dataesr/scientific-paragraphs-categorization huggingface dataset:
(2016). Therefore, one can directly apply the SLM analytical formulas (see Materials and Methods) on the available SC emp as input, without the need for performing direct simulations to generate surrogate BOLD first. Extended Data Figure  3 -1B,C analyzes the expected performance of this "simulation-less" procedure, as benchmarked by applying it on the ADNI SC emp 1 FC emp subset. The boxplot in Extended Data Figure  3 -1B (centermost box) reports a median Pearson correlation between the linear virtual FC SLM and the actual empirical FC emp close to ;0. 24 for the ADNI dataset. This correlation is larger and rise to ;0. 37 for the healthy aging dataset, in which FC SLM are generated from SC emp using precisely the same algorithm. Extended Data Figure  3 -1C indicates then the percent loss in correlation that has been caused by using the common value G* ref and the analytical formula to evaluate the linear virtual FC SLM rather than direct simulations at the actual personalized optimum G* for each of the ADNI SC emp 1 FC emp subjects.
The median quality loss is ;0. 5%, indicating that the lack of personalized tuning of the SLM working point is only a minor issue and that is acceptable to speed-up completion by relying on analytical evaluations. The median Pearson correlations of ;0. 24 or ;0. 37 between the linear virtual FC SLM and the actual empirical FC emp for the ADNI and the healthy aging datasets, respectively, are significant but still absolutely weak. A way to assess whether linear SC-to-FC completion is worthy, despite these low correlation values, it is possible to compare the achieved reconstruction quality with the one that one could trivially achieve by simply taking the SC emp connectome itself as surrogate FC, since we know that SC and FC connectomes are already strongly related  (Hagmann et al. , 2008).
This strategy of using the other connectome to perform FC completion would be even faster than SLM-based completion. We thus computed the percent improvement in rendering FC emp via FC SLM for subjects in the ADNI SC emp 1 FC emp subset and for subjects in the healthy aging datasets. As shown in Extended Data Figure  2 -1A, for the ADNI dataset, the use of FC SLM resulted systematically in a worse performance (median drop D trivial ¼ À15%; for definition, see Materials and Methods) in reproducing the actual FC emp than using the other available connectome SC emp. However, in the case of the healthy aging dataset, the use of FC SLM resulted in a clearly better performance than when using the other connectome (median improvement D trivial ¼ 140%). Thus, the performance of linear SC-to-FC completion can be good but was not robustly maintained across the two considered datasets.
Nevertheless, it remains necessary to check, as previously for the FC SLM , that it constitutes an improvement on the trivial strategy over taking the other connectome as substitute (i. e. , taking FC to be identical to SC emp ). In Extended Data Figure  2 -1A, we show that this is indeed the case, unlike for linear SC-to-FC completion. The procedure sketched in Extended Data Table  1 -1 led to a median improvement on using the other connectome approaching ;20% for both datasets that can go as high as 160% in some subjects.
For this ADNI dataset, we measured a median Pearson correlation between the linear virtual SC SLM and the actual empirical SC emp close to ;0. 22. On the healthy aging dataset, this correlation rose even up to ;0. 42. Extended Data Table  2 -1 provides a pseudo-code for the linear FC-to-SC completion procedure (for all details, see Materials and Methods). linear FC-to-SC completions for the BOLD-only subjects in the considered ADNI and the healthy ageing datasets can be downloaded as part of Extended Data 1 SC_SLM. As for SC-to-FC completions, we confirmed if the performance reached by linear FC-to-SC completion is superior to the one that is obtainable through the trivial strategy of using the other connectome (in this case, the available FC emp ). In Extended Data Figure  2 -1B, we show that using SC SLM rather than FC emp as an ersatz for SC emp leads to drops of improvements in quality with a pattern similar to the reverse SC-to-FC completion, i.
