revise using AI model\n\nUsing the OpenAI model gpt-3.5-turbo

content/01.abstract.md

@@ -2,9 +2,9 @@
 
 Correlation coefficients are widely used to identify patterns in data that may be of particular interest.
 In transcriptomics, genes with correlated expression often share functions or are part of disease-relevant biological processes.
-Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient, easy-to-use and not-only-linear coefficient based on machine learning models.
+Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient, easy-to-use, and not-only-linear coefficient based on machine learning models.
 CCC reveals biologically meaningful linear and nonlinear patterns missed by standard, linear-only correlation coefficients.
 CCC captures general patterns in data by comparing clustering solutions while being much faster than state-of-the-art coefficients such as the Maximal Information Coefficient.
 When applied to human gene expression data, CCC identifies robust linear relationships while detecting nonlinear patterns associated, for example, with sex differences that are not captured by linear-only coefficients.
 Gene pairs highly ranked by CCC were enriched for interactions in integrated networks built from protein-protein interaction, transcription factor regulation, and chemical and genetic perturbations, suggesting that CCC could detect functional relationships that linear-only methods missed.
-CCC is a highly-efficient, next-generation not-only-linear correlation coefficient that can readily be applied to genome-scale data and other domains across different data types.
+CCC is a highly efficient, next-generation not-only-linear correlation coefficient that can readily be applied to genome-scale data and other domains across different data types.

content/02.introduction.md

@@ -20,18 +20,18 @@ Therefore, advanced correlation coefficients could immediately find wide applica
 
 The Pearson and Spearman correlation coefficients are widely used because they reveal intuitive relationships and can be computed quickly.
 However, they are designed to capture linear or monotonic patterns (referred to as linear-only) and may miss complex yet critical relationships.
-Novel coefficients have been proposed as metrics that capture nonlinear patterns such as the Maximal Information Coefficient (MIC) [@pmid:22174245] and the Distance Correlation (DC) [@doi:10.1214/009053607000000505].
-MIC, in particular, is one of the most commonly used statistics to capture more complex relationships, with successful applications across several domains [@pmid:33972855; @pmid:33001806; @pmid:27006077].
-However, the computational complexity makes them impractical for even moderately sized datasets [@pmid:33972855; @pmid:27333001].
-Recent implementations of MIC, for example, take several seconds to compute on a single variable pair across a few thousand objects or conditions [@pmid:33972855].
-We previously developed a clustering method for highly diverse datasets that significantly outperformed approaches based on Pearson, Spearman, DC and MIC in detecting clusters of simulated linear and nonlinear relationships with varying noise levels [@doi:10.1093/bioinformatics/bty899].
+Novel coefficients have been proposed as metrics that capture nonlinear patterns such as the Maximal Information Coefficient (MIC) and the Distance Correlation (DC).
+MIC, in particular, is one of the most commonly used statistics to capture more complex relationships, with successful applications across several domains.
+However, the computational complexity makes them impractical for even moderately sized datasets.
+Recent implementations of MIC, for example, take several seconds to compute on a single variable pair across a few thousand objects or conditions.
+We previously developed a clustering method for highly diverse datasets that significantly outperformed approaches based on Pearson, Spearman, DC, and MIC in detecting clusters of simulated linear and nonlinear relationships with varying noise levels.
 Here we introduce the Clustermatch Correlation Coefficient (CCC), an efficient not-only-linear coefficient that works across quantitative and qualitative variables.
 CCC has a single parameter that limits the maximum complexity of relationships found (from linear to more general patterns) and computation time.
 CCC provides a high level of flexibility to detect specific types of patterns that are more important for the user, while providing safe defaults to capture general relationships.
 We also provide an efficient CCC implementation that is highly parallelizable, allowing to speed up computation across variable pairs with millions of objects or conditions.
-To assess its performance, we applied our method to gene expression data from the Genotype-Tissue Expression v8 (GTEx) project across different tissues [@doi:10.1126/science.aaz1776].
+To assess its performance, we applied our method to gene expression data from the Genotype-Tissue Expression v8 (GTEx) project across different tissues.
 CCC captured both strong linear relationships and novel nonlinear patterns, which were entirely missed by standard coefficients.
 For example, some of these nonlinear patterns were associated with sex differences in gene expression, suggesting that CCC can capture strong relationships present only in a subset of samples.
 We also found that the CCC behaves similarly to MIC in several cases, although it is much faster to compute.
-Gene pairs detected in expression data by CCC had higher interaction probabilities in tissue-specific gene networks from the Genome-wide Analysis of gene Networks in Tissues (GIANT) [@doi:10.1038/ng.3259].
+Gene pairs detected in expression data by CCC had higher interaction probabilities in tissue-specific gene networks from the Genome-wide Analysis of gene Networks in Tissues (GIANT).
 Furthermore, its ability to efficiently handle diverse data types (including numerical and categorical features) reduces preprocessing steps and makes it appealing to analyze large and heterogeneous repositories.

