dataesr/scientific-paragraphs-categorization huggingface dataset:
IV. CONCLUSIONS This paper has presented the fundamentals of the platform developed, within the iTesla project, for improving the operation security of the network under load and renewable generation uncertainty. The ultimate goal of the platform developed is to support the decision making process during network operation from two-days ahead to real time based on three main features: (a) to provide a risk-based assessment taking into account different sources of uncertainties (e. g. load and renewable power generation) and contingency probability; (b) to perform accurate and fast online SA using time-domain simulations and machine learning techniques; (c) to provide operators with relevant proposals of preventive and curative actions to keep the system in a secure state. As a shared tool, the iTesla platform, whose code has been released opensource on Github (MPL 2.
Hence, in the proposed method, the coding of vectors is intrinsically adapted to the data and the computations involved remain very simple despite the strengths. This helps us avoid the above mentioned limitations of the previous methods -(i) instead of a fixed quantization, we learn a data driven, and hence, adaptive quantization using Gaussian mixture models (GMM), (ii) quantizing using GMM also avoids any heuristic pruning as any low occupancy region in the feature space will be automatically ignored by the GMM learning and (iii) learning GMM allows us to use Fisher vectors  [3]  which are higher-order statistics of the feature distribution. We discuss in more detail on this in the following sections. A preliminary version of this work appeared in Sharma et al. [13]. We validate the proposed representation by extensive experiments on four challenging datasets: (i)  Brodatz 32  texture dataset  [14, 15] , (ii) KTH TIPS 2a materials dataset  [16] , (iii) Japanese Female Facial Expressions (JAFFE) dataset  [17] , and (iv) Labeled Faces in the Wild (LFW) dataset  [18].
Two dataset, Brodatz-32 and JAFFE, are relatively easier with limited variations while the other two, KTH TIPS 2a and LFW, are more challenging with realistic high levels of variation in illumination, pose, expressions etc. We show that using higher-order statistics gives a more expressive description and lead to state-of-the-art performance in low complexity settings, for the above datasets. Further, with the challenging LFW dataset as the experimental testbed, we also show that the proposed representation is complementary to the recent high complexity state-of-the-art representations. However, in case of challenging variations, like in LFW, unsupervised approach is not sufficient and hence we show that when used with supervised metric learning the performance of the proposed representation improves substantially.
The local vectors are derived in multiple ways, incorporating different invariances like rotation, view point etc. E. g. [22, 23]  generate an image specific texton representation from rotation and scale invariant descriptors and compare them using Earth Movers distance, whereas  [10, 9, 21, 24]  use a dictionary learned over the complete dataset to represent each image as histogram over this dictionary. In a more recent line of work, Cimpoi et al. [29]  show that traditional image classification methods when applied to the more challenging textures in the wild scenario give good performances. They use classic local features such as the Scale Invariant Feature Transform (SIFT)  [30]  with different encoding methods, particularly Fisher scores  [3] , similar to those employed in the present work.
The main contribution of this paper is motivated by these observations; we describe small neighborhoods with their higher-order statistics, without coarse approximations, and show with extensive experimental results that this leads to a more expressive representation which performs better on challenging benchmark datasets. In more recent works on facial analysis, deep learning based methods for face recognition/verification  [32, 33, 34, 35, 36, 37, 38, 39, 40, 41]  have gained much success. Most of the deep learning based works aim to leverage large amount of data along with the impressive model capacity of deep networks. Taigman et al. [38]  showed that learning a deep convolutional neural network, for predicting thousands of identities using millions of training images, and then using the output of the penultimate layer of trained network as features for faces results in very good face verification performance.
Experimental results We now report various experimental results which validate the proposed method. We use four challenging publicly available datasets of textures and faces and address the challenging tasks of texture recognition, texture categorization, facial expression categorization and face verification. In the following, we first discuss implementation details then present the datasets and finally give the experimental results for each dataset. In the first set of experiments (upto Sec. 5. 6), as our focus is on rich and expressive representation, we use a standard classification framework based on linear SVM. As linear SVM works directly in the input feature space, any improvement in the performance is directly related to a better encoding of local regions, and thus helps us gauge the quality of our representation vs.
1). We use the average of all the features from the image as the representation for the image. However, for the facial expression dataset we first compute the average vectors for non overlapping cells of 10×10 pixels and concatenate these for all cells to obtain the final image representation. Such gridding helps in capturing spatial information in the image and is standard in face analysis  [51, 52]. We crop the 250×250 face images to a ROI of  (66, 96, 186, 226) , to focus on the face, before feature extraction and do not apply any other pre-processing. Finally, we use linear SVM as the classifier with the cost parameter C set using five fold cross validation on the current training set. In the supervised setting for face verification, we use the metric learning formulation described above in Sec.