The expected quality of reconstruction, as estimated from results on the ADNI SC emp 1 FC emp subset is reported in Figure  4B  and amounts to an expected correlation between SC MFM and SC emp of ;0. 31. For the healthy aging dataset, we obtain a slightly smaller median value of ;0. 28, but the difference is not statistically significant. Table  2  provides a compact pseudo-code for the nonlinear FC-to-SC completion procedure (for all details, see Materials and Methods). Non-linear FC-to-SC completions for the BOLD-only subjects in the considered ADNI dataset can be downloaded as part of Extended Data 1 SC_MFM. As for SC-to-FC completion, we then confirmed if the nonlinear FC-to-SC completion SC MFM does provide a superior reconstruction of SC emp than the trivial alternative offered by just taking the other connectome (the available FC emp ).
As shown in Extended Data Figure  2 -1B, the use of nonlinear FC-to-SC completion led to a median improvement on the order of ;15% for the ADNI dataset and of ;10% for the healthy aging dataset. If the improvement achieved by nonlinear completion is smaller than for linear completion in the healthy aging dataset, nonlinear FC-to-SC completions succeeds in the ADNI dataset where its linear counterpart failed. Therefore, nonlinear FC-to-SC computational generation provides a worthy strategy for data completion, although not yet as efficient as SC-to-FC completion. We note that nonlinear FC-to-SC completion, as for nonlinear SC-to-FC completion, is a non-deterministic procedure, meaning that a different SC MFM is generated depending on the starting initial condition SC* (0). However, the different nonlinear virtual surrogates lie at distances from the common actual ground truth SC emp which are tightly concentrated around the median correlation.
58 for the ADNI datast and 0. 64 for the healthy ageing dataset (blue boxplot). B, For 168 subjects from the ADNI-subset with only FC emp available, considering the linear bivirtual completion chain FC emp to SC SLM to FC bi- SLM , we obtained a median correlation between FC emp and FC bi-SLM equal to 0. 12 and 0. 42 for 49 subjects from healthy ageing dataset (green boxplot); simultaneously, considering the nonlinear bivirtual completion chain FC emp to SC MFM to FC bi-MFM , we obtained a median correlation between FC emp and FC bi-MFM equal to 0. 59 for the ADNI dataset and 0. 45 for the healthy ageing dataset (blue boxplot). SC bi-MFM we obtained a median correlation between SC emp and SC bi-MFM of ;0. 58 for ADNI dataset and ;0. 64 for the healthy aging dataset. This quality of rendering aligned well with the performance of the linear bivirtual completion with a correlation between SC emp and SC bi-SLM of ;0.
63 for the ADNI dataset. On the healthy aging dataset, linear bivirtual duals SC bi-SLM were of exceptionally high quality, reaching a correlation with SC emp nearly as high as ;0. 92. We then evaluated the quality of FC bivirt generation over the ADNI-subset of 168 subjects for which an FC emp matrix was available and over the healthy aging dataset (Fig. 5B ). Considering the nonlinear bivirtual completion chain FC emp to SC MFM to FC bi-MFM the median correlation between FC emp and FC bi-MFM was of ;0. 59 for the ADNI dataset and of ;0. 45 for the healthy aging dataset. Moving to linear bivirtual FC bi-SLM , the performance on the healthy aging dataset was of ;0. 42, equivalent to the nonlinear duals. However, linear bivirtual dualization failed for the ADNI dataset, with a correlation dropping to ;0.
The coefficient D Pers (see Materials and Methods) quantifying the percent improvement obtained by using personalized connectomes are tabulated in Table  5  for the different types of completion. Improvements by personalization were always positive, indicating that on average some subject-specific information is preserved. These numbers, however, are diverse between datasets and completion types. Furthermore, they should be compared with the uncertainty itself existing on empirical connectomes. Indeed the D Pers analysis implicitly assume that empirical connectomes are exact reference comparison terms. In reality, there is a strong uncertainty on empirical connectome themselves, with an elevated test-retest variability within individual subjects  (Wang et al. , 2012; Chen et al. , 2015; Termenon et al.
