dataesr/scientific-paragraphs-categorization huggingface dataset:
Introduction Feature selection is a critical task in classification problems, especially when dealing with noisy data of complex structure. Common feature selection techniques rely on individual feature evaluations  [1]  assuming independence between features. However, this condition is rarely met in practice  [2, 3]. For example, in micro-array datasets, the expression of certain genes, known to be biologically important for class differentiation, may appear relevant only when evaluated within groups  [4]. This suggests that in complex data domains, even if the support of an individual feature may be small, its contribution to the support of feature subsets may be significant. Diverse techniques have been proposed for evaluating the support of feature subsets in classification problems, including genetic algorithms  [5] , statistical methods based on mutual information  [6]  and fuzzy measures  [7, 8, 9].
This can be accomplished by computing the generalized interaction index proposed in  [23] , hereafter called GI. Its computation requires reliable fuzzy measures and thus, special attention must be paid to raw data preprocessing steps and to the fuzzy measures identification process itself. In this paper, a robust feature selection strategy, based on the GI characterization of feature subsets regarding their relevance to classification problems, is proposed. With this intention, we first analyze GI results when standard raw data conversion procedure is used for the HLM Sr estimation of fuzzy measures. As a result of this study, a raw data conversion procedure based on normalized confidence degrees and an improved version of the HLM Sr algorithm are proposed. Aiming to understand some unexpected GI results previously reported in literature  [14, 23] , we study the GI behavior on homogeneous datasets, i.
e. , datasets where, in each class, all features are either redundant or complementary possibly including noisy features. As a result of this study, some guidelines for the efficient GI characterization of feature subsets in homogeneous datasets are introduced. The outline of the paper is as follows. In Section 2, fuzzy measures, the discrete Choquet integral and GI are briefly reviewed. Then, fuzzy measure identification process with HLM Sr is analyzed, and some modifications to the algorithm are introduced in Section 3. Section 4 deals with the conversion from raw data into confidence degrees. In Section 5, the GI behavior is studied yielding two theorems (proofs are in the appendix). The usefulness of feature subset selection guided by GI characterizations is evaluated in Section 6 with UCI 1  benchmark classification problems.
xj ik represents the normalized confidence degree over all the classes. This normalization remarkably improved classification results (100% of accuracy for the Atom dataset). However, anomalous GI results were still observed for completely redundant features, i. e. , with features having exactly the same values. Although, these type of features rarely occur in practice, they are frequent after raw data conversion into confidence degrees. Let us consider the data shown in Figure  2. The problem involves two completely relevant redundant features (V 1 and V 2) as well as a noisy one, V 3, not shown). For both classes, any of the V 1 or V 2 features is able to classify the samples. This leads to binary confidence degrees, either {1, 1} or {0, 0} for the pair V 1-V 2. In this case only the pair, and none of the singletons, would be updated, yielding unexpected GI values.
Characterization of feature subsets by fuzzy measures and the GI index To gain insight into the GI behavior, simulations were performed using a synthetic Master dataset with seven normalized and commensurable features, i. e. , normalized confidence degrees, A1 to A7, and one binary target T (see Table  3 ). It can be observed that features A1 and A2 are redundant for class 1 (T=1) since either A1 or A2 can be used for class identification. Features A3 and A4 are complementary for class 1. Finally, features A5 to A7 can be considered noise for both classes. From the Master data, three datasets, Inf , Red and Comp. They correspond to typical situations like noise, redundancy or complementariness. The Inf dataset, A1, A5 to A7 and T , contains only one informative feature, A1. The Red one, A1, A2, A5, A6 and T , includes two redundant features, A1 and A2.
In the Comp dataset, A3, A4, A5, A6 and T , A3 and A4 are complementary for class 1. These three datasets are used to analyze the effectiveness of HLM Sr for fuzzy measure estimation and the posterior computation of GI values. In these experiments, HLM Sr was set to work with a maximum of 1000 iterations and a learning rate α = 0. 01. Results on the Inf dataset are shown in Table  4. Fuzzy measure coefficients turn to be binary valued, being one for the informative feature A1, and for all subsets containing it, in agreement with the monotonicity constraint. As expected, they are zero for all subsets including only noisy features. Although being informative, fuzzy measure coefficient may be difficult to analyze due to the monotonicity constraint. The GI values make the analysis easy: in this case, the only non null value is the one of the informative feature.
