scholarly journals On the dimensionality of olfactory space

2015 ◽  
Author(s):  
Marcelo O Magnasco ◽  
Andreas Keller ◽  
Leslie B Vosshall
Keyword(s):  
Dimensional Space ◽  
Human Subjects ◽  
Estimation Method ◽  
Odorant Receptors ◽  
High Dimensional ◽  
Significance Threshold ◽  
Olfactory Stimuli ◽  
Order Of Magnitude ◽  
Central Argument ◽  
Olfactory Space

We recently presented an estimate of the number of mutually discriminable olfactory stimuli at one trillion (1). Subjects were asked to sniff mixtures of molecules with increasing component overlap selected from a panel of 128 isointense structurally and perceptually diverse monomolecular odorants (2). We considered stimulus pairs discriminable when the majority of subjects could significantly discriminate them at p=0.05, a conventional statistical threshold given our sample size. From these empirical data, we estimated that human discriminative capacity exceeds one trillion olfactory stimuli. Several readers have pointed out that such extrapolations are sensitive to underlying assumptions about the chosen significance threshold (3) and the dimensionality of olfaction (4). It is important to note that any exponential function will be sensitive in this way, and the goal of our model was not to identify the exact number of discriminable olfactory stimuli, or even the exact mathematical bounds, but an estimate of the order of magnitude of human discriminatory power across a population of human subjects. This was not clearly stated in our paper, and we agree that contradictory references to a “lower limit” and an “upper bound” were confusing. The central argument in (4) is that our estimation method assumes that the dimensionality of olfactory space is large. We agree that the high-dimensional nature of olfaction is indeed an assumption, and we should have stated this explicitly in our paper (1). Even if we follow this logic of the models presented in (4), purely geometrical calculations show that our results hold if the dimensionality of olfactory representations is D≥25. The dimensionality of olfaction is a question of interest to everyone, and while we do not know for sure, all available evidence suggests that olfaction is a high-dimensional sense. The olfactory system is wired to keep information from the ~400 odorant receptors strictly separated, so it is plausible that olfaction operates at least in 400-dimensional space. This is an important topic of discussion in olfaction, and we welcome continued debate of the dimensionality of smell and how this impacts human olfactory perception.

Neural networks trained with high-dimensional functions approximation data in high-dimensional space

2021 ◽  
pp. 1-12
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
Data Distribution ◽  
High Dimensional ◽  
Sufficient Information ◽  
Sufficient Data ◽  
High Dimensional Space ◽  
Positive Effects ◽  
The Neural Networks ◽  
Using Data

Neural networks can approximate data because of owning many compact non-linear layers. In high-dimensional space, due to the curse of dimensionality, data distribution becomes sparse, causing that it is difficulty to provide sufficient information. Hence, the task becomes even harder if neural networks approximate data in high-dimensional space. To address this issue, according to the Lipschitz condition, the two deviations, i.e., the deviation of the neural networks trained using high-dimensional functions, and the deviation of high-dimensional functions approximation data, are derived. This purpose of doing this is to improve the ability of approximation high-dimensional space using neural networks. Experimental results show that the neural networks trained using high-dimensional functions outperforms that of using data in the capability of approximation data in high-dimensional space. We find that the neural networks trained using high-dimensional functions more suitable for high-dimensional space than that of using data, so that there is no need to retain sufficient data for neural networks training. Our findings suggests that in high-dimensional space, by tuning hidden layers of neural networks, this is hard to have substantial positive effects on improving precision of approximation data.

scholarly journals A System to Assess the Semantic Content of Student Essays

2001 ◽  
Vol 24 (3) ◽  
pp. 305-320 ◽  
Author(s):  
Benoit Lemaire ◽  
Philippe Dessus
Keyword(s):  
Latent Semantic Analysis ◽  
Semantic Analysis ◽  
Dimensional Space ◽  
Semantic Content ◽  
High Dimensional ◽  
High Dimensional Space

This paper presents Apex, a system that can automatically assess a student essay based on its content. It relies on Latent Semantic Analysis, a tool which is used to represent the meaning of words as vectors in a high-dimensional space. By comparing an essay and the text of a given course on a semantic basis, our system can measure how well the essay matches the text. Various assessments are presented to the student regarding the topic, the outline and the coherence of the essay. Our experiments yield promising results.

