dataesr/scientific-paragraphs-categorization huggingface dataset:
3) DATA DIMENSIONS In  [22] , the authors assert that IForest provides good results even on large-dimensional data, since several of these dimensions are insignificant. They also proposed to apply statistical tests like Kurtosis to select the relevant dimensions and thus reduce the dimensions. The number of dimensions m is not taken into account in the choice of the input parameters in IForest. Anomalies which are carried by several dimensions at the same time are more difficult to detect. Figure  6  shows two types of data where the anomalies are respectively carried by both 2 dimensions (a) and 3 dimensions (b). In both cases, with the default settings of IForest, we obtain a high false positive rate (of the order of 15%). In addition, anomalies are only detected if they are enough far away from the normal data for 2 dimensions.
B. RANDOMNESS EFFECT IN IForest IForest is a multi-step random choice method. Indeed, the choice of the sample is random for each tree in the forest. The choice of the addressed dimension as well as the split value is random for each node. It is worth checking the impact of this randomness on the results of IForest by inspecting the variance of the results on several runs of IForest. We carried out this experiment by executing IForest 10 times with the same decision threshold ie threshold = 0. 5 on the shuttle dataset described in the subsection V-A. The table  3  shows that the 10 successive executions of IForest give fairly constant results in terms of ROC AUC, specificity and recall. The standard deviations of these three metrics are very close to zero. These results illustrate the stability of IForest despite its randomness.
C. IMPACT OF PARAMETERS ON IForest The input parameters of IForest: sample size (ψ) and number of trees (t) are of a high importance for the performance of IForest. We carried out some experiments to assess the impact of these parameters on the results. These parameters must be well chosen by the user to optimize the results. In particular, when applying IForest to a data stream with a concept drift, the input parameters should ideally automatically be adapted to the varying characteristics of the stream. We study here the impact of these parameters on the efficiency of IForest.
1) IMPACT OF SAMPLE SIZE The execution time of IForest is related to the number of samples or trees t and the size of each sample ψ. In this part, we are interested into the impact of ψ. We have therefore set t to its default value (100 trees) in the experiments. Figure  9  shows the results of running IForest on the Shuttle dataset with different values of sample size. Note that when the sample size increases, the execution time is longer. This can be explained by the fact that the maximum length of the trees depends on the size of the sample. Also, each tree is built from a sample so the training phase of the IForest method closely depends on the size of the tree. A large tree size does not necessarily mean a gain in performance. This is highlighted in the other metrics in the figure. From a given threshold, the more the sample size increases, the less IForest is able to detect anomalies (decreasing recall).
Normal data, however, are well classified (as the specificity reaches the value 1 quickly). For a very large sample, IForest tends to classify all data as normal. One possible reason would be the poor quality of the built trees: the larger the sample size, the more the trees in the forest look alike and become redundant, which affects their collective decision. In summary, with IForest, the sample size is an important parameter which has a great influence on the performance of the detection. A good sample size should therefore be small enough for a better performance of IForest, while being careful to keep the sample as representative as possible of the initial data. The optimal sample size depends therefore on the nature and variance of the addressed dataset. In the figure  10 , the study was carried out on the 4 datasets described in V-A, with the aim of finding the ideal size of the sample in each case.
Note that for these different datasets,  the sample size that gives the best results differs. Indeed, for Shuttle and SMTP, the best ROC AUC was obtained with ψ = 1024. Whereas for Forest Cover ψ = 2048 was the optimal sample size, and ψ = 4096 for HTTP. Unlike SMTP and HTTP where ROC AUC remained constant after the optimal sample size, IForest is less performant for ForestCover and Shuttle beyond the correct sample size. These results confirm that the optimal sample size for a good classification of data (normal and abnormal) depends on the characteristics of the dataset. The ability of IForest to detect anomalies depends on the maximum length of trees built in the forest. However, the length of the tree depends on the size of the sample. Hence, it is important to provide the adapted sample size as input for a good performance of IForest.
2) IMPACT OF THE NUMBER OF TREES IForest is based on a random forest of several random and independent binary trees. Their independence comes from the fact that each tree is built on the basis of a single random sample of the same size. All trees participate equally in the decision-making regarding the classification of a data: normal or abnormal. The number of trees to be built in the forest is an input parameter of the method. Memory requirement is closely related to the number of trees in the forest. In this subsection, we conducted experiments to assess the impact of the number of trees on the performance of IForest. For that, we used different values for this parameter t. We set the sample size to its default value: ψ = 256. As expected, when the number of trees increases, the execution time becomes longer, which corresponds to the fact that all the trees are created during the learning phase and also that during the test phase, data item must pass through each tree in the forest for decision-making.
