Non-numerical Variables Research Articles

Stock Daily Return Prediction of Amazon and Alibaba using Linear Regression and LSTM

The stock plays a key role in the economy market. As an individual investor, predicting stock return is always a hot research topic. In recent years, Amazon and Alibaba have become the head of e-commerce and the competition between them is becoming intense. In this paper, linear regression model and LSTM model based on machine learning are introduced and applied to predict the stock return of these two companies. RMSE and R2 are used to choose the number of variables and evaluate those models. This study finds that the simplest linear regression is even better than LSTM model with limited sources. The negative R2 scores of these two methods implies the nonlinearity and instability of stock return. However, predicting stock return is still possible. To investigate more about predicting stock return, more information such as the turnover rate and other non-numerical variables can be included in other models. Different types of LSTM model with different parameter setting can be applied to investigate deeply.

Zebrafish excel in number discrimination under an operant conditioning paradigm

Numerical discrimination is widespread in vertebrates, but this capacity varies enormously between the different species examined. The guppy (Poecilia reticulata), the only teleost examined following procedures that allow a comparison with the other vertebrates, outperforms amphibians, reptiles and many warm-blooded vertebrates, but it is unclear whether this is a feature shared with the other teleosts or represents a peculiarity of this species. We trained zebrafish (Danio rerio) to discriminate between numbers differing by one unit, varying task difficulty from 2 versus 3 to 5 versus 6 items. Non-numerical variables that covary with number, such as density or area, did not affect performance. Most fish reached learning criterion on all tasks up to 4 versus 5 discrimination with no sex difference in accuracy. Although no individual reached learning criterion in the 5 versus 6 task, performance was significant at the group level, suggesting that this may represent the discrimination threshold for zebrafish. Numerosity discrimination abilities of zebrafish compare to those of guppy, being higher than in some warm-blooded vertebrates, such as dogs, horses and domestic fowl, though lower than in parrots, corvids and primates. Learning rate was similar in a control group trained to discriminate between different-sized shapes, but zebrafish were slightly more accurate when discriminating areas than numbers and males were more accurate than females. At the end of the experiment, fish trained on numbers and controls trained on areas generalized to the reciprocal set of stimuli, indicating they had used a relational strategy to solve these tasks.

Towards a standardization of non-symbolic numerical experiments: GeNEsIS, a flexible and user-friendly tool to generate controlled stimuli

Several studies have suggested that vertebrate and invertebrate species may possess a number sense, i.e. an ability to process in a non-symbolic and non-verbal way the numerousness of a set of items. However, this hypothesis has been challenged by the presence of other non-numerical continuous physical variables, which vary along with numerosity (i.e., any change in the number of visual physical elements in a set naturally involves a related change in visual features such as area, density, contour length and convex hull of the stimulus). It is therefore necessary to control and manipulate the continuous physical information when investigating the ability of humans and other animals to perceive numerousness. During decades of research, different methods have been implemented in order to address this issue, which has implications for experiment replicability and inter-species comparisons, since no general standardized procedure is currently being used. Here we present the ‘Generation of Numerical Elements Images Software’ (GeNEsIS) for the creation of non-symbolic numerical arrays in a standardized and user-friendly environment. The main aim of this tool is to provide researchers in the field of numerical cognition a manageable and precise instrument to produce visual numerical arrays controlled for all the continuous variables. Additionally, we implemented the ability to actively guide stimuli presentation during habituation/dishabituation and dual-choice comparison tasks used in human and comparative research.

Food Quantity Discrimination in Angelfish (Pterophyllum scalare): The Role of Number, Density, Size and Area Occupied by the Food Items.

