bold-italic">f</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>+</mo><msub><mi
   mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">b</mi></msub><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>;</mo></mrow>
   :MATH]
   12:
   [MATH: <mrow><mi mathvariant="bold-italic">n</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>←</mo><mi
   mathvariant="bold-italic">n</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>+</mo><mn>1</mn><m
   o>;</mo></mrow> :MATH]
   13: end for
   Output The score
   [MATH: <mrow><mi mathvariant="bold-italic">s</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow><mo>=</mo><mfrac><mrow
   ><mi mathvariant="bold-italic">f</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow></mrow><mrow><mi
   mathvariant="bold-italic">n</mi><mrow><mo>(</mo><mi
   mathvariant="bold-italic">x</mi><mo>)</mo></mrow></mrow></mfrac><mo>,</
   mo><mi mathvariant="bold-italic">f</mi><mi
   mathvariant="bold-italic">o</mi><mi
   mathvariant="bold-italic">r</mi><mtext> </mtext><mi
   mathvariant="bold-italic">x</mi><mi>ϵ</mi><mtext> </mtext><mi
   mathvariant="bold-italic">U</mi><mi
   mathvariant="bold-italic">N</mi><mo>.</mo></mrow> :MATH]
   [94]Open in a new tab

   The basic combination of the sub-vectors is to merge the disease gene
   distribution entropy sub-vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   and lncRNA sequence's k-mer frequency sub-vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   Here, we set k=3 (k-mer size for lncRNA sequence) and k1=9 (k-mer size
   for disease gene series) in the previous section. This basic feature
   vector is a 109-dimensional (45+64) feature vector, simply denoted by
   sf1+sf3. We name it the type-0 feature vector. Adding other sub-vectors
   such as the disease pathway distribution entropy vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   (sf2, 30-dimensional), lncRNA expression profile
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   (sf4, 16-dimensional), the basic feature vector can be expanded into
   another three feature types, i.e., the feature type 1∼3 in Table [95]1.
   Furthermore, the co-expression feature namely the fifth sub-vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><mi
   >exp</mi></mrow></msub><mo>></mo></mrow> :MATH]
   (sf5, 3-dimensional) was added to each of the former combinations to
   form four more feature types which are showed in the last four lines of
   Table [96]1.

Table 1. Feature types and their corresponding performance.

  Type Combination of sub-vectors    Liner kernel            RBF kernel
  0             sf1, sf3          C = 7, F1 = 0.6668 C = -1, G = -1, F1 = 0.6734
  1          sf1, sf2, sf3        C = 2, F1 = 0.6895 C = 3, G = -5, F1 = 0.7024
  2          sf1, sf3, sf4        C = 7, F1 = 0.6692 C = 6, G = -2, F1 = 0.6734
  3        sf1, sf2, sf3, sf4     C = 0, F1 = 0.6942 C = 5, G = -7, F1 = 0.7058
  4          sf1, sf3, sf5        C = 8, F1 = 0.6658 C = 0, G = -2, F1 = 0.6768
  5        sf1, sf2, sf3, sf5     C = 0, F1 = 0.6906  C = 4, G = -6, F1 =0.7032
  6        sf1, sf3, sf4, sf5     C = 1, F1 = 0.6708 C = 0, G = -2, F1 = 0.6748
  7     sf1, sf2, sf3, sf4, sf5   C = 2, F1 = 0.7004 C = 3, G = -5, F1 = 0.7114
   [97]Open in a new tab

   Under these different types of vector representation, we tested the
   liner kernel and RBF kernel with parameter c = 2^C, where C ranges from
   -8 to 8 with the step size of 1 (liner kernel and RBF kernel) and g =
   2^G, where G ranges from -8 to 8 with the step size of 1 (RBF kernel).
   The best 5-fold cross validation results (F1 scores) on the
   lncRNADisease dataset are shown in the third and fourth columns of
   Table [98]1.