D. IMPACT OF THE PRESENCE OF ABNORMAL DATA IN THE SAMPLE When training the dataset model, since the choice of data in the sample is random, the samples may not contain any abnormal data. We evaluate in this section the impact of the presence of abnormal data in the samples during the learning phase. Two experiments were carried out for this purpose. From the Synthetic_3 dataset (7b) we made first a random choice in the whole dataset (normal and abnormal data) noted ''AllDataset'' then applied IForest. Then in the second experiment the random sample is selected only on the normal data denoted ''NormalOnly''. The result is recorded in the table 4. IForest is more efficient when tree construction is performed on the basis of a mixture of normal and abnormal data. When we build the forest with only normal data, we obtain a ROC AUC of 0.
E. IMPACT OF THE NUMBER OF DIMENSIONS ON IForest The data are often multivariate, describing the variation of at least two observables over the time. In order to evaluate the performance of IForest according to the number of dimensions in the dataset, we used the two and three dimensional synthetic datasets presented in section V-B. The particularity of these datasets is that the anomalies are carried by several dimensions at the same time. It will therefore be necessary to consider several dimensions to detect anomalies. When the anomalies are carried by several dimensions at the same time (Figure  13 ), IForest is less efficient. Anomalies are only detected in these latter cases when the difference in density and distance between the normal data and the anomalies is very clear. IForest always makes a lot of false alerts, especially on the borders of normal data.
Several real anomalies were not detected due to the split process of the nodes in the learning phase of IForest. Indeed, IForest performs splits by choosing an attribute randomly. The split is therefore done with only one attribute at a time. However, considering only one dimension, the abnormal data seem to be normal because it is in the same range of values as the normal data. We also notice that with a high number of dimensions, the false positive rate increases. The number of dimensions is therefore a very important parameter, to be taken into account in order to improve the scalability of IForest and adapt it to large-dimension data. A possible evolution of IForest would be to choose the sample size ψ depending on the size of the data and also on the number of their dimensions. Indeed, in order to detect an anomaly carried by m dimensions, it is obvious that a tree of minimum depth m must be used.
F. CHOICE OF DECISION THRESHOLD Anomaly detection methods are generally based on a score generated for each data item and compared to a detection threshold. Using this score, those methods classify the different items separating abnormal and normal data. In the original paper, IForest authors suggested to use 0. 5 as a threshold for the decision making by computing the score s(x, n) = 2 -E(h(x)) C(n) , as follows: • when s (x, n) is very close to 1 then x is an anomaly; • when s (x, n) is much less than 0. 5 then x is normal. In practice, the anomaly decision is taken when the score is greater than 0. 5. But, this rule can cause false alarms or false negatives, because the optimal decision threshold is not always equal to 0. 5. In order to illustrate this observation, we considered the two synthetic datasets Synthetic_2 and and we represented, in the figure  14 , the distribution of the scores first for all the data, then for the normal data only and finally for abnormal data only.
To complete the study, we deduced, from the scores, the lengths of the paths and we represented their distribution. The aim of this experiment is to assess whether we can easily find a score threshold or a depth threshold allowing to separate the normal data from the abnormal data. The score or depth threshold is represented by the red vertical line. We notice that a lot of normal data has a score between 0. 5 and 0. 6. It is clear that the threshold score 0. 6 is much more suitable than 0. 5 for the two datasets. With a score threshold of 0. 6, for the Synthetic_2 dataset, where the normal data density is low, only some abnormal data were detected. The distributions show that true abnormal data have a path longer than the threshold and a score below the score threshold (0. 6). On the other hand, with the Synthetic_3 dataset, all anomalous data have a score above the decision threshold.
Using about 100 trees seems to be a good compromise. From a given threshold, the sample size increases the execution time of IForest and decreases the anomalies detection performances. Thus, IForest can be improved by establishing the optimal sample size according to the dataset characteristics. The performed experiments show also that the optimal decision threshold is difficult to fix as it is dependent on the similarity between normal and abnormal data according to the IForest trees. We propose in the next section Majority Voting IForest, an extension of IForest improving its execution time.
VII. MAJORITY VOTING ISOLATION FOREST A. THE MAJORITY VOTING IFOREST (MVIFOREST) METHOD IForest identifies anomalies based on a collective decision produced by all the trees built during the training phase. Indeed, each tree i participates in the decision making by the path h i (x) for each data x. The average path of a data is used in the calculation of its score as follows: s(x, n) = 2 - t i=1 (h i (x))/t C(n). This formula implies that it is necessary to calculate for all the trees of the forest, the path of x to deduce its score. This way of proceeding can be improved by applying the majority voting. The execution time as well as the memory requirement may be considerably reduced with the majority voting without losing efficiency. We propose a new version of IForest based on majority voting that we call MVIForest.