Quantity discrimination, the ability to identify, process, and respond to differences in number, has been shown in a variety of animal species and may have fitness value. In fish, the ability to distinguish between numerically different shoals has been well studied. However, little work has been devoted to the investigation of such ability in a foraging context. Nevertheless, angelfish (Pterophyllum scalare) have been previously shown to be able to discriminate numerically different sets of food items, with variables such as size and density of the food items playing important roles in making the choice. Here, we examine the possible role of other numerical and non-numerical variables. Using a spontaneous binary choice task, we contrasted sets of food items differing in specifically controlled ways: (1) different numerical size but equal inter-item distance; (2) different numerical size and different inter-item distance; and (3) identical total contour length and area occupied but different individual food size and inter-food distance between the contrasted food sets. In Experiment 1, angelfish were found to prefer the sets with a large number of food items. In Experiment 2, they preferred the numerically smaller sets with clustered items to the numerically larger sets with scattered items, but only when the sets were in the large number range (10 vs. 5 food items). Finally, in Experiment 3 fish preferred numerically smaller sets with large-sized and scattered food items in the large number range sets. We conclude that food item number, density, and size may not be considered individually by angelfish, but instead, the fish respond to all these factors attempting to maximize energy gained from eating the food while minimizing energy expenditure collecting and/or protecting the food.

EGA-STLF: A Hybrid Short-Term Load Forecasting Model

As the development of smart grids and electricity markets around the world, short-term load forecasting (STLF) plays an increasingly important role in safe and economical operations of power systems. Facing massive multivariate and heterogeneous data from smart grid environment, traditional STLF methods no longer meet the requirements of comprehensive prediction performance in big data era. Therefore, a novel STLF model named EGA-STLF is proposed in this paper. The core idea of the proposed model is mainly based on distributed representation, bidirectional gated recurrent unit (Bi-GRU), and attention mechanism. EGA-STLF encodes non-numerical variables in input data into sparse vectors by distributed representation during preprocessing, which can more reasonably reflect the correlations between different variables across the temporal sequence. Moreover, the Bi-GRU layer in EGA-STLF processes the past and the future information simultaneously to fully extract temporal and nonlinear features from input data for the improvement of forecasting accuracy. In addition, the introduction of attention mechanism highlights the role of key features in load forecasting, which is beneficial to generate more accurate forecasting results for EGA-STLF. The validity and superiority of EGA-STLF is verified by taking the actual data from Victoria state and Queensland state in Australia for experimental research in which mean absolute percentage error (MAPE) and root mean square error (RMSE) are selected as evaluation metrics. The experimental results indicate that EGA-STLF outperforms the state-of-the-art models based on SVR and MLP in term of comprehensive forecasting accuracy. Hence, EGA-STLF is a promising method to create economic benefits in power industry.

Multiple regression model on categorical factors

Purpose. To find a quantitative assessment of the influence of categorical factors on the variable being explained. To predict the value of a numerical variable depending on the values of other numerical variables, a regression analysis of a statistical model based on observational data is used. However, in many situations, categorical variables must be included in the model. Method. Categorical factors are included in the model as dummy variables whose values 1 or 0 correspond to the presence or absence of a certain categorical level of the explanatory variable.However, such an approach is justified only if the category variable has only two levels: the presence or absence of a certain quality. Then the value of the dummy variable is due to be equal to 1 in the first case and 0 − in the second one. If there are several categorical levels, it is proposed to introduce dummy variables corresponding to each level and taking the value 1 into the multiple regression model if the categorical explanatory variable takes the value of the corresponding level and is 0 for all its other values (levels). In addition, the model makes it possible to take into account the possible interaction of categorical levels of various explanatory non-numerical variables and the effect of such interaction when quantifying their influence on the explained variable. Results. Proposed model of multiple regression on the categorical factors , which allows to find a quantitative assessment of the impact on the explanatory variable, not only numerical but also categorical independent variables. Moreover, the model takes into account the fact that in the absence of any influence from the explanatory variables, i.e. when they are all 0, the regression should also be 0 . Moreover, the so-called “shift” of direct regression is absent ( and, moreover, cannot be negative, as for the mathematical line ) . Scientific novelty. The proposed model extends and generalizes the capabilities of the regression analysis of statistical models for the case of categorical factors. Practical relevance. The model of multiple regression on categorical factors allows us to solve the following problems: selection of categorical levels of non-numeric parameters when designing systems; deciding on the choice of strategy in financial activities and management.