, 2016). In particular, the connectomic dataset released together with the study by  Termenon et al. (2016)  allows an evaluation of what would be the expected "empirical personalization improvement" in the case in which we actually had to compare two connectomes obtained empirically for a same subject and assess how more similar are they between them, than to a connectome of the same type but obtained from a different subject. Termenon et al. (2016)  considers data mediated from the Human Connectome Project and provides for 100 subjects two different FC emp matrices deriving from different scans. Using a definition of the D Pers coefficient analogous to the one used for virtual and bivirtual completions but adapted to these test-retest empirical dataset, one can estimate a value of D Pers of about ;122% for empirical FCs.
As shown in Figure  6  and Extended Data Table  5 -1, the correlation between the intersubject distances in real and bidual spaces were noticeable and significant, for both ADNI and healthy aging datasets and for both MFM-based and SLMbased approaches (Extended Data Table 5-1), apart from the very poor performance of bivirtual linear FC completion in the ADNI (expected, given previously reported failures in this case). We also noticed that distances between bivirtual duals were often amplified, with respect to the original empirical distances. The space of dual bivirtual connectomes can thus be considered as a "virtual mirror" of the real connectome space, reproducing to a reasonable extent despite some deformation of the geometry of the original distribution of subjects.
Subject classification based on real and virtual connectomes The compilation of large datasets, including connectivity data from structural and functional neuroimaging is considered essential for the development of algorithmic patient stratification and predictive approaches. Here, we have described approaches for connectomic data completion and studied their consistency. We now show that such completion procedures are also compliant, in perspective, with the extraction via machine learning algorithms of the personalized information preserved in duals. As a first proof-of-concept, we studied here two simple (and academic) supervised classification problems in which subjects are separated into different classes based on connectomic features, empirical and/or virtual, used as input. First, in the ADNI dataset, we try separating subjects into two subgroups of control and patients (i.
e. , MCI or AD) subjects. Second, in the healthy aging dataset, we separate subjects into four classes of age, from the youngest to the oldest. Importantly, input features can be computed from all different types of connectomes (at least for the subjects for which they were available): empirical SC emp or FC emp ; their virtual duals FC MFM or SC MFM ; or their bivirtual duals SC bi- MFM or FC bi-MFM (see Fig. 7 ).
Discriminating control and patient subjects in the ADNI dataset For the first toy classification problem, we used target classification labels already provided within the ADNI A, Data completion procedures can be seen as bridges between different connectome spaces, mapping empirical connectomes in real space to subject-specific dual connectomes in virtual or bivirtual spaces, depending on the number of virtualization steps applied to the original connectome. Subjects classifications into controls (light blue) or MCI (yellow) and AD (red) patients are shared between empirical connectomes and their virtual and bivirtual duals. Virtual duals have a different nature than their associated empirical connectomes (empirical SCs are mapped to virtual FCs and vice versa), while bivirtual duals have the same nature.
In panel B, we show an dataset, assuming them to be exact (for a summary of the used stratification criteria, see Materials and Methods). We performed then classification based on input vectors of regional node strengths estimated subject-by-subject from the connectome matrices of interest (Q = 96 input features, corresponding to the number of brain regions in the used parcellation, see Materials and Methods). As supervised classifier algorithm, we chose a variant  (Seiffert et al. , 2010)  of the random forest algorithm, which is particularly suitable when the number of input features is of the same order of the number of available data-points in the training set  (Breiman, 2001) , as in our case. Examples of ADNI classifications based on empirical connectomes are shown in Figure  7 , notably, based on SC emp matrices (Fig.
69 for the SC emp on SC emp classifier and to ;0. 75 for the FC emp on FC emp classifier. AUC scores for different types of classification on the ADNI dataset are compiled in Extended Data Table  3-1, Table 3-2. We considered then ADNI classification based on virtual and bivirtual duals instead of empirical connectomes. In this case of "dual space classification" (Fig. 7B ), virtual and bivirtual duals are used both when training the classifiers and when evaluating them. Therefore, to classify a new empirical connectome with a "dual space classifier," it is first necessary to "lift" it in dual space, i. e. , to map it via data completion algorithms to the suitable type of dual for which the classifier has been trained. Figure  7B  shows two examples of dual space ADNI classification based on FC MFM (blue curve, median AUC ;0.