Theorem 1 -Complementary features Let N be a dataset with n features among which, for a given class, c of them are fully complementary and n-c are noise. Let C be the subset defined by the c fully complementary features. The GI for power set members of C with cardinality a ∈ {1,. , c} is: GI(a) = 1 c -a + 1 This yields 1/c for each of the c singletons and 1 for the whole feature subset C.
Theorem 2 -Redundant features Let N be a dataset with n features among which, for a given class, r of them are fully redundant and n -r are noise. Let R be the subset defined by the r fully redundant features. The GI for power set members of R with cardinality a ∈ {1,. , r} is: GI(a) = (-1) a+1 r -a + 1 This yields 1/r for each of the r singletons, 1 for the whole feature subset R when r is odd and -1 when r is even. The above results are used to propose some feature selection guidelines. Pairs: In this case, the union of complementary feature pairs, i. e. , those with a significant positive GI, must be enriched with features coming from redundant feature pairs, i. e. , those with a significant negative GI. This can be accomplished by checking that at least one of the features in each redundant feature pair is in the final set of selected features.
Experimental results The fuzzy measure and interaction index approach for feature selection and classification was evaluated on three UCI benchmark datasets (see Datasets were first pre-processed with the raw data conversion method described in Section 4. Fuzzy measure coefficients required for the computation of the GI were estimated with the modified HLM Sr algorithm described in Section 3. For this purpose, the HLM Sr algorithm was set to work with a maximum of 2000 iterations and a learning rate α = 0. 05. Classification performance was evaluated by means of the classification accuracy in 5-Fold cross validation experiments taking care that the original proportion of samples per class was preserved. Finally, the robustness CI classification under GI feature selection was also evaluated.
Iris dataset As shown in Table  8 , fuzzy measure coefficients of V 1, V 2 and V 1-V 2 are null in all classes suggesting that they are irrelevant for the classification task. For class 1, the GI = -1 for coalition V 3-V 4 points out that these features are completely redundant, i. e. , only one of them is needed. This is confirmed by the data projection in V 3-V 4, shown in Figure  3 , and by the high relevance, GI = 0. 5, of individual features V 3 and V 4. Table  10 : Breast Cancer -Features rankings induced by the SV M -RF E and the GI methods. Features relevant to at least one class in the GI method are marked with *. The number of misclassified samples by SV M and CI classifiers is shown at the bottom of each of partition, from P 1 to P 5.
Wine dataset As reported in  [32] , classes in the wine dataset are separable. However, only the regularized discriminant analysis method has been able to accom-Table  11 : Wine -Features rankings induced by the SV M -RF E and the GI methods. Features relevant to at least one class in the GI method are marked with *. The number of misclassified samples by SV M and CI classifiers is shown at the bottom of each of partition, from P 1 to P 5. The four most significant features according SV M -RF E, (V 7, V 1, V 12 and V 13) belong to set of relevant features selected by GI. As with Breast cancer, GI selected features are also good for SVM classification but the converse does not hold. Stability of CI classification under GI feature selection with a global rank V 13, V 7, V 10, V 11, V 12, V 1, V 2, V 4, V 3, V 5, V 6, V 9, V 8 is shown Fig.
A more reliable estimation of fuzzy measure coefficients has been gained by identifying and solving the HLM Sr sensitivity to equal valued features. A detailed analysis of the GI index on synthetic datasets containing noisy together with either redundant or complementary features uncovered a surprising GI behavior. The GI turns to be always positive in datasets with complementary features and of alternating sign in those with redundant ones. This result was used to propose some feature selection guidelines. Experimental results on benchmark datasets involving a dozen of features showed that competitive and interpretable fuzzy integral classifiers can be designed in this way. Furthermore, selected features seem to be also useful for the design of accurate SVM classifiers. Further work is still needed to allow interpretable feature selection in datasets involving hundreds of features.