Spontaneous perception of numerosity in pre-school children

There is strong evidence that humans can make rough estimates of the numerosity of a set of items, almost from birth. However, as numerosity covaries with many non-numerical variables, the idea of a direct number sense has been challenged. Here we applied two different psychophysical paradigms to demonstrate the spontaneous perception of numerosity in a cohort of young pre-school children. The results of both tasks showed that even at that early developmental stage, humans spontaneously base the perceptual choice on numerosity, rather than on area or density. Precision in one of these tasks predicted mathematical abilities. The results reinforce strongly the idea of a primary number sense and provide further evidence linking mathematical skills to the sensory precision of the spontaneous number sense, rather than to mechanisms involved in handling explicit numerosity judgements or extensive exposure to mathematical teaching.

Key Factors Affecting Environmental Protection Values in China

Utilizing a total of 31 non-numerical variables on environmental protection values from 1990–2014 in the World Values Survey (WVS) database (i.e., WVS2, WVS3, WVS4, WVS5 and WVS6), this study analyses the temporal changes of environment protection values in China and identifies the key factors related to these changes. We define indices for the standardized values of action and attitudes to environmental protection after clustering the 31 variables into two categories according to the meanings of their variable labels. Through statistical analysis on the possible impacting variables (e.g., GDP (gross domestic product) per capita, carbon emissions per capita, industrial wastes, and rural township enterprises), we find that the variable rural township enterprises is the main factor that causes obvious changes in action and attitude, coupled with other environmental impacts at home and abroad, such as economic globalization, the financial crisis, and frequent natural disasters. In particular, the significant improvement in action during the period from the late 2000s to early 2010s is mainly due to switching the emphasis from quantity to quality. The structural adjustment and industrial upgrade of township enterprises were promoted as important measures to improve environmental values according to Document No. 1 of the Central Committee of the People’s Republic of China in 2010.

A quantitative analysis of global environmental protection values based on the world values survey data from 1994 to 2014

The four most recent sub-datasets of the World Value Survey (WVS) database (i.e., WVS3, WVS4, WVS5, and WVS6) contain a total of 25 non-numerical variables of environmental protection values and cover the period from 1994 to 2014. This study utilized these datasets to obtain the spatiotemporal distributions of the values and provided a preliminary analysis of the environmental protection values in different cultural districts. The work includes 4 parts. First, the information from the values included in the 25 variables is subjectively classified into action values and attitude values according to the meanings of the variable labels. Then, quantitative clustering is used to verify the results of the first step. These two steps consistently classify the 25 variables into “action” and “attitude” families. At the third step, all variables are processed as horizontal distributions in terms of the country using the arithmetic mean of the serial numbers chosen by the respondents because these numbers reflect the grade of the behavior or attitude toward environmental protection. A clustering procedure is also included in this step to reconfirm the classification results of the previous two steps. Finally, the two families are quantified using their common factors, which are the first leading modes of the empirical orthogonal function for each family. The multiyear averaged cultural district mean “action” and “attitude” indices are analyzed according to the World Culture Map. The results show that districts with different cultures have very different environmental protection values.

Accumulation of non-numerical evidence during nonsymbolic number processing in the brain: An fMRI study.