   Adding the disease pathway distribution entropy sub-vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   (i.e., sf2) can improve the performance for predicting disease-lncRNA
   associations (type1 vs. type0, type3 vs. type2, type7 vs. type6,
   averagely improved by 0.0257 for liner SVM and 0.0307 for RBF SVM
   respectively). However, the improvement by adding the lncRNA expression
   profile is not as high as adding the disease pathway distribution
   entropy sub-vector (0.0052 for liner SVM, 0.0021 for RBF SVM
   averagely). The co-expression feature vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><mi
   >e</mi><mi>x</mi><mi>p</mi></mrow></msub><mo>></mo></mrow> :MATH]
   can further improve the prediction performance averagely by 0.0039 and
   0.0033 for liner SVM and RBF svm respectively. The combination of all
   the 5 sub-vectors (i.e., the type 7 feature vector) worked the best
   among the 8 types of feature vectors (on average improving by 0.0223
   for liner SVM and 0.0243 for RBF SVM). Furthermore, the RBF kernel
   outperforms the liner kernel (on average improving by 0.0092). Thus,
   our baseline classifier is the RBF SVM (C = 3, G = -5) with the type 7
   feature vector representation (W=7).

   Using all the sub-vectors (i.e., the type 7 feature vector) to
   represent a pair of disease and lncRNA gene, the 5-fold cross
   validation AUC results on the lncRNADisease dataset by bagging SVM are
   shown in Figure [99]5, using different bootstrap sample size R and the
   bootstrap number V. Here, we repeated the experiment 10 times. The AUC
   values were computed via comparing the scores of known pairs (set to be
   unknown during the cross validation) with those unknown ones. We note
   that we simply set R=|PO| as Mordelet [[100]24] had proved that setting
   R to be the same as the size of positive samples is a safe choice for
   the bagging SVM.

Figure 5. The boxplot graph of the AUC values for the 5-fold cross validation
experiments.

   [101]Figure 5
   [102]Open in a new tab

   The x-axis is the value of V, and the y-axis is the corresponding AUC
   values. The changes of the AUC values with different V are tiny. For a
   given V, the prediction results are stable.

   The AUC values change in a narrow scope (0.79-0.81) when the bootstrap
   number V varies from 10 to 400. In fact, the running time for computing
   the scores of unknown samples increases significantly when V is
   increasing. As bigger V achieves weak improvement of the performance
   but results in significant increase of time cost, we suggest to fix
   V=10. This is consistent with the conclusion of Mordelet's report that
   when R is large, the SVM usually rarely benefits from bagging. Thus,
   our final PU learning classifier is built with following parameters:
   RBF kernel SVM with C = 3, G = -5, V = 10, R= |PO| and W = 7.

Performance comparison and case studies

   In comparison with two state-of-the-art disease-lncRNA association
   prediction methods LRLSLDA [[103]14] and LRLSLDA_ILNCSIM [[104]27], our
   leave-one-out cross-validation AUC performance is much better on the
   three datasets (Figure [105]6). We note that the source codes of these
   two existing methods are not available, but we implemented their
   algorithms for a fair comparison. Their datasets are not available
   either.

Figure 6. The leave-one-out cross validation results based on three datasets
with different methods.

   [106]Figure 6
   [107]Open in a new tab

   Four methods were compared, our method with type 7 (W=7) feature and
   type 1 (W=1) feature, LRLSLDA method and the LRLSLDA_ILNCSIM method.
   Our type 7 method works best for all three datasets.

   Our method with type 7 feature vector has a superior performance
   (AUC=0.8016, 0.8335 and 0.7527 on the three datasets) over the other
   three methods: the type 1 vector method (AUC=0.7889, 0.8266 and
   0.7216), the LRLSLDA (AUC=0.6882, 0.7308 and 0.6346) and the
   LRLSLDA_ILNCSIM (AUC=0.6949, 0.7390 and 0.6435). We note that our type
   1 vector needs just the accessible information such as disease genes
   and lncRNA sequences, but it can achieve close performance as the type
   7 vector method did.