Texture categorization Brodatz -32 Textures dataset 4  [14, 15]  is a standard dataset for texture recognition. It contains 32 texture classes e. g. bark, beach-sand, water, with 16 images per class. Each of the image is used to generate 3 more images by (i) rotating, (ii) scaling and (iii) both rotating and scaling the original image -note that Brodatz-32  [14]  dataset is more challenging than original Brodatz dataset and includes both rotation and scale changes. The images are 64×64 pixels histogram normalized grayscale images. We use the standard protocol  [12] , of randomly splitting the dataset into two halves for training and testing, and report average performance over 10 random splits. KTH TIPS 2a dataset 5 [16] is a dataset for material categorization. It contains 11 materials e.
g. cork, wool, linen, with images of four samples for each material. The samples were photographed at 9 scales, 3 poses and 4 different illumination conditions. All these variations make it an extremely challenging dataset. We use the standard protocol  [12, 16]  and report the average performance over the 4 runs, where every time all images of one sample are taken for test while the images of the remaining 3 samples are used for training. We now analyze the performance of the proposed LHS vs. the LBP/LTP based image representations. Tab. 1 (col. 1 and 2) gives the results for the different methods on the texture datasets. On the texture recognition experiment, i. e. when a sample seen on training is presented for testing with scale and rotation changes, we achieve a near perfect accuracy of 99.
5%. Our best method outperforms the best LBP and LTP baselines by 12. 2% and 4. 5% respectively. We thus conclude that data-adaptive encoding, using higher-order statistics, of local neighborhoods is advantageous when compared to fixed quantization and heuristics as used in LBP and LTP representations. The high accuracy achieved on the texture recognition dataset, Brodatz-32, leads us to conclude that texture recognition, under the presence of rotation and scale variations, can be done almost perfectly. On the more challenging KTH TIPS 2a dataset for texture categorization, the best performance we obtain is far from saturated at 73%. LHS performs better than LBP  and LTP baselines by 3. 2% and 1. 7% respectively. KTH TIPS 2a dataset has much stronger variations in scale, illumination conditions, pose, etc.
than the Brodatz dataset and the experiment is of texture categorization of unseen sample i. e. the test images are of a sample not seen in training. LHS again outperforms LBP/LTP on the task of texture categorization. More recently better results have been reported on the task of texture categorization. It has been demonstrated that standard object image classification pipeline of Fisher Vectors  [3, 53]  with dense SIFT  [30]  when applied to texture categorization  [29]  achieves excellent results. We note that such features are of much higher complexity than the proposed LHS. We analyze LHS wrt. such features in Sec. 5. 7, albeit on the task of face verification. Also, it has been shown that representations learnt for image classification tasks, using large amounts of external data, transfer successfully to texture recognition as well  [29].
Facial analysis Japanese Female Facial Expressions (JAFFE)  6  [17] is a dataset for facial expression recognition. It contains 10 different females expressing 7 different emotions e. g. sad, happy, angry. We perform expression recognition for both known persons, like earlier works  [55] , and for unknown person. In the first (experiment E1), one image per expression for each person is used for testing while remaining ones and used for training. Thus, the person being tested is present (different images) in training. In the second (experiment E2), all images of one person are held out for testing while the rest are used for training. Hence, there are no images of the person being tested in the training images, making the task more challenging. For both cases, we report the mean and standard deviation of average accuracies of 10 runs.
Tab. 1 (col. 3 and 4) gives the performance of the different methods on the expression categorization task. On the first experiment (E1) we obtain very high accuracies  as the task is of recognition of expressions, from a never seen image, of a person who was already seen at training. The proposed LHS again outperforms LBP and LTP based representation by 2% and 1. 2%, respectively. On the more challenging second experiment (E2), i. e. when the test subject was not seen during training, we see that the accuracies are much less than E1. LHS again outperforms the best LBP and LTP accuracies by 2. 8% and 4% respectively. Fig. 2  shows one image of each of the 10 persons in the dataset along with the expression recognition accuracy for that person. This dataset has highly variable intra-person differences i.
e. for some individuals different expression images are close while for others they are very different. This results in very different accuracies for the different persons and hence high standard deviation, for all the methods. We conclude that LHS, owing to more accurate description of local pixel neighborhoods, is able to perform better than the LBP/LTP based image description for the task of facial expression categorization on the JAFFE dataset. Labeled Faces in Wild (LFW)  [18]  is a popular dataset for face verification by unconstrained pair matching. Face verification is the task where two face images are given and the system has to predict whether they are of the same person or not, with the possibility that the(those) person(s) might not have been seen at training. Hence, it is different from face recognition, where the system has to recognize a person already seen at training.