Discriminating age classes in the healthy aging dataset For the second toy classification problem, we split the subjects in the healthy aging datasets into four age categories and used the ordinal number of the age class from I to IV as target classification label. As input features we did not use any more high-dimensional vectors of connection strengths but the loadings on the first 10 principal components of each connectivity matrices. As classifier we still used random forests Breiman algorithm (for full detail, see Materials and Methods). As before, we highlight here a few examples of classification with real empirical connectomes (Fig. 7D ), classification in dual space (Fig. 7E ) and continued example of cross-space classification, compared with a real connectome space classification: in green classification with classifiers trained on empirical FCs evaluated on other empirical FCs; and in orange, classification with classifiers trained on bivirtual FCs evaluated directly on other empirical FCs, without prior "lifting" into bivirtual dual space.
In all the shown cases, classifications performed with classifiers trained in virtual or bivirtual connectomes are slightly less performing than for classifiers trained on empirical data, but the drop in performance is not significant for most thresholds. D-F, The confusion matrix for classification of four age classes of the healthy aging database using the random forest Breiman algorithm is shown. D, When the classifier was trained and tested on the empirical SC and FC connectome, the accuracy was closed to ;0. 37 and ;0. 43, respectively. E, The classification accuracy for the classifier which was trained and tested on the virtual connectomes was above the chance level (;0. 25) with ;0. 43 for SC SLM and ;0. 43 for FC MFM connectomes which the performance was better or equivalent to the empirical connectome (D).
F, Here, we shown the classification performance of cross-training, when the classifier was trained on SC MFM and tested on FC emp with accuracy equal to ;0. 35 (F-center) and when the classifier was trained on FC SLM and tested on FC emp with accuracy of ;0. 30 (F-right; see Extended Data Fig. 7 -1 for the classification performances on other virtual connectomes from healthy aging dataset). cross-space classification (Fig. 7F ). We characterize performance both in terms of general accuracy (fraction of subjects correctly classified in their age class) and of detailed confusion matrices between the actual and the predicted age classes, revealing typical error syndromes. General accuracies were typically above the chance level of ;25%, approaching (or exceeding), for instance, ;37% for classifiers: trained and tested on SC emp (Fig.
, 2020). The analysis of factors explaining misclassification goes however beyond the scope of the present study. As a matter of fact, we are still far from providing authentically useful examples of classification, neither on the ADNI dataset nor on the healthy aging dataset. However, this was not our aim here, the chosen classification problems themselves being rather academic and serving as first proofs-of-concept. Importantly, we can at least show that dual and cross-space classification performance, if not good, was not much worse than for real empirical connectomes. This step is already sufficient to show that empirical and virtual duals share an extractable part of information and that this shared information can be still relevant for classification. Such information preservation, despite loose correspondence, can be explained by revealing the similarity of network topology features between real connectomes and their bivirtual duals, independently from our capacity to achieve more or less performing classifications based on these features.
Matching network topology between real and virtual connectomes The connectome matrices describe the weighted undirected topology of graphs of structural or FC. All information conveyed by these connectomes about pathology or other conditions is potentially encoded into this network topology. While genuine model-free analyses of network topology across all scales are still under development, see, for instance, promising topological data analyses approaches  (Petri et al. , 2014; Sizemore et al. , 2018) , classic graph theoretical features provide a first multifaceted characterization of the specific features of each individual connectome object  (Bullmore and Sporns, 2009). We evaluated here for each empirical connectome SC emp or FC emp a spectrum of different graph theoretical features. In particular we evaluated for both the ADNI and the healthy aging datasets and for each brain region within each of the connectomes (for details, see Materials and Methods): the total strengths (sum of the connection weights of all the links incident the region), the clustering coefficients (tendency of the regions neighboring to the considered node to also be interconnected between them), and the centrality coefficients (tendency for any path linking two different nodes in the network to pass through the considered node), evaluated via the PageRank algorithm  (Brin and Page, 1998).