   We also did the leave-one-disease-out cross validation when assuming
   that all the related lncRNAs of a given disease are unknown. Then we
   computed the possibilities of the lncRNAs to be associated with the
   disease. The AUC value was used to test how are those already known
   related lncRNAs ranked comparing with the unknown ones. There are more
   than 40% (68 out of 162 diseases) of the diseases can achieve an AUC
   value higher than 0.9. The average AUC of all the diseases is 0.7356.
   This suggests that our method is capable of predicting disease-lncRNA
   associations even without knowing any association with a given disease.

   We did an experiment to predict disease related lncRNAs using the known
   454 positive samples and the 29840 unlabeled samples by PU learning.
   The predicted results were validated using two other datasets (166
   lnc2cancer samples and 29 MNDR samples overlap with the 29840 unlabeled
   samples). The ranking scores of the 29840 unlabeled samples and a ROC
   curve are plotted in Figure [108]7.

Figure 7. The final prediction test on the lncRNADisease dataset.

   [109]Figure 7
   [110]Open in a new tab

   The x-axis is the unknown disease-lncRNA pairs' predicted ranks. The
   y-axis are the predicted scores which means the possibilities of the
   samples to be positive. The predicted results were validated via the
   lnc2cancer and MNDR datasets. The validated samples were marked on the
   score curve. The ROC curve that compares the scores of the validated
   samples and the remain unknown samples is drawn at the top right of
   this figure. The AUC value achieves 0.9005.

   Figure [111]7 shows that most of the validated samples are ranked at
   good positions. We regarded those 166 lnc2cancer samples and 29 MNDR
   samples as positive while remaining unknown samples as negative and
   draw the ROC curve at the top right of Figure [112]7. It achieves the
   AUC value of 0.9005, which reveals that our prediction can always rank
   the positive samples well. We also did case studies for breast cancer
   and prostate cancer. Breast cancer is the leading type of cancer in
   women, accounting for 25% of all women cancer patients [[113]28].
   Prostate cancer is the second most common type of cancer and the fifth
   leading cause of cancer-related death in men [[114]28]. We list in
   Table [115]2 top 5 lncRNAs that are (possibly) related to these two
   cancer types.

Table 2. Case studies for predicting breast cancer and prostate cancer
related lncRNAs.

   Cancer type Predicted related lncRNA Predicted scores Validated status
   breast cancer UCA1 0.8685 validated by lnc2cancer
   breast cancer DLEU2 0.8375 validated by literatures
   breast cancer EPB41L4A-AS1 0.8356 not validated
   breast cancer LINC00271 0.8297 validated by literatures
   breast cancer 7SK 0.8280 validated by literatures
   prostate cancer UCA1 0.9220 validated by lnc2cancer
   prostate cancer BCYRN1 0.8983 not validated
   prostate cancer HOTAIR 0.8952 validated by lnc2cancer
   prostate cancer ZFAS1 0.8810 not validated
   prostate cancer BOK-AS1 0.8800 not validated
   [116]Open in a new tab

   The most-top ranked lncNA that is related to breast cancer is UCA1.
   This annotation has been already recorded in the lnc2cancer database.
   The second highest ranked lncRNA is DLEU2. In fact, DLEU2 is frequently
   deleted in malignancy [[117]29]. It functions as a critical host gene
   of the cell cycle inhibitory microRNAs miR-15a and miR-16-1. Both of
   these two microRNAs are related to the breast cancer [[118]30]. The
   4^th and 5^th top-ranked lncRNAs LINC0271 [[119]31] and 7SK [[120]32]
   are related to breast cancers. As to prostate cancer, two top-ranked
   lncRNAs UCA1 and HOTAIR have been actually stored in the lnc2cancer
   database. These case studies support that our disease vector
   representation and PU learning methods are effective to prioritize
   disease related lncRNA genes.

MATERIALS AND METHODS

   Datasets of diseases and disease related genes were collected and
   relevant human KEGG pathways were collected as well for the
   construction of the disease vectorization model and the disease gene
   prediction method. The details of the datasets and prediction
   algorithms are presented below.