It stresses the system to find characteristics which are general and make the faces similar or not, rather than characteristics which are specific to a known set of persons. LFW contains 13,233 face images of 5749 different individuals of different ethnicity, gender, age, etc. It is an extremely challenging dataset and contains face images with large variations in pose, lighting, clothing, hairstyles, etc. (Fig. 3  shows example pairs from the dataset). LFW dataset is organized into two parts: 'View 1' is used for training and validation (e. g. for choosing the parameters) while 'View 2' is only for final testing and benchmarking. In our setup, we follow the specified training and evaluation protocol. We use the, publicly available, aligned version of the faces as We first report results in the restricted unsupervised task of the LFW dataset, i.
We classify image pairs into same or not same by thresholding on their similarity. We choose the testing threshold as the one which gives the best classification accuracy on the training data. LHS gives an accuracy of 73. 4% with a standard error on the mean of 0. 4%. This is a competitive performance in the unsupervised setting for the dataset. Unlike other methods, it neither uses external data e. g. as by PAF  [65] ,  nor does it do feature-specific post-processings e. g. as by LQP  [64]. We compare with other existing approaches, including those based on LBP in Sec. 5. 6. Also, we show in Sec. 5. 7 that LHS is one of the best performing methods, among methods of similar low complexity, in the supervised face verification setting.
Effect of sampling and number of components Table  1  shows the results with (a) rectangular 3×3 pixel neighborhood and (b) LBP/LTP like circular sampling of 8 neighbors with the diagonal neighbor values bilinearly interpolated. Performance on the Brodatz-32 dataset is similar for both the samplings while that for KTH and JAFFE datasets differ. In general, the circular sampling performs better for all the datasets. We note that the variations in, and hence difficulty of, the Brodatz-32 dataset is much less compared to the other two datasets and hence images in Brodatz-32 dataset are possibly well represented by either of the two samplings. Thus, we conclude that, in general, circular sampling is to be preferred as it performs better on most of the datasets and generates more discriminative statistics.
Fig. 4  shows the performance on the two texture datasets for different number of mixture model components. The length of the vector, and hence the space and time complexity of the method, varies proportional to the number of components in the GMM. Relatively higher number of components leads to a higher likelihood, i. e. a better fit to the data, and hence a better description of the space but also leads to vectors which are longer to compute and store. On this trade-off of size and accuracy of description, we observe that the performance, for both texture datasets, improves with the number of components and saturates at 128. On the Brodatz-32 dataset, LHS is able to give more than 99% accuracy with just 16 components, highlighting the relatively easier nature of this dataset. While for the KTH dataset, performance improves significantly when the number of components increase from 16 to 128 (by absolute 6.
Comparison with existing methods Table  2  shows the performance of the proposed LHS along with existing methods. On the Brodatz dataset we outperform all methods and to the best of our knowledge report, near perfect, state-of-the-art performance. On the JAFFE dataset, as well, we achieve the best results reported till date. On the KTH dataset, Chen et al. [12]  report an accuracy of 64. 7% using their Weber law descriptors (WLD) with KNN classifier. Caputo et al. [16]  report 71. 0% for their 3-scale LBP and non-linear chisquared radial basis function kernel based SVM classifier. In comparison we use linear classifiers which are not only fast to train but also need only a vector dot product at test time (cf. kernel computation with support vectors which is of the order of number of training features).
Note Caputo et al. obtain their best results with multi scale features and a complex decision tree (with non-linear classifiers at every node). We expect our features to outperform their features with similar complex classification architecture. The higher complexity Fisher vectors with SIFT features (SIFT-FV)  [29]  achieves substantially better on the KTH dataset (82. 2% vs. 73. 0%), however they are orders of magnitude longer and slower than the proposed method. We provide space and time comparisons with the proposed method and SIFT-FV method below Sec. 5. 8, Tab. 5, with images from LFW dataset without loss of generality. Tab. 2(d) reports accuracy rates of our method and those of competing unsupervised methods 8  on LFW dataset. Our method outperforms the LBP baseline (LBP with χ 2 distance)  [62]  by 3.
9% and gives 1. 2% better performance than Locally Adaptive Regression Kernel (LARK) features of  [63]. The better performance of our features, compared to the LBP baseline and fairly complex LARK features, on this difficult dataset once again underlines the fact that local neighborhood contains a lot of discriminative information. It also demonstrates the representational power of our features, which are successful in encoding the information missed by other methods. More recent works have reported higher performances e. g. Local Quantized Patterns (LQP)  [64]  achieves 75. 3% without any postprocessing and gain even higher when postprocessed with whitened PCA and compared with cosine similarity. However, LQP have higher complexity than LHS and hence gain 2%. While the current LHS features are only 3584 dimensional, the LQP features are 36000 dimensional i.
e. 10× longer. Pose Adaptive Filters (PAF)  [65]  use external data to learn pose robust features using 3D fitting of faces and achieve substantially more. This underlines the fact that the dataset has very challenging pose variations, correcting which will arguably improve the performance of the proposed LHS features as well. Since they use external data while the proposed method does not, their performance is not directly comparable to that of the proposed method. Also, adding pose robustness with additional effort, e. g. 3D fitting of face and using external data, is another challenging problem in itself and has not been explored further in this work. Thus, we conclude, the proposed method is capable of achieving competitive results while being computationally simple and efficient.