Mathematical formalization of features characterization for complementary and redundant features using GI In extreme situations, when the only relevant features are either redundant or complementary, the GI expressions are easy to compute. Theorem 1 -Complementary features. Let N be a dataset with n features among which, for a given class, c of them are fully complementary and n-c are noise. Let C be the subset defined by the c fully complementary features. The GI for power set members of C with cardinality a ∈ {1,. , c} is: GI(a) = 1 c -a + 1 19 This yields 1/c for each of the c singletons and 1 for the whole feature subset C. Proof : The set N of n features includes a set C ⊂ N of c fully complementary features, while the remaining, N \ C, only bring noise. In this extreme situation, the only coefficients different from zero are the ones of C and the ones needed to keep monotonicity, i.
2 Recurrence relation: Hence, the only non-zero GI index values for a set N of n features where c of them are fully complementary and n -c are noise are those belonging to subsets A in P(C). Furthermore, GI values depend just on the cardinality a of such subsets: GI(A) = 1 c -a + 1. n+1 s=0 m + s s = m + n + 1 n + m + n + 1 n + 1 = m + n + 2 n + 1 Theorem 2 -Redundant features. Let N be a dataset with n features among which, for a given class, r of them are fully redundant and n -r are noise. Let R be the subset defined by the r fully redundant features. The GI for power set members of R with cardinality a ∈ {1,. , r} is: GI(a) = (-1) a+1 r -a + 1 This yields 1/r for each of the r singletons, 1 for the whole feature subset R when r is odd and -1 when r is even. Proof : The set N of n features includes a set R ⊂ N of r fully redundant features, while the remaining , N \ R, only bring noise.
[21]or-produced version of the article published in Fuzzy Sets and Systems, 2015, N°270, p. 74-89 The original publication is available at http://www. sciencedirect. comhttp://dx. doi. org/10. 1016/j. fss. 2014. 09. 015 7). The Iris dataset is a well known dataset, easy to analyze, and allows for a fair comparison with results reported in[21].
Algorithm 1 for j ∈ examples do 10 : 110 Revised HLMS 1: Input: Training dataset D with samples (x j , T j ), j = 1,. , m 2: Output: Fuzzy measure coefficients u = [u p ] , p ∈ P(X) 3: for p ∈ P(X) do {Initialization} e j = C u (x j ) -T j {Individual error calculation} 11:.
7 Author-produced version of the article published in Fuzzy Sets and Systems, 2015, N°270, p. 74-89 The original publication is available at http://www. sciencedirect. com http://dx. doi. org/10. 1016/j. fss. 2014. 09. 015 4 Coalition Class 1 Class 2 V1 0. 52 0. 22 2 V2 0. 33 0. 69 V2 0 x x x V3 0. 14 0. 07 x x x V1-V2 0. 61 -0. 41 -2 V1-V3 0. 15 0. 06 -4 V2-V3 -0. 24 -0. 11 -4 -2 0 2 4 V1 Figure 1: The synthetic Atom dataset in the V1-V2 projection. Class 1 is plotted with triangles (nucleon) and class 2 with circles (ring). Misclassified samples are marked with crosses.
The former restriction would allow to extend the scope of the framework by handling simple theorems involving inductive definitions (e. g. about natural numbers), but is not treated here. The latter restriction better suits our needs (since an asynchronous context fits the spirit of model checking) and is respected by all our examples. Example 2. Horn clauses (in the sense of Prolog) can be encoded as purely positive fixed point expressions. For example, here is the Horn clause logic program (using the λ Prolog syntax, the sigma Y\ construction encodes the quantifier ∃Y ) for specifying the graph in Figure  3. i ((p = u i ) ∧ + (a = v i ) ∧ + (q = w i )) and the simulation and bisimulation relations can be defined as the following greatest fixed point expressions (note: the second contains both ∧ -and ∧ + ).
A reference proof checker The framework for foundational proof certificates described in  [13, 5]  was based on proof theory without fixed point definitions. In that setting, a standard logic programming language (in that case, λ Prolog  [14] ) was an ideal prototyping language for implementing and testing FPCs. The FPCs described in this paper are not so easily implemented in standard logic programming languages since the unification of eigenvariables must be done alongside the usual unification of "logic variables" that makes proof reconstruction possible. The implementation of λ Prolog, for example, considers eigenvariables as constants during unification. We have built a prototype proof checker for testing the FPCs described in this paper using the Bedwyr extension to logic programming  [21, 4].