Diseases, disease genes and KEGG pathways

   The Medical Subject Headings (MeSH) [[121]33], Comparative
   Toxicogenomics Database (CTD) [[122]34], Disease Ontology (DO)
   [[123]35] and Online Mendelian Inheritance in Man (OMIM) [[124]36] are
   widely visited databases containing massive amount of disease related
   information. However, there is no standard for the adoption of disease
   names or ids between these databases. We mapped disease names to DO ids
   using the DO, MeSH and CTD as dictionaries. Similarly, for genes, we
   did id or name conversion using the data records from the HUGO Gene
   Nomenclature Committee (HGNC) [[125]37] database. It contains reference
   records of genes among a great number of widely used databases. In this
   work, we mainly mapped the genes obtained from various resources to
   entrez gene ids [[126]38]. We downloaded the HGNC database on Jun 17,
   2016. There are totally 39670 approved gene records with entrez gene
   ids including 19025 protein coding genes and 20645 non-protein coding
   genes.

   We downloaded disease-gene associations from the supplementary file of
   a published article [[127]18] which contains 117,190 associations
   between 2817 diseases and 12063 genes. The authors collected these data
   records from database SIDD [[128]39]. Each of the diseases has a unique
   id from database DO. After data correction and redundancy removal
   according to the latest version of the databases DO, MeSH, CTD and
   HGNC, we obtained a set of 114754 disease-gene associations between
   2802 diseases and 10893 genes (including 10321 protein coding genes and
   572 non-protein coding genes). The human KEGG pathways were extracted
   from the KEGG database on June 21, 2016. There are 303 unique pathways
   containing 7060 unique genes (all have an entrez gene id). All these
   datasets are listed in [129]Supplementary File 3 and [130]Supplementary
   File 4.

Associations between diseases and lncRNAs

   The disease-lncRNA associations were obtained from three databases:
   lncRNADisease (downloaded on April 18, 2016), lnc2cancer (downloaded on
   July 4, 2016) and MNDR (downloaded on June 30, 2016). There are 1102,
   1239 and 754 disease-lncRNA associations (redundant and unclear
   information are existing). For the diseases, we mapped them to DO. To
   construct our PU learning model for disease related lncRNA prediction,
   we collected the sequences and expression profiles of the lncRNAs.

   We mapped each of these lncRNAs to its corresponding ensembl gene id,
   RefSeq accession id, entrez gene id and other detail information. This
   process was manually finished via searching and comparing the lncRNA
   related databases such as ensembl [[131]40], NONCODE [[132]41],
   Lncipedia [[133]42], lncRNAdb [[134]43], and HGNC. Then, lncRNA
   sequences were extracted from the RefSeq [[135]44]. We downloaded the
   expression level of 60245 genes (coding or non-coding genes matched
   with an ensembl id and gene symbol) in 16 tissues from the Expression
   Atlas [[136]45].

   Finally, we obtained 454 disease-lncRNA associations from lncRNADisease
   (between 162 diseases having known disease genes and 187 lncRNAs with
   known sequences and expression levels). Those 594 (79 cancers, 310
   lncRNAs) and 176 (86 diseases, 57 lncRNAs) more pairs were extracted
   from lnc2cancer and MNDR respectively. For those diseases that not
   exist in the above 2802 ones, disease genes were obtained from the CTD,
   DisgeNet [[137]46], OMIM and malaCard [[138]47]. The datasets are
   stored in [139]Supplementary File 5.

Disease gene chromosome preference analysis and disease vectorization method

   Human genes are located on mitochondrion and 24 unique chromosomes
   including 22 autosomes and two sex chromosomes. The genes’ locations on
   the chromosomes or mitochondrion have been labeled by the HGNC
   database. As disease related genes are distributed at varies locations
   and have a different number of each disease, we hypothesize that the
   gene distribution differences between diseases on the chromosomes or
   mitochondrion may reflect the divergences of the diseases. We also
   hypothesize that disease genes may have some preferred chromosomes for
   some diseases. This hypothesis can be investigated by the disease
   genes’ chromosomes enrichment analysis via fisher's exact test
   [[140]48]. Thus, it is better to characterize the distribution
   properties of disease genes on each of the chromosomes instead of on
   the whole known gene set (we call it a “part overcomes the whole”
   hypothesis).

