dataesr/scientific-paragraphs-categorization huggingface dataset:
Several conclusions can be safely drawn from this study. First, the selected electrical features can be justified by the power supply topologies included in an HEA (the front-end circuitry that connects them to the power grid), which affect their current waveforms. Each subset of selected features contains for the most part odd-order harmonics related to power components. The performance of a designed classifier can be improved by the use of an optimal subset of features. Some features, such as P, P 1 , P H , Q, Q 1 , andQ H , are retrieved in most of the subsets of selected features, which shows their importance for HEAs' identification. Secondly, several observations can be made according to the chosen classifier: DNN requires many training data and works poorly on the small proposed dataset (and works better on the PLAID dataset); LDA is sensitive to unbalanced datasets, and it works less well on PLAID; KNN method is efficient and sensitive to the choice of descriptors; RF is a state-of-the art method in automatic classification before the arrival of deep learning and is robust and gives good results in most cases.
where V k are the covariance matrices built from the corresponding n k individuals (number of individuals of class k ∈ {1,. , K}); g = 1 the mean over all the individuals of the whole dataset X and the mean over all the individuals in the class k, respectively. Then, the tested individuals are projected into the discriminative linear space before being assigned to the class whose centroid is the closest in terms of the Euclidean distance. •The proposed DNN classification method uses the same fully connected DNN architecture as presented in Section 4. 1. 3 for FS. Our implementation is based on tensorflow/keras (https://keras. io/). The training is completed with a batch size equal to 64 and a maximal number of 350 epochs (one epoch is reached each time the whole training dataset is processed once).
Category of HEA Number Number Category of HEA Number Number Category of HEA Number of HEAs of power of HEAs of power of HEAs of power levels levels levels lists the considered categories of HEAs. Number 2 Flat iron 1 1 Plasma TV 1 1 Microwave 1 1 LCD TV 1 2 Hand Mixer 1 1 Washing machine 9 1 Fryer 1 1 Coffee Maker 1 1 Rice cooker 2 1 Waffle iron 1 2 Laptop 1 1 Vacuum 1 5 1 Iron 1 2 Fridge 1 1 Vacuum 2 2 1 Fan 3 1 Oven 2 1 Radiator 3 2 Hair dryer 4 2 LED lamp 1 3 Kettle 1 3 Incandescent lamp 1 1 Iron 1 2 Low energy lamp 1 Figure 2. Measured appliances included in our new proposed dataset.
The integrals are independent of the Cauchy surface chosen. Here, dVol Σ is the Lorentzian surface measure. In case g is even and ψ is even this simplifies to g(s)Υ (1) ν,ψ (s)ds = 2 Σ (ν xG(x, ỹ)) ỹ=x dVol Σ(x). Proof. The trace formula follows from Theorem 5. 3, in particular the simpler form (46). To obtain (52) from (  46 ), it suffices to observe that the trace in (52) replaces (s, s ′ ) by α(s ′ , s) = (s ′ , sνs ′ ) and then integrates in s ′ against ψ(s ′ ). We now give a second proof that does not use [SZ18, Theorem 4. 1] or Theorem 5. 3 explicitly. Proof. We introduce the Σ-dependent ladder projector: Π Σ ν,ψ ∶= R ψ(s)Re -isD θ ○ e isνD Z Eds ∶ H 1 ( Σ) ⊕ L 2 ( Σ) → H 1 ( Σ) ⊕ L 2 ( Σ). ( 54 ) as an operator on the Cauchy data space H 1 ( Σ) ⊕ L 2 ( Σ). Note that under the extension-restriction identification in Definition 4.