B. EVALUATION OF MVIFOREST ON REAL DATASETS To evaluate the MVIForest method, we carried out different experiments on the four previously described real public datasets (V-A). We choose to consider the datasets used in the original IForest paper. The objective of these experiments is to compare the performances of MVIForest and IForest. The used metrics for these evaluations are described in V-C. The table 5 summarizes the selected values of the parameters used to carry out the experiments. The experiments on this section were performed on a 64 bits computer with an Intel Core i5-4570 CPU @ 3. 20GHZ * 4. The different results are presented in the table  6. One can notice that MVIForest gives similar results to IForest in terms of ROC AUC. However, MVIForest is always faster than IForest with an execution time shortened by 35% in average.
The best result is obtained with HTTP dataset, the largest considered dataset, where the execution time of MVIForest represents only 60% of the execution time of IForest. When anomalies are obvious and easy to detect with a high distance to normal data and a very different density, MVIForest can save up to 50% of the execution time of the test phase. However when most of the data are in the area of uncertainty between the anomalies and the normal data, the execution time will be almost the same.
VIII. IFOREST VS EXTENDED IFOREST VS MVIFOREST ON SYNTHETIC DATASETS The table 7 and figures 15 and 16 show the results of running IForest, EIF and MVIForest on the synthetic datasets described in section V-B. As can be seen from this table, unlike for real datasets, MVIForest gives better or similar results than IForest in terms of ROC AUC. On this criterion, MVIForest also exceeds the performance of EIF in almost all cases. The only dataset for which all the three methods were efficient is Synthetic_3 where there is a high density of normal data, a low density of anomalous data, and a high distance between normal data and abnormal data. The difference in density between and abnormal data is an important criterion for anomalies detection. This density must also be considered after sampling, i.
e the density of the data used for each tree. In fact if the data density of the sample is close to the density of the anomalies in the test dataset (the sample), the anomalies can be missed. According to the table 7, for the Synthetic_5 dataset, all the anomalies were missed by the three methods. This is explained by the high density of anomalies (although they are relatively few) in this dataset. Because of this high density  these anomalies are globally seen as normal data. This is the effect of masking. The figure  16  shows the anomalies detected by each method for each of the 5 datasets. One can notice that for all these datasets, IForest and MVIForest give quite similar results in terms of detection. Moreover they generate each time false alarms by classifying the normal data at the border as abnormal.
As explained above, this is due to the way the nodes are split: IForest randomly selects an attribute at each split. This problem has been corrected by EIF by introducing hyperplanes. As can be noticed, on the same datasets, EIF did not make any false alarms and performed a maximum specificity (always equal to 1 in Table  7 ). EIF classifies correctly all normal data, however, it misses abnormal data when there is a small distance separating them from the normal data. In such a configuration, EIF produces a very low recall (null for Synthetic_2). Furthermore, considering all data dimensions at the same time when splitting nodes makes EIF slower than IForest. As can be seen in the table 7, the execution of EIF takes about 3 times longer than IForest. The time is mainly consumed during the learning phase corresponding to the construction of the forest.
MVIForest remains the fastest of the three methods, with a more efficient detection than IForest (a higher or similar ROC AUC). Memory requirement of the three methods is also reported on table  7. One can notice that EIF has always the highest memory requirement. In fact, for each node of the t trees, EIF stores the parameters of the hyper-plane used to split this node, which represents additional information compared to IForest. MVIForest and Iforest have almost the same memory requirements. MVIForest uses slightly less memory than IForest because the execution is interrupted as soon as a majority vote is identified. The score of all the trees are not stored to compute an average, and the data item will not pass through all the trees. Since the detection of anomalies requires speed and efficiency, MVIForest would be a wise choice.
However, depending on the objective, one can choose EIF. EIF classifies normal data better, but may miss some anomalies while MVIForest is better at quickly detecting anomalies, but may generate false alarms. The application constraints as well as the context has to guide the choice for the most suitable method. Figure  17  presents an exploration of the path depth distribution of all data, with IForest and EIF, for the Synthetic_5 dataset. We focused on this dataset because no anomalies were detected. MVIForest was not considered in this experiment because with MVIForest, each data item does not have a unique average score, but many scores given by the different used trees. We recall that an anomaly is characterized by a high score, resulting from a shallow average path on the trees in the forest.
Starting from the threshold score (0. 5), we calculated the threshold depth which we represented by a vertical red line. The distribution of depths allows us to situate this threshold depth first relatively to all data, then using only normal data and finally using only abnormal data. We notice, for both methods, a large overlap in the path depths of the normal and anomalous data. This overlap highlights the impossibility of separating the two classes of data based on their depths in the IForest trees, regardless of the threshold depth. With IForest, some normal data have a depth below the threshold depth and are therefore classified as anomalies, which is not the case with EIF. The Synthetic_5 dataset described in Figure  7d  highlights the limitations of IForest in terms of dealing with swamping and masking effects.