   On the basis of these hypotheses, we considered to vectorize a disease
   via modeling the distribution property of its related gene set.
   However, with just the gene distribution characteristics, there may be
   no gene function information involved. Thus, we considered to extract
   the distribution properties of disease gene enriched KEGG pathways
   comparing to all the known pathways to inject complementary information
   for our vector representation of diseases. This vectorization process
   includes the following steps:

   Step1: Initialization. Sorting all known genes according to their
   chromosome locations and sorting all the human KEGG pathways by their
   ids.

   Step2: Grouping. Dividing the genes and pathways into groups. Producing
   a status series for each group with the length equals to the number of
   genes or pathways it contains. These statuses are initialized to be 0
   (inactivated).

   Step3: Mapping. For a given disease related gene set, mapping it to the
   gene groups and mapping its enriched pathways to the pathway groups.
   Then, setting the corresponding status of a gene or pathway in the
   status series to be 1 (activated) if it has been mapped.

   Step4: Vectorization. Calculating the status series’ k-mer information
   entropy of each gene group or pathway group to quantify them and
   constructing two sub-vectors for a given disease.

   Here, dividing all the genes and pathways into groups is to apply our
   “part overcomes the whole” hypothesis. In our Results section, we
   demonstrate that this strategy (part) is more effective for
   characterizing diseases comparing to the status series without dividing
   (the whole). As a chromosome always contains a p-arm and a q-arm, we
   divide the genes into groups according to the natural chromosome
   substructures. For the pathway status series, we divide it into T
   groups on average. (There is no guidance for us to divide pathways
   similar to chromosome structure). Finally, this vectorization model
   includes two parts: disease gene set vectorization and disease gene
   enriched pathway set vectorization.

   Let d represent a disease, and d[g] = {g[1], g[2], …, g[c], …, g[n]} be
   its related gene set. Let all of the approved genes from HGNC be G =
   {g[1], g[2], …, g[i], …, g[N]}, and the pathway set from KEGG database
   be P = {p[1], p[2], …, p[j], …, p[M]}. Let the unique genes in P be
   represented as G[p] = {g[1], g[2], …, g[A]} while each pathway related
   gene set as g[pj]. We define a k-mer sub-status series as (s1, s2, …,
   s[r], …, s[k]), where s[r] = 0 or 1. By definition, there can be 2^k
   possible k-mer sub-status series. The detail process is described as a
   pseudo codes in Algorithm [141]1 and outlined in Figure [142]1. The
   source codes can be referred to Supplementary Codes.