Compared to the 62,478 reads that mapped to the LIMPs, this indicates a very low degree of variability within the population of DNA molecules sequenced. In particular, this analysis confirms that most LIMP stems in the genome are indeed asymmetrical, i. e. , with different numbers of A-and T-units. The propensity of the LIMPs to form hairpins as RNA and cruciforms as DNA, as depicted on Fig. 2b  and c , respectively, was evaluated using mfold  [19] , a program that calculates the free energy (ΔG) of a DNA or RNA secondary structure. For the RNA hairpin, ΔG ranged between -101. 7 and -21. 7 kcal/mol (Table  2 ), compatible with the formation of at least some of these structures in vivo. To evaluate the propensity of the DNA to form cruciforms at the LIMP loci, we compared the free energy of the linear double-stranded B-DNA with that of the second-best structure, a cruciform where each strand folds onto itself according to the palindromic nature of the LIMP.
Another family of repetitive palindromes, the HyLIMP We systematically searched the mitochondrial genome for palindromes using the program Palindrome from the EM-BOSS 6. 4. 0 package  [23] , requesting a stem longer than 15 bp and a loop shorter than 21 nt. Among the 27 palindromes found (excluding the LIMPs), four, those with the highest predicted stability (ΔG < -65 kcal. mol -  ), were associated with a drop or loss of RNA-Seq coverage (blue arrows in Fig. 1 ). Three of them, unrelated to each other, were not internally repetitive and in two cases they obviously derive from the head-to-head assembly of two repeat elements (repeat_2 and repeat_4, respectively), probably brought together by recombination. But the fourth one (boxed sequence in Fig. 5 ) showed internal repetitivity in the stem, similar but different from that observed in the LIMPs.
05  [58] , Velvet 1. 2. 08  [59] , and CLC Genomics Workbench 5. 1. 64 (CLC bio, Denmark; http://www. clcbio. com/) with k-mer values of 23, 35, 51, or 63 for each assembler. An assembly was also made with the super-read-based assembler MSR-CA (MaSuRCA) 1. 9. 3  [60]  with an automatically set k-mer value of 31. In order to assemble specifically the mitochondrial genome, potentially mitochondrial sequences were identified by searching for similarity between the scaffolds and contigs of all assemblies and the complete sequences of 41 mitochondrial genomes from Chlorophyta available at the NCBI GenBank database. Searches were done both at the nucleotide level using BLASTN 2. 2. 25  [61]  and the aminoacid level using BLASTX. A total of 1828 scaffolds/contigs were retained. All reads mapping to these selected scaffolds/ contigs using SOAP 2.
Understanding the extent of morphological variation in the wild population of Aldabra giant tortoises is important for conservation, as morphological variation in captive populations has been interpreted as evidence for lingering genes from extinct tortoise lineages. If true, this could impact reintroduction programmes in the region. The population of giant tortoises on Aldabra Atoll is subdivided and distributed around several islands. Although pronounced morphological variation was recorded in the late 1960s, it was thought to be a temporary phenomenon. Early researchers also raised concerns over the future of the population, which was perceived to have exceeded its carrying capacity. We analyzed monthly monitoring data from 12 transects spanning a recent 15-year period (1998-2012) during which animals from four subpopulations were counted, measured, and sexed.
In addition, we analyzed survival data from individuals first tagged during the early 1970s. The population is stable with no sign of significant decline. Subpopulations differ in density, but these differences are mostly due to differences in the prevailing vegetation type. However, subpopulations differ greatly in both the size of animals and the degree of sexual dimorphism. Comparisons with historical data reveal that phenotypic differences among the subpopulations of tortoises on Aldabra have been apparent for the last 50 years with no sign of diminishing. We conclude that the giant tortoise population on Aldabra is subject to varying ecological selection pressures, giving rise to stable morphotypes in discrete subpopulations. We suggest therefore that (1) the presence of morphological differences among captive Aldabra tortoises does not alone provide convincing evidence of genes from other extinct species; and (2) Aldabra serves as an important example of how conservation and management in situ can add to the scientific value of populations and perhaps enable them to better adapt to future ecological pressures.