Considering a single dimension separately, abnormal data look like normal data and these two classes can not be separated. Unlike EIF which, thanks to its way of constructing the forest was able to avoid swamping, IForest and MVIForest have misclassified several normal data because they only consider one dimension at once. Moreover, because of the high density of abnormal data, they could not be isolated early enough in the forest. They obtained depths greater than the threshold (see Figure  17 ) for all methods. We performed the same experiments on the 3-dimensional datasets described in V-B. None of the methods detect anomalies at any time. IForest and MVIForest make only false alarms. This result confirms the intuition that the detection performance of IForest and even MVIForest drops considerably with the increase of the number of significant dimensions in the data.
IX. CONCLUSION AND FUTURE WORK Isolation Forest is one of the best methods for detecting anomalies. It is fast, accurate and does not require huge resources compared to other techniques such as clustering or nearest neighbor. In this paper, we carried out a state of the art of isolation-based anomaly detection methods. Most of them are improvements of IForest. Each new method addresses a limit or an adaptation of IForest to a new context. In this paper, we highlight some weaknesses of IForest not addressed in these improvements, notably the choice of input parameters and the impact of the characteristics of the datasets (number of significant dimensions, density of normal and abnormal data, etc. ). We tested IForest and its extended version (EIF) on several real and synthetic datasets to illustrate the weaknesses we identified.
IForest Isolation  RAJA CHIKY (Member, IEEE) received the bachelor's degree in computer science (engineering), the master's degree in data mining, and the Ph. D. degree in computer science from Telecom Paris-Tech. She is currently a Full Professor in computer science and data science and the Head of innovation at ISEP. Before that, she was the Research Director and the Head of the LISITE Laboratory, ISEP, and in charge of research teams (more or less 50 researchers). She gives lectures on statistics, databases, and big data in many universities in France and abroad. She is a reviewer for many journals and conferences and has deeply published in the fields of datamining and databases. She took part to many European and National projects in collaboration with universities, research laboratories, and companies.
He is currently pursuing the Ph. D. degree with the Superior Institute of Electronics of Paris, Sorbonne University, Paris, France. His research interests include anomalies detection, machine learning, distributed machine learning, and data stream management. ALIOU BOLY received the master's degree in computer science from the University of Paris Dauphine and the Ph. D. degree in computer science from Telecom ParisTech. He is currently an Associate Professor at the University Cheikh Anta Diop of Dakar (UCAD), Senegal, where he is responsible for the master in business intelligence. His research interests include data warehousing, databases, data mining, and data stream management.
Numerical Simulation Set-Up and Results To determine the local information impeller inlet and outlet flow characteristics that cannot been obtained from local measurement accessibility, Reynolds Average Numerical Simulations (RANS) were performed using a k-ω SST turbulent model. The 3D fluid domain was created using commercial software UG, as shown in Figure  10. This approach has been widely used thanks to the development of numerical techniques, which have been validated to some extent for specific local studies on cavitation, for example  [26] , or to obtain more precise information on vibration source detection using unsteady approaches that have been adapted for conventional axial or centrifugal pump designs  [27]. For conventional centrifugal pump designs, the value of the head coefficient is equal to 1 for the zero mean flow rate when using the straight-line extrapolation.
Numerical Simulation Set-Up and Results To determine the local information impeller inlet and outlet flow characteristics that cannot been obtained from local measurement accessibility, Reynolds Average Numerical Simulations (RANS) were performed using a k-ω SST turbulent model. The 3D fluid domain was created using commercial software UG, as shown in Figure  10. This approach has been widely used thanks to the development of numerical techniques, which have been validated to some extent for specific local studies on cavitation, for example  [26] , or to obtain more precise information on vibration source detection using unsteady approaches that have been adapted for conventional axial or centrifugal pump designs  [27]. The fluid domain corresponding to the inlet pipe was properly extended to ensure stable inlet conditions.
Conclusions An experimental analysis on global performance and on flow field inside the impeller of a TBD pump was performed using the CFD approach. Data reduction was performed using the overall data from the experiments to extract several loss coefficients from each element of the pump based on existing loss models that were initially developed for conventional pump designs. This procedure has never been presented before for the present disc pump geometry. The following conclusions can be drawn: (1) The overall results of the experiments were determined in a specific pump design for two different rotational speeds: 1500 and 2900 rpm. Similarity laws that usually are applied for conventional pump designs can also be applied in the present pump geometry. The maximum global pump efficiency reached 35% for a flow coefficient ψ = 0.