We also evaluated for each connectome its modular partition into communities, by using a Louvain algorithm with default parameters  (Blondel et al. , 2008). Finally, we also inspected the global link weight distributions. We then evaluated analogous quantities for the dual connectomes associated with each of the connectomes, focusing here, for conciseness and simplicity, on bivirtual duals, sharing a common nature (structural or functional) with their correspondent empirical partner. In Figure  8 , we illustrate this correspondence between graph-theoretical features evaluated for different real/bivirtual dual connectome pairs in the ADNI dataset. An analogous figure for the healthy aging dataset is shown in Extended Data Figure  8 -1, showing qualitatively equivalent results. To compare node degrees, clustering and centrality features we plot, for every brain region in every connectome, the feature value evaluated in a real connectome against the corresponding feature value evaluated in the associated bivirtual dual.
55 (95% bootstrap confidence interval) for regional centralities. Correlations are found even for regional clustering coefficients, even if the small values of clustering coefficients observed in SC emp connectomes are systematically overestimated in the denser bivirtual dual SC biMFM. Finally, concerning community matching, for SC and FC real/bivirtual dual pairs we found a median relative mutual information of ;61% and ;45%, respectively, for the ADNI dataset, safely above chance level (estimated at ;16%, permutation-based 95% confidence interval; see Table  3  for the superior correspondence at the single subject level). For the healthy aging dataset, for both SC and FC these correlations were even higher (Extended Data Fig. 8-1 ) with CC median % 0. 8 for regional strengths, centralities, and clustering coefficients of SC real/bivirtual dual parts and CC median % 0.
7 for the FC real/bivirtual dual parts. Finally, for the community matching for SC pairs the median relative mutual information was ;44% and for FC pairs ;50% (see Table  4  for the superior correspondence at the single subject level for healthy aging dataset). The analyses of Figure  8  and Extended Data Figure  8 -1 are performed at the ensemble level, i. e. , pooling network features estimated from different subjects into a same point cloud. However, network features can have important variations of values not only across regions but also across subjects, which is expected to be a key indicator of subject-specific traits useful for classification. The for the healthy aging dataset). In both cases, there is a remarkable correlation at the ensemble level between network topology features for empirical bivirtual connectomes (see Table  3  for the even superior correspondence at the single subject level for the ADNI dataset).
capability to preserve these traits would thus be a crucial factor allowing the achievement of personalization when generating virtual and bivirtual duals. Therefore, we computed correlations between vectors of regional features in real and empirical connectomes but now limited to be within individual subjects obtaining thus, for every feature type, a different correlation value for every subject. Table  3  (for the ADNI dataset) and Table  4  (for the healthy aging dataset) show that within-subject correlations were also high (apart for SC clustering) and, for FC, even superior to ensemble-level correlations, manifesting, once again, the personalized nature of bivirtual dual connectomes. Indeed, when computing personalized correlations for pairs of real and bivirtual connectomes associated to a same matching subject, they resulted systematically superior to unpersonalized control correlations evaluated over real/bivirtual connectome pairs assembled out of different subjects (see Materials and Methods).
Percent improvements in same-subject real/dual correlations with respect to average correlations in cross-subject pairs are compiled as well in Tables  3, 4. Personalization can lead to very strong percent improvements in real/virtual topology correlations, particularly in the case of FC connectomes. The operation of dualization thus preserves aspects of network topology which are specific to each subject and not just generic to a connectome ensemble. Finally, we plot in Extended Data Figure  6 -1, global distributions of link weights for the different types of connectomes and both datasets. Most distributions displayed an overall similarity in shape: SC weights distributions with a peak at small values and a fat right tail; FC weights distribution more symmetric and with a broader peak at intermediate strengths.