   The outputs of our vectorization algorithm are two fix length vectors:
   the disease gene distribution entropy vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   with length of S and the disease pathway distribution entropy vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   with length of T. To test whether our disease vectors are effective and
   to determine the parameters such as the k-mer sizes, we apply them to
   compute the disease similarities. For two given diseases d1 and d2, we
   derive their disease gene distribution entropy vectors
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><mr
   ow><mi>c</mi><mi>h</mi><mi>r</mi></mrow></msubsup><mo>></mo></mrow>
   :MATH]
   ,
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>d</mi><mn>2</mn></mrow><mr
   ow><mi>c</mi><mi>h</mi><mi>r</mi></mrow></msubsup><mo>></mo></mrow>
   :MATH]
   and their disease pathway distribution entropy vectors
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><mr
   ow><mi>p</mi><mi>a</mi><mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   ,
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>d</mi><mn>2</mn></mrow><mr
   ow><mi>p</mi><mi>a</mi><mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   with Algorithm [143]1. Then we compute the similarity between d1 and d2
   with their vectors. The similarity between d1 and d2 is denoted as Sim
   (d1, d2) and computed by:
   [MATH:
   <mrow><mo>{</mo><mtable><mtr><mtd><mrow><mi>s</mi><mi>i</mi><mi>m</mi><
   mi>G</mi><mi>e</mi><mrow><mo>(</mo><mrow><mi>d</mi><mn>1</mn><mo>,</mo>
   <mi>d</mi><mn>2</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mtext>
    </mtext><mi>i</mi><mi>f</mi><mrow><mo>‖</mo></mrow><mrow><mrow><msubsu
   p><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup></mrow><mo>‖</mo></mrow><mo>×</mo><mrow><mo>
   ‖</mo><mrow><mrow><mrow><msubsup><mi>V</mi><mrow><mi>d</mi><mn>2</mn></
   mrow><mrow><mi>c</mi><mi>h</mi><mi>r</mi></mrow></msubsup></mrow><mo>‖<
   /mo></mrow></mrow></mrow><mo>=</mo><mn>0</mn><mo>;</mo></mrow></mtd></m
   tr><mtr><mtd><mi>s</mi><mi>u</mi><mi>b</mi><mi>s</mi><mi>p</mi><mi>a</m
   i><mi>c</mi><mi>e</mi><mrow><mo>(</mo><mrow><msubsup><mi>V</mi><mrow><m
   i>d</mi><mn>1</mn></mrow><mrow><mi>c</mi><mi>h</mi><mi>r</mi></mrow></m
   subsup><mo>,</mo><msubsup><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><m
   row><mi>c</mi><mi>h</mi><mi>r</mi></mrow></msubsup></mrow><mo>)</mo></m
   row><mtext> </mtext><mi>e</mi><mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr
   ></mtable></mrow> :MATH]
   (1)
   [MATH:
   <mrow><mo>{</mo><mtable><mtr><mtd><mrow><mi>s</mi><mi>i</mi><mi>m</mi><
   mi>P</mi><mi>e</mi><mrow><mo>(</mo><mrow><mi>d</mi><mn>1</mn><mo>,</mo>
   <mi>d</mi><mn>2</mn></mrow><mo>)</mo></mrow><mo>=</mo><mn>0</mn><mtext>
    </mtext><mi>i</mi><mi>f</mi><mrow><mo>‖</mo></mrow></mrow><mrow><mrow>
   <msubsup><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><mrow><mi>p</mi><mi
   >a</mi><mi>t</mi><mi>h</mi></mrow></msubsup></mrow><mo>‖</mo></mrow><mo
   >×</mo><mrow><mo>‖</mo><mrow><mrow><mrow><msubsup><mi>V</mi><mrow><mi>d
   </mi><mn>1</mn></mrow><mrow><mi>p</mi><mi>a</mi><mi>t</mi><mi>h</mi></m
   row></msubsup></mrow><mo>‖</mo></mrow></mrow></mrow><mo>=</mo><mn>0</mn
   ><mo>;</mo></mtd></mtr><mtr><mtd><mi>s</mi><mi>u</mi><mi>b</mi><mi>s</m
   i><mi>p</mi><mi>a</mi><mi>c</mi><mi>e</mi><mrow><mo>(</mo><mrow><msubsu
   p><mi>V</mi><mrow><mi>d</mi><mn>1</mn></mrow><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>,</mo><msubsup><mi>V</mi><mrow
   ><mi>d</mi><mn>1</mn></mrow><mrow><mi>p</mi><mi>a</mi><mi>t</mi><mi>h</
   mi></mrow></msubsup></mrow><mo>)</mo></mrow><mtext> </mtext><mi>e</mi><
   mi>l</mi><mi>s</mi><mi>e</mi></mtd></mtr></mtable></mrow> :MATH]
   (2)
   [MATH:
   <mrow><mi>S</mi><mi>i</mi><mi>m</mi><mrow><mo>(</mo><mrow><mi>d</mi><mn
   >1</mn><mo>,</mo><mi>d</mi><mn>2</mn></mrow><mo>)</mo></mrow><mo>=</mo>
   <msup><mi>e</mi><mrow><mo>−</mo><mrow><mo>[</mo><mrow><mi>θ</mi><mo>×</
   mo><mi>s</mi><mi>i</mi><mi>m</mi><mi>G</mi><mi>e</mi><mo>+</mo><mrow><m
   o>(</mo><mrow><mn>1</mn><mo>−</mo><mi>θ</mi></mrow><mo>)</mo></mrow><mo
   >×</mo><mi>s</mi><mi>i</mi><mi>m</mi><mi>P</mi><mi>e</mi></mrow><mo>]</
   mo></mrow></mrow></msup></mrow> :MATH]
   (3)

   where θ is a parameter to mediate the ratio of each vector's
   contribution to the similarity. || ● || means the norm. subspace(x, y)
   is the function to obtain the angle between two vectors x and y. A
   larger value of Sim(d1, d2) shows more similar between the two
   diseases.