Behavioral evidence has shown that when performing a nonsymbolic number comparison task (e.g., deciding which of two dot arrays contains more dots), participants' responses are sensitive to affected by both numerical (e.g., number of items) and non-numerical magnitudes (i.e., area, density, etc.). Thus far it is unclear what brain circuits support this process of accumulating non-numerical variables during nonsymbolic number processing. To investigate this, 21 adult participants were asked to engage in a dot comparison task. To measure the neural correlates of accumulating numerical and non-numerical variables, we manipulated the number of the non-numerical magnitudes that were congruent (correlated with number) or incongruent (anticorrelated with number). In a control task, participants were asked to choose the darker of two gray rectangles (brightness task). The tasks were matched in terms of their difficulty. The results of a whole brain analysis for regions sensitive to the congruity of numerical and non-numerical magnitudes revealed a region in the right inferior frontal gyrus (rIFG). Activation in this region was found to be correlated with the relative congruency of numerical and non-numerical magnitudes. In contrast, this region was not modulated by difficulty of the brightness control task. Accordingly in view of these findings, we suggest that the rIFG supports the accumulation of non-numerical magnitudes that are positively correlated with number. Therefore taken together, this study reveals a brain region whose pattern of activity is influenced by the congruency between numerical and non-numerical variables during nonsymbolic number judgments. Hum Brain Mapp 38:4908-4921, 2017. © 2017 Wiley Periodicals, Inc.

Dual-mode nested search method for categorical uncertain multi-objective optimization

Categorical multi-objective optimization is an important issue involved in many matching design problems. Non-numerical variables and their uncertainty are the major challenges of such optimizations. Therefore, this article proposes a dual-mode nested search (DMNS) method. In the outer layer, kriging metamodels are established using standard regular simplex mapping (SRSM) from categorical candidates to numerical values. Assisted by the metamodels, a k-cluster-based intelligent sampling strategy is developed to search Pareto frontier points. The inner layer uses an interval number method to model the uncertainty of categorical candidates. To improve the efficiency, a multi-feature convergent optimization via most-promising-area stochastic search (MFCOMPASS) is proposed to determine the bounds of objectives. Finally, typical numerical examples are employed to demonstrate the effectiveness of the proposed DMNS method.

Asymmetric Processing of Numerical and Nonnumerical Magnitudes in the Brain: An fMRI Study.

It is well established that, when comparing nonsymbolic magnitudes (e.g., dot arrays), adults can use both numerical (i.e., the number of items) and nonnumerical (density, total surface areas, etc.) magnitudes. It is less clear which of these magnitudes is more salient or processed more automatically. In this fMRI study, we used a nonsymbolic comparison task to ask if different brain areas are responsible for the automatic processing of numerical and nonnumerical magnitudes, when participants were instructed to attend to either the numerical or the nonnumerical magnitudes of the same stimuli. An interaction of task (numerical vs. nonnumerical) and congruity (congruent vs. incongruent) was found in the right TPJ. Specifically, this brain region was more strongly activated during numerical processing when the nonnumerical magnitudes were negatively correlated with numerosity (incongruent trials). In contrast, such an interference effect was not evident during nonnumerical processing when the task-irrelevant numerical magnitude was incongruent. In view of the role of the right TPJ in the control of stimulus-driven attention, we argue that these data demonstrate that the processing of nonnumerical magnitudes is more automatic than that of numerical magnitudes and that, therefore, the influence of numerical and nonnumerical variables on each other is asymmetrical.

Non-symbolic halving in an Amazonian indigene group.

Much research supports the existence of an Approximate Number System (ANS) that is recruited by infants, children, adults, and non-human animals to generate coarse, non-symbolic representations of number. This system supports simple arithmetic operations such as addition, subtraction, and ordering of amounts. The current study tests whether an intuition of a more complex calculation, division, exists in an indigene group in the Amazon, the Mundurucu, whose language includes no words for large numbers. Mundurucu children were presented with a video event depicting a division transformation of halving, in which pairs of objects turned into single objects, reducing the array's numerical magnitude. Then they were tested on their ability to calculate the outcome of this division transformation with other large-number arrays. The Mundurucu children effected this transformation even when non-numerical variables were controlled, performed above chance levels on the very first set of test trials, and exhibited performance similar to urban children who had access to precise number words and a surrounding symbolic culture. We conclude that a halving calculation is part of the suite of intuitive operations supported by the ANS.