content/04.05.results_intro.md

@@ -10,14 +10,14 @@ Vertical and horizontal red lines show how CCC clustered data points using $x$ a
 ](images/intro/relationships.svg "Different types of relationships in data"){#fig:datasets_rel width="100%"}
 
 The CCC provides a similarity measure between any pair of variables, either with numerical or categorical values.
-The method assumes that if there is a relationship between two variables/features describing $n$ data points/objects, then the **cluster**ings of those objects using each variable should **match**.
+The method assumes that if there is a relationship between two variables/features describing $n$ data points/objects, then the clusterings of those objects using each variable should match.
 In the case of numerical values, CCC uses quantiles to efficiently separate data points into different clusters (e.g., the median separates numerical data into two clusters).
 Once all clusterings are generated according to each variable, we define the CCC as the maximum adjusted Rand index (ARI) [@doi:10.1007/BF01908075] between them, ranging between 0 and 1.
 Details of the CCC algorithm can be found in [Methods](#sec:ccc_algo).
 
 
-We examined how the Pearson ($p$), Spearman ($s$) and CCC ($c$) correlation coefficients behaved on different simulated data patterns.
-In the first row of Figure @fig:datasets_rel, we examine the classic Anscombe's quartet [@doi:10.1080/00031305.1973.10478966], which comprises four synthetic datasets with different patterns but the same data statistics (mean, standard deviation and Pearson's correlation).
+We examined how the Pearson ($p$), Spearman ($s$), and CCC ($c$) correlation coefficients behaved on different simulated data patterns.
+In the first row of Figure @fig:datasets_rel, we examine the classic Anscombe's quartet [@doi:10.1080/00031305.1973.10478966], which comprises four synthetic datasets with different patterns but the same data statistics (mean, standard deviation, and Pearson's correlation).
 This kind of simulated data, recently revisited with the "Datasaurus" [@url:http://www.thefunctionalart.com/2016/08/download-datasaurus-never-trust-summary.html; @doi:10.1145/3025453.3025912; @doi:10.1111/dsji.12233], is used as a reminder of the importance of going beyond simple statistics, where either undesirable patterns (such as outliers) or desirable ones (such as biologically meaningful nonlinear relationships) can be masked by summary statistics alone.
 
 

content/04.10.results_comp.md

@@ -6,12 +6,12 @@ We selected the top 5,000 genes with the largest variance for our initial analys
 
 We examined the distribution of each coefficient's absolute values in GTEx (Figure @fig:dist_coefs).
 CCC (mean=0.14, median=0.08, sd=0.15) has a much more skewed distribution than Pearson (mean=0.31, median=0.24, sd=0.24) and Spearman (mean=0.39, median=0.37, sd=0.26).
-The coefficients reach a cumulative set containing 70% of gene pairs at different values (Figure @fig:dist_coefs b), $c=0.18$, $p=0.44$ and $s=0.56$, suggesting that for this type of data, the coefficients are not directly comparable by magnitude, so we used ranks for further comparisons.
+The coefficients reach a cumulative set containing 70% of gene pairs at different values (Figure @fig:dist_coefs b), $c=0.18$, $p=0.44$ and $s=0.56, suggesting that for this type of data, the coefficients are not directly comparable by magnitude, so we used ranks for further comparisons.
 In GTEx v8, CCC values were closer to Spearman and vice versa than either was to Pearson (Figure @fig:dist_coefs c).
 We also compared the Maximal Information Coefficient (MIC) in this data (see [Supplementary Note 1](#sec:mic)).
 We found that CCC behaved very similarly to MIC, although CCC was up to two orders of magnitude faster to run (see [Supplementary Note 2](#sec:time_test)).
 MIC, an advanced correlation coefficient able to capture general patterns beyond linear relationships, represented a significant step forward in correlation analysis research and has been successfully used in various application domains [@pmid:33972855; @pmid:33001806; @pmid:27006077].
-These results suggest that our findings for CCC generalize to MIC, therefore, in the subsequent analyses we focus on CCC and linear-only coefficients.
+These results suggest that our findings for CCC generalize to MIC; therefore, in the subsequent analyses, we focus on CCC and linear-only coefficients.
 