1999 ) and compared with data from a first census taken in  1973 -1974 (Bourn and Coe 1978). However, the two datasets are not ideal for such a comparison, as the censuses were conducted at different times of year (tortoise movements are highly seasonal;  (Swingland and Lessells 1979; Gibson and Hamilton 1983) ) and used different methodologies. To account for these differences, adjustments were made to the later census data, which are not clearly specified, so it is difficult to assess their suitability. However, the resulting comparison concluded that differences in density among the subpopulations, although still apparent, were substantially reduced  (Bourn et al. 1999). This convergence was suggested to be in part due to a population "crash" in the southeast, apparently confirming earlier fears about tortoises damaging their environment  (Bourn and Coe 1978)  and raising concerns about the long-term viability of the giant tortoise population.
As a direct result of this analysis, a more detailed long-term monthly monitoring program was established in January 1998, which continues to the present day. Here, we analyze data from a recent 15-year monitoring period (January 1998 to December 2012) to test: (1) whether there is evidence for recent changes in population size; (2) whether tortoise density differs among subpopulations; (3) whether differences in size and degree of sexual dimorphism persist or whether there has been convergence in morphological traits among subpopulations; and (4) whether subpopulations differ in their sex ratios. Additionally, we use data from a subsample of marked individuals to investigate rates of population turnover.
Data collection We analyzed a database of monthly population counts collected over a period of 15 years: January 1998 to December 2012, which is publically available via Dryad. Monthly counts were made on 12 transects distributed around the atoll on three of the four main islands: Grand Terre, Picard, and Malabar (there is no extant population of tortoises on Polymnie, although it may have had tortoises in the past). The largest island, Grand Terre, has a central area of deeply dissected and fissured limestone, considered difficult for tortoises to traverse. In all previous studies, it has therefore been treated as having two subpopulations: Grand Terre East and Grand Terre West, although we acknowledge that the real extent of tortoise movements between these two areas is unknown. Transects were deliberately located in a range of vegetation types and are not, therefore, an unbiased sample of the island as a whole.
However, the features used for sexing are less well-developed in smaller animals; hence, individuals with a third-scute measurement <20 cm are usually, but not always, recorded in the database as "sex unknown". To be conservative, we assigned all those animals with a third-scute measurement <20 cm as "sex unknown". When examining trends through time, we analyzed males, females, and unknowns separately. Most animals encountered on transects are unmarked; however, during the time of the Royal Society Expedition to Aldabra, numbered titanium disks were attached to the carapace of some animals on Grand Terre and Malabar. Disks were attached to 700 tortoises by  Gaymer in 1969 and 1970 (Gaymer 1973) , while a further 6182 tortoises were marked in the same way by Bourne in  1973 -1974 (Coe et al.
Statistical analysis To quantify the spatial distribution of tortoises and trends through time, we analyzed: (1) occupancy (presence/absence of tortoises) on all sections; and (2) mean densities in occupied sections (i. e. , those sections containing at least one tortoise in at least 1 month of the year). Analyses were carried out using generalized linear mixed-effects models within the statistical package R version 3. 1. 0 (R Core Team 2014). We accounted for the spatial structure in the data in the random effects: sections are nested within transects, which in turn are nested within subpopulations. For the occupancy (presence/absence) analysis, we used a generalized linear mixed-effects model with a binomial error structure; for the mean densities in occupied sections, we applied a log transformation to the data (this produced excellent residual plots).
Because the same individuals are likely to be encountered and measured repeatedly, we also performed an analysis for each year separately. To investigate the possibility of changes in the size of animals through time, we also considered models using the whole data set in which the fixed effects included year and its interactions with sex and subpopulation. Finally, we analyzed the sex ratios on sections, again using generalized linear mixed-effects models (glmer) with a binomial error structure. The functions lmer and glmer are within the R package lme4  (Bates et al. 2014). Survival of tagged individuals was analyzed using a mark-recapture model implemented using Program MARK  (White and Burnham 1999)  and RMark interface  (Laake and Rexstad 2010). Because transect counts were performed monthly and we are interested in annual survival, we pooled the re-sighting data annually and estimated apparent survival and recapture rates using the Cormack-Jolly-Seber model  (Lebreton et al.