LHS with supervised discriminative metric learning We now provide results of the proposed Local Higherorder Statistics (LHS) features with supervised discriminative metric learning (ML) on the challenging Labeled Faces in the Wild (LFW)  [18]  dataset. We show that when used with such supervised ML, which can be equivalently seen as a projection to a lower dimensional discriminative subspace (see Sec. 4), the LHS features can obtain very high performance while being much more efficient than the competition. We operate in the 'Supervised, unrestricted, label-free outside data' protocol. Tab. 3 gives the performance of LHS for different values of the parameters. We see that the increasing the number of Gaussian components steadily increases the performance from k = 4 to k = 24 by a little less than 2% absolute while beyond that the results seem to saturate.
Similarly, for a fixed number of Gaussian components, increasing the projection dimension increases the results but with a pronounced diminishing returns effect. It is quite interesting to note these performances in the context of existing methods. Tab. 4 shows the performance of LHS wrt. state-of-the-art methods on LFW dataset. LFW achieves the best results among the features in the low complexity regime, and competitive results among features with high complexity or methods that combine multiple features. In particular our own implementation of Local Binary Patterns (LBP) using the (default parameters of the) vlfeat library  [54]    Methods with similar complexity Method Accuracy LBP + ITML  [66]  85. 1 ± 0. 6 LBP + PLDA  [67]  87. 3 ± 0. 6 LHS + JML (proposed) 88. 2 ± 0. 2 Methods with multiple feats/higher complexity Method Accuracy comb.
LDML-MkNN  [47]  87. 5 ± 0. 4 comb. PLDA  [67]  90. 1 ± 0. 5 SIFT-FV  [49]  93. 0 ± 1. 1 High dim LBP  [68]  93. 2 ± 1. 1 LBP + LHS (proposed) 89. 0 ± 0. 1 SIFT-FV + LHS (proposed) 93. 5 ± 0. 2 Methods using large amts of external labeled data Method Accuracy High dim LBP  [68]  95. 2 ± 1. 1 Deep learning  [36, 38]  97. 4 ± 0. 3    [49] ), and when combined with LHS the performance improves to 93. 5%, which is a modest improvement over the state-of-the-art in the 'Supervised, unrestricted, label-free outside data' protocol  9. Thus, we conclude that LHS features are competitive in the low complexity domains and are complementary to the high complexity features for supervised face verification on LFW. In the next section we discuss their time and space benefit over the high complexity features.
Conclusions We have presented a model that captures higher-order statistics of small local neighbohoods to produce a highly discriminative representation of the images. Our experiments, on two challenging texture datasets and two challenging facial analysis datasets, validate our approach and show that the proposed model encodes more local information than the competing methods and achieves competitive results. Two of the datasets we used, one each for textures and faces, were relatively simpler while two other were more difficult. The results on the simpler datasets served to demonstrate that the method is capable of having a richer appearance descriptor compared to existing methods. While on the more challenging case, we showed with experiments on the supervised task of face verification on the challenging Labeled Faces in the Wild (LFW) dataset that the proposed method achieves best results for low complexity features and is complementary to the high dimensional features.
When combine with the state-ofthe-art method it improves the performance to establish a new state-of-the-art on the LFW dataset when no external labeled data is used. Compared to the best method the proposed method is two orders of magnitude faster to compute and an order of magnitude compact making it a very appropriate choice for low complexity devices e. g. embedded systems. While the current state-of-the-art systems, based on deep networks trained with large amounts of external data  [32, 33, 34, 35, 36, 37, 38, 39, 40, 41]  have gained, the proposed method is still relevant due to its speed -we could use it as an initial low complexity stage of a cascade based system. Also, in very low complexity/cost systems the size of the model might also limit the use of deep networks and make the proposed method relevant.
Getting expertise on such solver inside a library like Selalib is a key point, as such tool can be used for different solvers (semi-Lagrangian, PIC) and different geometries. Previous Poisson solvers using FFT (for polar or cartesian mesh) are no more valid in this context. Alternative possible strategies are to interface the code with other existing softwares (like Mudpack, used in  [24] ). Note that these difficulties were not present in the context of semi-Lagrangian simulations on simple grids. To see the robustness of the numerical method, we test the method both on sinusoidal perturbations of cartesian grids  [11]  and polar grids. In another work  [4] , the method is successfully tested for 2D × 2D Vlasov-Poisson simulations. Next steps of validation concern drift kinetic and gyrokinetic simulations.