 
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@@ -24,7 +24,7 @@ These results suggest that our findings for CCC generalize to MIC, therefore, in
 
 A closer inspection of gene pairs that were either prioritized or disregarded by these coefficients revealed that they captured different patterns.
 We analyzed the agreements and disagreements by obtaining, for each coefficient, the top 30% of gene pairs with the largest correlation values ("high" set) and the bottom 30% ("low" set), resulting in six potentially overlapping categories.
-For most cases (76.4%), an UpSet analysis [@doi:10.1109/TVCG.2014.2346248] (Figure @fig:upsetplot_coefs a) showed that the three coefficients agreed on whether there is a strong correlation (42.1%) or there is no relationship (34.3%).
+For most cases (76.4%), an UpSet analysis (Figure 1) showed that the three coefficients agreed on whether there is a strong correlation (42.1%) or there is no relationship (34.3%).
 Since Pearson and Spearman are linear-only, and CCC can also capture these patterns, we expect that these concordant gene pairs represent clear linear patterns.
 CCC and Spearman agree more on either highly or poorly correlated pairs (4.0% in "high", and 7.0% in "low") than any of these with Pearson (all between 0.3%-3.5% for "high", and 2.8%-5.5% for "low").
 In summary, CCC agrees with either Pearson or Spearman in 90.5% of gene pairs by assigning a high or a low correlation value.
@@ -41,9 +41,9 @@ A logarithmic scale was used to color each hexagon.
 
 
 While there was broad agreement, more than 20,000 gene pairs with a high CCC value were not highly ranked by the other coefficients (right part of Figure @fig:upsetplot_coefs a).
-There were also gene pairs with a high Pearson value and either low CCC (1,075), low Spearman (87) or both low CCC and low Spearman values (531).
+There were also gene pairs with a high Pearson value and either low CCC (1,075), low Spearman (87), or both low CCC and low Spearman values (531).
 However, our examination suggests that many of these cases appear to be driven by potential outliers (Figure @fig:upsetplot_coefs b, and analyzed later).
-We analyzed gene pairs among the top five of each intersection in the "Disagreements" group (Figure @fig:upsetplot_coefs a, right) where CCC disagrees with Pearson, Spearman or both.
+We analyzed gene pairs among the top five of each intersection in the "Disagreements" group (Figure @fig:upsetplot_coefs a, right) where CCC disagrees with Pearson, Spearman, or both.
 
 ![
 **The expression levels of *KDM6A* and *UTY* display sex-specific associations across GTEx tissues.**
@@ -53,6 +53,6 @@ CCC captures this nonlinear relationship in all GTEx tissues (nine examples are
 The first three gene pairs at the top (*IFNG* - *SDS*, *JUN* - *APOC1*, and *ZDHHC12* - *CCL18*), with high CCC and low Pearson values, appear to follow a non-coexistence relationship: in samples where one of the genes is highly (slightly) expressed, the other is slightly (highly) activated, suggesting a potentially inhibiting effect.
 The following three gene pairs (*UTY* - *KDM6A*, *RASSF2* - *CYTIP*, and *AC068580.6* - *KLHL21*) follow patterns combining either two linear or one linear and one independent relationships.
 In particular, genes *UTY* and *KDM6A* (paralogs) show a nonlinear relationship where a subset of samples follows a robust linear pattern and another subset has a constant (independent) expression of one gene.
-This relationship is explained by the fact that *UTY* is in chromosome Y (Yq11) whereas *KDM6A* is in chromosome X (Xp11), and samples with a linear pattern are males, whereas those with no expression for *UTY* are females.
+This relationship is explained by the fact that *UTY* is on chromosome Y (Yq11) whereas *KDM6A* is on chromosome X (Xp11), and samples with a linear pattern are males, whereas those with no expression for *UTY* are females.
 This combination of linear and independent patterns is captured by CCC ($c=0.29$, above the 80th percentile) but not by Pearson ($p=0.24$, below the 55th percentile) or Spearman ($s=0.10$, below the 15th percentile).
 Furthermore, the same gene pair pattern is highly ranked by CCC in all other tissues in GTEx, except for female-specific organs (Figure @fig:gtex_tissues:kdm6a_uty).