In this paper, we make use of the 2-dimensional data obtained through t-Stochastic Neighborhood Embedding (t-SNE) when applied on high-dimensional data of Urdu handwritten characters and numerals. e instances of the dataset used for experimental work are classified in multiple classes depending on the shape similarity. We performed three tasks in a disciplined order; namely, (i) we generated a state-of-the-art dataset of both the Urdu handwritten characters and numerals by inviting a number of native Urdu participants from different social and academic groups, since there is no publicly available dataset of such type till date, then (ii) applied classical approaches of dimensionality reduction and data visualization like Principal Component Analysis (PCA), Autoencoders (AE) in comparison with t-Stochastic Neighborhood Embedding (t-SNE), and (iii) used the reduced dimensions obtained through PCA, AE, and t-SNE for recognition of Urdu handwritten characters and numerals using a deep network like Convolution Neural Network (CNN).
e accuracy achieved in recognition of Urdu characters and numerals among the approaches for the same task is found to be much better. e novelty lies in the fact that the resulting reduced dimensions are used for the first time for the recognition of Urdu handwritten text at the character level instead of using the whole multidimensional data. is results in consuming less computation time with the same accuracy when compared with processing time consumed by recognition approaches applied to other datasets for the same task using the whole data.
Introduction Data visualization deals with presenting the data in some visual context to make it trivial for the human to understand the nature of the data  [1]. Furthermore, this activity helps in finding the patterns and hidden information, if they exist, in the data for further processing like data clustering and data classification. Nowadays, it is of common observation that the information related to the data science is of high dimensions, and therefore, its visualization in low-dimensional space becomes impractical (Buja et al. [2] ; Saeed et al. [1] ). In almost all of the data science datasets, the researchers have had to deal with this acute and critical issue. While analyzing the high-dimensional data, almost every other researcher is interested in finding the optimal number of dimensions (or features) in order to apply any appropriate classifier for giving better performance (Nguyen and Holmes  [3] ; Song et al.
[4] ; ur Rehman et al. [5] ). It is pertinent to mention that the terms "high-dimensional data visualization" and "high-dimensional visualization" are used interchangeably in the literature; however, there is a succinct difference between these. In the first, the term high refers to data itself, whereas, in the second, it refers to the visualization. e interesting fact lies in visualizing the high-dimensional data on 2D or 3D plane that we have to apply some appropriate dimensionality reduction approaches on the whole data, since it is next to impossible in order to visualize the high-dimensional data on low-dimensional space (Engel et al. [6] ; Song et al. [4] ; ur Rehman et al. [5] ). e term "dimensionality" refers to the number of variables, characteristics, or features in which most of the datasets exist in the field of data science nowadays.
Our Motivation In this work, we performed experiments in two phases, namely, (i) the visualization of Urdu handwritten characters and numerals containing pixel-based features embedded with structural-based features using dimensionality reduction approaches and (ii) the recognition of these characters and numerals using deep network model of CNN using both pixel-based and structural based features and then using reduced dimensions of the same instances obtained through t -SNE and other approaches. In order to perform the abovementioned tasks, we prepared a novel data set of Urdu handwritten characters and numerals. One of the issues associated with Urdu script is the shape similarity among its characters and numerals, as shown in Figure  2. ese issues may result in generating overlapping clusters during visualization in low-dimensional space, which may directly affect the accuracy rate in the recognition process.
erefore, we have to apply some suitable approach that results in precise and correct clusters with perfect separations. Moreover, intracluster separations of the data instances should be clear to depict the separations among the individual instances of the Urdu characters and numerals. e following factors and issues are the cause of our motivation to perform some experiments to resolve these issues. To the best of our knowledge, there is a lack of noteworthy work done to date in order to transform faithfully the high-dimensional data of the Urdu handwritten characters to low-dimensional space. (i) ere is no dataset associated with the Urdu handwritten characters and numerals that is available publicly to perform text recognition tasks at the character level. (ii) Also, there is no process of recognition adopted at the character level in Urdu handwritten text using reduced dimensions obtained through dimensionality reduction approaches.