   The four parameters k1(the size of k-mer for gene series), k2 (the size
   of k-mer for pathway series), T and θ can be determined via a
   performance test through comparing the disease similarity with a
   benchmark dataset. We first set θ=1 to optimize k1 and set θ=0 to
   optimize k2, T with the objective of achieving the best performance.
   Then, the three parameters are set as the optimal values to select the
   best θ. Similarly, we can also apply subspaces between the disease gene
   status series (a disease is represented as a fixed-length vector with
   the elements equal to 0 or 1) or the pathway status series themselves
   instead to measure the similarities of diseases. We call them the
   disease gene status series vector method and the pathway status series
   vector method. In the Results section, we compare the performances of
   our status series methods and our entropy vector methods to prove our
   “part overcomes the whole” hypothesis.

Prioritizing disease related lncRNA genes

   We always just have the positive samples of disease-lncRNA
   associations, as the negative samples, namely the lncRNAs that do not
   relate to the diseases, are neglected or even cannot be obtained.
   Supervised learning algorithms are unable to deal with these
   situations. However, the Positive Unlabeled learning (PU learning)
   method [[144]49] can address this issue effectively. PU learning has
   been an effective method for solving similar problems in bioinformatics
   such as disease gene prediction [[145]50], predicting conformational
   B-cell epitopes [[146]51], splicing elucidation [[147]52] and kinase
   substrate prediction [[148]53]. These PU learning approaches are mainly
   derived from two types of PU learning algorithms: the biased-svm
   [[149]54] and Elkan et al's lemmas [[150]55]. The application of Elkan
   et al's lemmas requires the satisfaction of “selected completely at
   random assumption”, while the biased-svm methods need to tune a set of
   parameters. Mordelet et al [[151]24] proposed a bagging svm model for
   PU learning and proved that their model can match and even outperform
   the biased-svm algorithm. Especially, the bagging svm for PU learning
   algorithm can run considerably faster. We adopt this bagging svm PU
   learning to prioritize disease related lncRNA genes.

   Let Lnc be a lncRNA gene, represented as Lnc=l[1]l[2]… l[e] …l[O]. We
   calculate its k-mer frequency
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   and its expression profile
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   . As there are four kinds of nucleotides in a lncRNA sequence (i.e.,
   l[e] ϵ {A, G, C, T} ), there are 4^k possible k-mers. These k-mers are
   sorted by their alphabetic order. Their frequencies are counted via the
   window sliding mechanism with the window size of k and a step size 1,
   which are then the elements of the vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   . The expression profile of Lnc can be extracted from the Expression
   Atlas [[152]45]. The expression levels of the lncRNA gene in the 16
   tissues are the elements of the vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   .

   Then for a disease-lncRNA pair, e.g. d-Lnc, we construct another
   feature namely vector
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><mi
   >exp</mi></mrow></msub><mo>></mo></mrow> :MATH]
   , called the co-expression levels. This sub-vector can be constructed
   on the basis of the principle that a disease related lncRNA gene may
   show the preference of co-expressing with other genes associating with
   this disease (such as the lncRNA’s targets). This sub-vector contains
   three elements, i.e. the maximum, minimum and average spearman
   correlation coefficients
   [MATH:
   <mrow><mrow><mo>(</mo><mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><
   mi>o</mi><mo>−</mo><mi>exp</mi></mrow></msub><mo>></mo><mo>=</mo><mo><<
   /mo><msub><mrow><mi>m</mi><mi>a</mi><mi>x</mi></mrow><mrow><mi>c</mi><m
   i>o</mi><mo>−</mo><mi>e</mi><mi>x</mi><mi>p</mi></mrow></msub><mo>,</mo
   ><msub><mrow><mi>m</mi><mi>i</mi><mi>n</mi></mrow><mrow><mi>c</mi><mi>o
   </mi><mo>−</mo><mi>e</mi><mi>x</mi><mi>p</mi></mrow></msub><mo>,</mo><m
   i>a</mi><mi>v</mi><msub><mi>g</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><
   mi>e</mi><mi>x</mi><mi>p</mi></mrow></msub><mo>></mo></mrow><mo>)</mo><
   /mrow></mrow> :MATH]
   between the expression profile of Lnc and all the known disease d
   related genes’ expression profiles.