Once upon a time there was complex numerical estimation

Once upon a time there was complex numerical estimation

Activity counts: the effect of swimming activity on quantity discrimination in fish.

Human infants and non-human animals can discriminate the larger of two sets of discrete items. This quantity discrimination may be based upon the number of items, or upon non-numerical variables of the sets that co-vary with number. We have demonstrated that angelfish select the larger of two shoals of conspecifics without using inter-fish distance or space occupied by the stimuli as cues. However, density appeared to influence the choice between large shoals. Here, we examine the role of another non-numerical cue, swimming activity of the stimulus fish, in quantity discrimination by angelfish. To control this variable, we varied the water temperature of the stimulus aquaria or restricted the space occupied by each fish in the stimulus shoals. We used the previously successfully discriminated contrasts consisting of large (10 vs. 5) and small (3 vs. 2) shoals. We also studied whether more active or less active shoals are preferred in case of equally sized shoals (10 vs. 10, 5 vs. 5, and 3 vs. 3). When differences in stimulus fish activity were minimized by temperature manipulation we found angelfish to prefer the larger shoal in the 3 vs. 2 comparison, but not in the 10 vs. 5 comparison. When activity was controlled by space restriction, angelfish preferred the larger shoal in both numerical contrasts. These results imply that the overall activity level of the contrasted shoals is not a necessary condition for small shoals discrimination in angelfish. On the other hand, the results obtained for the large shoals, together with results obtained in the control treatments (equal numerical contrasts and differing activity levels), suggest that activity is a sufficient condition for discrimination when large shoals are involved. Further experiments are needed to evaluate the influence of other continuous variables, and to assess whether the mechanisms underlying performance are comparable to those suggested for other animals.

Numerosity estimation in visual stimuli in the absence of luminance-based cues.

BackgroundNumerosity estimation is a basic preverbal ability that humans share with many animal species and that is believed to be foundational of numeracy skills.It is notoriously difficult, however, to establish whether numerosity estimation is based on numerosity itself, or on one or more non-numerical cues like—in visual stimuli—spatial extent and density. Frequently, different non-numerical cues are held constant on different trials. This strategy, however, still allows numerosity estimation to be based on a combination of non-numerical cues rather than on any particular one by itself.Methodology/Principal FindingsHere we introduce a novel method, based on second-order (contrast-based) visual motion, to create stimuli that exclude all first-order (luminance-based) cues to numerosity. We show that numerosities can be estimated almost as well in second-order motion as in first-order motion.Conclusions/SignificanceThe results show that numerosity estimation need not be based on first-order spatial filtering, first-order density perception, or any other processing of luminance-based cues to numerosity. Our method can be used as an effective tool to control non-numerical variables in studies of numerosity estimation.

Relevant and Non-Redundant Amino Acid Sequence Selection for Protein Functional Site Identification

In order to apply a powerful pattern recognition algorithm to predict functional sites in proteins, amino acids cannot be used directly as inputs since they are non-numerical variables. Therefore, they need encoding prior to input. In this regard, the bio-basis function maps a non-numerical sequence space to a numerical feature space. One of the important issues for the bio-basis function is how to select a minimum set of bio-basis strings with maximum information. In this paper, an efficient method to select bio-basis strings for the bio-basis function is described integrating the concepts of the Fisher ratio and “degree of resemblance”. The integration enables the method to select a minimum set of most informative bio-basis strings. The “degree of resemblance” enables efficient selection of a set of distinct bio-basis strings. In effect, it reduces the redundant features in numerical feature space. Quantitative indices are proposed for evaluating the quality of selected bio-basis strings. The effectiveness of the proposed bio-basis string selection method, along with a comparison with existing methods, is demonstrated on different data sets.