Dataset Preparation As mentioned in the earlier section, there is a lack of an appropriate and concise data corpus containing Urdu handwritten characters and numerals to perform text recognition tasks at the character level. ere are some publicly available datasets of Urdu handwritten text like Urdu Nastaliq Handwritten Dataset (UNHD) (Ahmed et al. [22] ; Das et al. [23] ; Husnain et al. [24] ; Sagheer et al. [25] ), but unfortunately, the data sets have only the Urdu handwritten numerals. Furthermore, these instances are not enough to apply state-of-the-art machine learning algorithms to get better results. In order to bridge the gap and provide the state-of-the-art dataset of this kind, we invited about 1000 native Urdu speaking persons from different academic, administrative, and social groups of different age groups and gender.
Moreover, the handicapped and physically disabled people are also involved to make the dataset more concise and comprehensive. All the authors were directed to write in a separate column of the printed sheets in his (or her) handwriting. Each of the sheets has printed images of 40 basic Urdu alphabets along with the 10 Urdu numerals in Nastaliq font. Figure  3  depicts the sample page of our dataset. Furthermore, we have also recorded the demographic information of each author to generate the ground truth values of the whole data set. is information includes the basic information about each author, namely, age, race, gender, level of education, type of job, physical disability (if any), preference of left (or right) hand while writing, etc. is activity helped us in making the dataset more concise and comprehensive.
After collection of an appropriate amount of data instances, the handwritten pages of both the Urdu characters and numerals were carefully scanned on a flatbed scanner at standard 300 dpi resolution. Furthermore, the scanned pages are then segmented manually into an image size of 28 × 28 to capture Urdu handwritten character and numeral individually. As mentioned earlier, the whole dataset consists of 1000 × 10 � 10,000 Urdu numerals and 1000 × 40 � 40,000. Urdu characters images: for experimental work, we randomly selected the 6000 (600 each for the ten numerals) images of Urdu numerals and 28, 000 (700 each of 40 characters) images of Urdu characters. It is pertinent to mention that we have planned to increase the number of participants to 1500 in order to include as many as possible the variations of different handwriting to create more comprehensive and multifaceted data.
e complete data set, after completion, will be made publicly available for the Complexity researchers, since there is no dataset of such kind that is available till date. It is common that noise and distortion may likely occur while scanning the images. In order to remove the noise, we directed the authors to write in black ink only. is activity makes the noise removal process rather trivial task in a way that the colors other than black were considered as noise and removed easily. Furthermore, before applying any dimensionality reduction approach, we make use of some data transformation algorithms, like gray-scale conversion, image segmentation, image resizing, extracting area of interest from the text image, normalizing the raw data, etc. , to prepare our data set in some appropriate form.
Experimental Results of Dimensionality Reduction Approaches In this section, we present the results obtained by applying PCA (Roweis and Saul  [13] ), AE, and t-SNE on our two variants of the dataset. One variant contains the pixel-based features of both the Urdu numeric and characters. e second variant contains structural-based features embedded with pixel-based data of both the Urdu numeric and characters. e experimental results depict that adding structural based features presents visualization results with accurate separations among the clusters and also maintains intracluster variations. As mentioned earlier, we represented each text image in our dataset in 28 × 28 � 784 pixel values (or dimensions). For evaluation purposes, we make use of the three different dimensionality reduction approaches, namely, Principal Component Analysis (PCA) (Roweis and Saul  [13] ); Autoencoders (Liou et al.
[26] ); and t-SNE (Van Der Maaten et al. [8] ) to our Urdu handwritten character and numeral dataset. We used the following parameter setting while using t-SNE (Van Der Maaten et al. [8] ) and its variant while producing visualization results: the number of iterations, T, set to 1000 in order to achieve the optimized value of gradient descent, the fine-tuned parameter momentum term, α(t), is regulated to 0. 5, where t is less than 250, while α(t) is set to 0. 8 for t is greater than 250. e initial value of learning rate η is set to 100 that may be regulated for each iteration equipped with a highly adaptive learning rate scheme. It is pertinent to mention that the experiments were executed using varying initial learning rates; however, we observed little variations in the quality of the resulting visualization results.