   The whole disease-lncRNA feature vector is formed by combining the five
   sub-vectors: the disease gene distribution entropy vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   (sf1), disease pathway distribution entropy vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>p</mi><mi>a</mi>
   <mi>t</mi><mi>h</mi></mrow></msubsup><mo>></mo></mrow> :MATH]
   (sf2), lncRNA sequence's k-mer frequency
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow></msubsup><mo>></mo><
   /mrow> :MATH]
   (sf3), lncRNA expression profile
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mrow><mi>L</mi><mi>n</mi><mi>c</mi>
   </mrow><mrow><mi>p</mi><mi>r</mi><mi>o</mi><mi>f</mi></mrow></msubsup><
   mo>></mo></mrow> :MATH]
   (sf4), and the co-expression features
   [MATH:
   <mrow><mo><</mo><msub><mi>V</mi><mrow><mi>c</mi><mi>o</mi><mo>−</mo><mi
   >e</mi><mi>x</mi><mi>p</mi></mrow></msub><mo>></mo></mrow> :MATH]
   (sf5). The pseudo codes for prioritizing the disease related lncRNAs
   with the bagging SVM for PU learning model are shown as Algorithm
   [153]2.

   In Algorithm [154]2, |PO| means the sample size of the positive
   dataset. The feature type means the type of combination of the five
   sub-vectors. The feature vector
   [MATH:
   <mrow><mo><</mo><msubsup><mi>V</mi><mi>d</mi><mrow><mi>c</mi><mi>h</mi>
   <mi>r</mi></mrow></msubsup><mo>,</mo><msubsup><mi>V</mi><mrow><mi>L</mi
   ><mi>n</mi><mi>c</mi></mrow><mrow><mi>s</mi><mi>e</mi><mi>q</mi></mrow>
   </msubsup><mo>></mo></mrow> :MATH]
   is used as the basic feature type. Adding the remaining sub-features to
   this basic type makes new feature types. The best one can be identified
   via comparing the results of the cross-validation experiments. After
   obtaining the scores for the unlabeled samples, we sort them. The
   larger scores imply that the samples are more likely to be positive
   ones.

CONCLUSION

   In this article, we proposed a novel disease vectorization
   representation and applied for a PU learning method to predict and
   prioritize disease related lncRNA genes. A disease is newly
   characterized here using the distribution properties of disease genes
   on the chromosome substructures and its related KEGG pathways to all
   the pathways. Our vectorization model can be applied to compute the
   disease similarities effectively. Testing on the benchmark datasets,
   our method can work better than the state-of-the-art methods.
   Especially, it can also work with only lncRNA sequences information or
   without known related association.

   Future work has been planned to improve the performance of our
   vectorization model. First, more accurate disease genes will be
   collected as our model critically relies on the reliability of disease
   genes. Secondly, more information will be introduced to decrease the
   disease gene dependency such as the disease symptom, the disease
   semantics and so on. Furthermore, the relationship between the disease
   genes and lncRNA targets will be considered to extract more effective
   features to predict disease-lncRNA gene associations.

SUPPLEMENTARY MATERIALS FIGURES AND TABLES

   [155]oncotarget-08-78901-s001.pdf^ (2.2MB, pdf)
   [156]oncotarget-08-78901-s002.xlsx^ (148KB, xlsx)
   [157]oncotarget-08-78901-s003.xls^ (7.2MB, xls)
   [158]oncotarget-08-78901-s004.xlsx^ (1.9MB, xlsx)
   [159]oncotarget-08-78901-s005.xlsx^ (4.8MB, xlsx)
   [160]oncotarget-08-78901-s006.zip^ (763.3KB, zip)

Acknowledgments