Use of Number by Fish

BackgroundResearch on human infants, mammals, birds and fish has demonstrated that rudimentary numerical abilities pre-date the evolution of human language. Yet there is controversy as to whether animals represent numbers mentally or rather base their judgments on non-numerical perceptual variables that co-vary with numerosity. To date, mental representation of number has been convincingly documented only for a few mammals.Methodology/Principal FindingsHere we used a training procedure to investigate whether mosquitofish could learn to discriminate between two and three objects even when denied access to non-numerical information. In the first experiment, fish were trained to discriminate between two sets of geometric figures. These varied in shape, size, brightness and distance, but no control for non-numerical variables was made. Subjects were then re-tested while controlling for one non-numerical variable at a time. Total luminance of the stimuli and the sum of perimeter of figures appeared irrelevant, but performance dropped to chance level when stimuli were matched for the cumulative surface area or for the overall space occupied by the arrays, indicating that these latter cues had been spontaneously used by the fish during the learning process. In a second experiment, where the task consisted of discriminating 2 vs 3 elements with all non-numerical variables simultaneously controlled for, all subjects proved able to learn the discrimination, and interestingly they did not make more errors than the fish in Experiment 1 that could access non-numerical information in order to accomplish the task.Conclusions/SignificanceMosquitofish can learn to discriminate small quantities, even when non-numerical indicators of quantity are unavailable, hence providing the first evidence that fish, like primates, can use numbers. As in humans and non-human primates, genuine counting appears to be a ‘last resort’ strategy in fish, when no other perceptual mechanism may suggest the quantity of the elements. However, our data suggest that, at least in fish, the priority of perceptual over numerical information is not related to a greater cognitive load imposed by direct numerical computation.

Do fish count? Spontaneous discrimination of quantity in female mosquitofish

The spontaneous tendency to join the largest social group was used to investigate quantity discrimination in fish. Fish discriminated between shoals that differed by one element when the paired numbers were 1vs2, 2vs3 and 3vs4, but not when 4vs5 or larger. Using large numerosities (>4), the ability to discriminate between two numbers improved as the numerical distance between them increased and a significant discrimination was found only with ratios of 1:2 or smaller (4vs8, 8vs16 and 4vs10). Experiments to control for non-numerical variables evidenced the role played by the total area of stimuli with both large and small numerosities; the total quantity of movement of the fish within a shoal appeared also important but only when large numerosities were involved. Even though the pattern of discrimination exhibited by female mosquitofish is not fully consistent with any of the existing models of quantity representation, our results seem to suggest two distinct mechanisms in fish, one used to compare small numbers of objects and one used when larger numerosities are involved.

Rough-Fuzzy C-Medoids Algorithm and Selection of Bio-Basis for Amino Acid Sequence Analysis

In most pattern recognition algorithms, amino acids cannot be used directly as inputs since they are nonnumerical variables. They, therefore, need encoding prior to input. In this regard, bio-basis function maps a nonnumerical sequence space to a numerical feature space. It is designed using an amino acid mutation matrix. One of the important issues for the bio-basis function is how to select the minimum set of bio-bases with maximum information. In this paper, we describe an algorithm, termed as rough-fuzzy c{\hbox{-}}{\rm{medoids}} (RFCMdd) algorithm, to select the most informative bio-bases. It is comprised of a judicious integration of the principles of rough sets, fuzzy sets, the c{\hbox{-}}{\rm{medoids}} algorithm, and the amino acid mutation matrix. While the membership function of fuzzy sets enables efficient handling of overlapping partitions, the concept of lower and upper bounds of rough sets deals with uncertainty, vagueness, and incompleteness in class definition. The concept of crisp lower bound and fuzzy boundary of a class, introduced in RFCMdd, enables efficient selection of the minimum set of the most informative bio-bases. Some new indices are introduced for evaluating quantitatively the quality of selected bio-bases. The effectiveness of the proposed algorithm, along with a comparison with other algorithms, has been demonstrated on different types of protein data sets.