Moreover, along with the other parameters, the perplexity is a tunable parameter that depicts how to correspond and normalize the local and global aspects of the data. In other words, we can say that perplexity helps in finding how many close neighbors each point has. It also has a complex effect on the resulting visualizations, as explained in the original t-SNE paper (Maaten and Hinton  [9] ). e selection of an optimal value of perplexity is of significant importance; therefore, one must have to take care, since it can be achieved only by producing multiple visualizations with varying perplexity values. erefore, in this paper, we chose the best result based on the quality of visualization. Furthermore, it is an interesting fact that both the standard and proposed versions of t-SNE work equally and uniformly on a single assumed value of the perplexity for the whole dataset.
Applying Standard t-SNE. e results obtained through the standard t-SNE on the dataset having only the pixelbased information of the Urdu handwritten numerals are shown in Figure  5. It is clear from the results that there are some overlapping clusters while considering pixel-based information only. We performed a series of experiments using t-SNE on the same dataset using multiple perplexity values. It was observed from the output that, with the perplexity value of 70, the results showed some little  improvement in terms of separations among the clusters of each clas of the Urdu handwritten numerals when compared with results using different perplexity values of 30, 50, and 100. It is of general observation that, with lower perplexity value, the local structure of the data tends to show higher perseverance, i.
e. , the clusters having a smaller number of data points plotted very close to each other resulting in a compact visualization. On the other hand, the higher the perplexity value, the higher the perseverance in the global structure of the data; i. e. , the data points will be plotted with some notable difference (intracluster difference) and also maintaining the separation between the clusters (intercluster difference). Figure  6  depicts the detailed description of the structural features of both the Urdu numerics and characters. e results obtained by applying the standard t-SNE on the dataset having a combination of both the pixel-and structural-based features are shown in Figure  7. e results depicted much improvement by producing the clusters with clear separations. From the results presented in Figure  7 , it can be observed easily that some of the Urdu numerals like 2, 3, and 4 have overlapping clusters.
is overlapping is based on the fact that these Urdu numerals share much shape similarity. A similar behavior can also be witnessed in the case of Urdu numerals 0 and 1. It can be concluded that combining the pixel-(i. e. , 784 features) and structural-based features (i. e. , 10 features) failed to be useful when applied to the standard t -SNE algorithm. e same approach of standard t-SNE is applied to the datasets of Urdu handwritten characters. One dataset contains the pixel-based data, and the other contains both the pixel and structural based features. It is pertinent to mention that only those Urdu characters are considered for the experiments that share much of the shape similarity. Figure  8  shows the Urdu characters grouped on the basis of shape similarity. e remaining characters are not considered to reduce the ink-noise ratio while visualizing the 40 characters individually.
Fused Data Matrix. In this section, we discussed a novel way to embed the two or multiple observation spaces by calculating the pairwise Euclidean distances of the instances resulting in a fusion matrix. Furthermore, we also modified the standard t -SNE to make it able to assist the data in a fused matrix form. In our dataset, we build a single fusion matrix by calculating pairwise Euclidean distance of the data instances of the two independent spaces, i. e. , pixel-and structure-based information. e resulting fusion matrix is then plugged into the modified t-SNE that makes use of both the features mentioned earlier. is modified t-SNE will give equal importance to both the features, thus generating even more clear and accurate clusters with precise separations. Our assumption lies in the fact that since the data from both the independent spaces sources are highly conjunctive and dependent, therefore, their fusion will produce the more accurate visualization results in some low-dimensional space when the visualization results are compared with the output generated using either the pixel-based data or the structural data alone.
e pixel-based features are saved in a matrix form of size 1 × n for a single image of Urdu handwritten character, where n is the pixel-wise binary data for each image of size 32 × 3. If we consider Urdu numerals (for example), we have used 5000 images of Urdu handwritten numerals (500 each of ten numerals) for our experimental work; therefore, the dataset is of size 500 × 32. is pixel-based information is then embedded with the structural features, using the Euclidean Distance, of the Urdu handwritten numerals. Since the Urdu numerals share shape similarity, for example, digits two and three (shown in Figure  2 ), these structural based features are embedded to the pixel-based features to reduce the visualization issues while plotting similar shape images. Furthermore, we introduced equation (  1 ) to balance the weighted combinations of both of the independent original spaces.