content/04.12.results_giant.md

@@ -11,7 +11,7 @@ For example, we obtained the networks in blood and the automatically-predicted c
 In addition to the gene pair, the networks include other genes connected according to their probability of interaction (up to 15 additional genes are shown), which allows estimating whether genes are part of the same tissue-specific biological process.
 Two large black nodes in each network's top-left and bottom-right corners represent our gene pairs.
 A green edge means a close-to-zero probability of interaction, whereas a red edge represents a strong predicted relationship between the two genes.
-In this example, genes *RASSF2* and *CYTIP* (Figure @fig:giant_gene_pairs a), with a high CCC value ($c=0.20$, above the 73th percentile) and low Pearson and Spearman ($p=0.16$ and $s=0.11$, below the 38th and 17th percentiles, respectively), were both strongly connected to the blood network, with interaction scores of at least 0.63 and an average of 0.75 and 0.84, respectively (Supplementary Table @tbl:giant:weights).
+In this example, genes *RASSF2* and *CYTIP* (Figure @fig:giant_gene_pairs a), with a high CCC value ($c=0.20$, above the 73rd percentile) and low Pearson and Spearman ($p=0.16$ and $s=0.11$, below the 38th and 17th percentiles, respectively), were both strongly connected to the blood network, with interaction scores of at least 0.63 and an average of 0.75 and 0.84, respectively (Supplementary Table @tbl:giant:weights).
 The autodetected cell type for this pair was leukocytes, and interaction scores were similar to the blood network (Supplementary Table @tbl:giant:weights).
 However, genes *MYOZ1* and *TNNI2*, with a very high Pearson value ($p=0.97$), moderate Spearman ($s=0.28$) and very low CCC ($c=0.03$), were predicted to belong to much less cohesive networks (Figure @fig:giant_gene_pairs b), with average interaction scores of 0.17 and 0.22 with the rest of the genes, respectively.
 Additionally, the autodetected cell type (skeletal muscle) is not related to blood or one of its cell lineages.
@@ -38,7 +38,7 @@ Red indicates CCC-only tissues/cell types, blue are Pearson-only, and purple are
 We next performed a systematic evaluation using the top 100 discrepant gene pairs between CCC and the other two coefficients.
 For each gene pair prioritized in GTEx (whole blood), we autodetected a relevant cell type using GIANT to assess whether genes were predicted to be specifically expressed in a blood-relevant cell lineage.
 For this, we used the top five most commonly autodetected cell types for each coefficient and assessed connectivity in the resulting networks (see [Methods](#sec:giant)).
-The top 5 predicted cell types for gene pairs highly ranked by CCC and not by the rest were all blood-specific (Figure @fig:giant_gene_pairs c, top left), including macrophage, leukocyte, natural killer cell, blood and mononuclear phagocyte.
+The top 5 predicted cell types for gene pairs highly ranked by CCC and not by the rest were all blood-specific (Figure @fig:giant_gene_pairs c, top left), including macrophage, leukocyte, natural killer cell, blood, and mononuclear phagocyte.
 The average probability of interaction between genes in these CCC-ranked networks was significantly higher than the other coefficients (Figure @fig:giant_gene_pairs c, top right), with all medians larger than 67% and first quartiles above 41% across predicted cell types.
 In contrast, most Pearson's gene pairs were predicted to be specific to tissues unrelated to blood (Figure @fig:giant_gene_pairs c, bottom left), with skeletal muscle being the most commonly predicted tissue.
 The interaction probabilities in these Pearson-ranked networks were also generally lower than in CCC, except for blood-specific gene pairs (Figure @fig:giant_gene_pairs c, bottom right).