Experimental Results Obtained through PCA, AE, and Modified t-SNE. In this section, we covered the visualization results of the fused matrix dataset of both the Urdu handwritten numerics and characters. e results showed (see Figure  10 ) that our modified t-SNE with fused data matrices of our dataset outperformed the classical approaches of PCA and AE. Similarly, while visualizing the fused matrix of Urdu handwritten characters, we applied the same set of  algorithms having the same parameter settings. Figure  11  shows the visualization results produced when applied to Urdu handwritten characters.
In order to resolve this issue, we make the standard t-SNE compatible with our data by implementing the pair-wise Euclidean distance formula to the data points of our dataset. is activity embedded the data points coming from two independent spaces in one space, thus making it compatible with the standard t-SNE. It is noteworthy that we have not reduced the size of the image; rather, we have reduced the dimension of the feature-space, that is, the embedded version of structural and pixel-based features. ese reduced dimensions are produced by the dimensionality reduction approaches discussed in detail in the sections above. is reduceddimensional data is then plugged into the proposed model of CNN in order to recognize the numeric (or character) data. is activity takes minimum time (12 CPU seconds) and reported same accuracy rate in the classification of both the Urdu handwritten characters and numerals as compared with the same model applied on the original dimensions of the text images, reported in our work (Husnain et al.
Conclusion In this paper, we made use of the reduced dimensions obtained through the dimensionality reduction approaches like PCA, AE, and t-SNE, in recognition of Urdu handwritten characters and numerals. Furthermore, the structural features of each handwritten character are extracted and embedded in pixel-based features to enrich the features of our dataset. In order to make it more compatible, we modified the standard t-SNE by including equations that support the pairwise Euclidean distances of the features from two independent spaces. is modification results in accelerating the efficiency of standard t-SNE by producing a quite better low-dimensional data that eventually helped in visualizing both the Urdu handwritten characters and numerals. Furthermore, this reduced dimensional data is fed to the CNN model to recognition purposes.
Generalizations to a higher number of independent spaces are practically not possible since the computation time increases while computing pairwise distances among the high-dimensional data instances. To the best of our knowledge, a very limited work is observed in the field of handwritten text recognition at character level, and the dataset of this kind is not available to date. Our results are the initiatives towards classification of the handwritten text at character level in the Urdu script, and there may be some lack of quality and comprehensiveness. e values in bold (in diagonal) are representing the accuracy percentage of the classification of Urdu handwritten characters obtained by applying using variations of the n-fold cross-validation approach. Table  5 : Comparison Analysis of our proposed approach for Urdu handwritten character classification with state-of-the-art approaches.
[38]  (MMCNN) fuzzy C-Means classifier ANN Pixel-based features 88. 00% Said et al. [39]  ANN Pixel-based features 94. 00% Mowlaei et al. [40]  ANN Wavelet-based features 97. 34% Our approach CNN Pixel-and geometrical-based 99. 01% Our future work will encompass the recent trends and resolve these issues observed in our current work. Furthermore, we have also created a state-of-the-art dataset containing the Urdu handwritten characters and numerals; to the best of our knowledge, there is no publicly dataset available of such kind. e existing datasets of Urdu handwritten text mainly consist of the Urdu handwritten words and sentences. e usage of these existing datasets cannot be used efficiently for recognition of the Urdu text at the character level. We also presented a comparative analysis of the results obtained through different approaches to propose recommendations based on parameter tuning.
It is also concluded that the deep network can help in performing the recognition and classification task of the handwritten text of cursive scripts in minimum time. Furthermore, our approach also helps in providing a platform to the researchers and developers to develop the applications for the children to learn how to write Urdu (and other cursive languages) characters and numerals with higher accuracy. As mentioned earlier, there is also a deficiency of some standard data repository in the Urdu domain for generating and comparing the benchmark results. In order to bridge this gap, we are working on generating and extending our dataset that will be published publicly in the near future.