Effective approximation of high-dimensional space using neural networks

2021 ◽  
Author(s):  
Jian Zheng ◽  
Jianfeng Wang ◽  
Yanping Chen ◽  
Shuping Chen ◽  
Jingjin Chen ◽  
...  
Keyword(s):  
Neural Networks ◽  
Dimensional Space ◽  
High Dimensional ◽  
High Dimensional Space ◽  
Effective Approximation

scholarly journals A Novel Bat Algorithm Based on Differential Operator and Lévy Flights Trajectory

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Jian Xie ◽  
Yongquan Zhou ◽  
Huan Chen
Keyword(s):  
Differential Operator ◽  
Dimensional Space ◽  
Bat Algorithm ◽  
High Dimensional ◽  
Local Minima ◽  
Lévy Flights ◽  
Levy Flights ◽  
Mutation Strategy ◽  
Differential Algorithm ◽  
Simulation Results

Aiming at the phenomenon of slow convergence rate and low accuracy of bat algorithm, a novel bat algorithm based on differential operator and Lévy flights trajectory is proposed. In this paper, a differential operator is introduced to accelerate the convergence speed of proposed algorithm, which is similar to mutation strategy “DE/best/2” in differential algorithm. Lévy flights trajectory can ensure the diversity of the population against premature convergence and make the algorithm effectively jump out of local minima. 14 typical benchmark functions and an instance of nonlinear equations are tested; the simulation results not only show that the proposed algorithm is feasible and effective, but also demonstrate that this proposed algorithm has superior approximation capabilities in high-dimensional space.

scholarly journals Semi-Supervised Deep Learning for High-Dimensional Uncertainty Quantification

2020 ◽  
Author(s):  
Zequn Wang ◽  
Mingyang Li
Keyword(s):  
Uncertainty Quantification ◽  
Reliability Analysis ◽  
Supervised Learning ◽  
Dimensional Space ◽  
Limit State ◽  
Failure Surface ◽  
Simulation Method ◽  
High Dimensional ◽  
State Function ◽  
Latent Space

Abstract Conventional uncertainty quantification methods usually lacks the capability of dealing with high-dimensional problems due to the curse of dimensionality. This paper presents a semi-supervised learning framework for dimension reduction and reliability analysis. An autoencoder is first adopted for mapping the high-dimensional space into a low-dimensional latent space, which contains a distinguishable failure surface. Then a deep feedforward neural network (DFN) is utilized to learn the mapping relationship and reconstruct the latent space, while the Gaussian process (GP) modeling technique is used to build the surrogate model of the transformed limit state function. During the training process of the DFN, the discrepancy between the actual and reconstructed latent space is minimized through semi-supervised learning for ensuring the accuracy. Both labeled and unlabeled samples are utilized for defining the loss function of the DFN. Evolutionary algorithm is adopted to train the DFN, then the Monte Carlo simulation method is used for uncertainty quantification and reliability analysis based on the proposed framework. The effectiveness is demonstrated through a mathematical example.

scholarly journals Forecasting of Steam Coal Price Based on Robust Regularized Kernel Regression and Empirical Mode Decomposition

2021 ◽  
Vol 9 ◽  
Author(s):  
Xiangwan Fu ◽  
Mingzhu Tang ◽  
Dongqun Xu ◽  
Jun Yang ◽  
Donglin Chen ◽  
...  
Keyword(s):  
Empirical Mode Decomposition ◽  
Kernel Function ◽  
Dimensional Space ◽  
Kernel Regression ◽  
Model Performance ◽  
Feature Space ◽  
Evaluation Index ◽  
High Dimensional ◽  
Polynomial Kernel ◽  
Mode Decomposition

Aiming at the problem of difficulties in modeling the nonlinear relation in the steam coal dataset, this article proposes a forecasting method for the price of steam coal based on robust regularized kernel regression and empirical mode decomposition. By selecting the polynomial kernel function, the robust loss function and L2 regular term to construct a robust regularized kernel regression model are used. The polynomial kernel function does not depend on the kernel parameters and can mine the global rules in the dataset so that improves the forecasting stability of the kernel model. This method maps the features to the high-dimensional space by using the polynomial kernel function to transform the nonlinear law in the original feature space into linear law in the high-dimensional space and helps learn the linear law in the high-dimensional feature space by using the linear model. The Huber loss function is selected to reduce the influence of abnormal noise in the dataset on the model performance, and the L2 regular term is used to reduce the risk of model overfitting. We use the combined model based on empirical mode decomposition (EMD) and auto regressive integrated moving average (ARIMA) model to compensate for the error of robust regularized kernel regression model, thus making up for the limitations of the single forecasting model. Finally, we use the steam coal dataset to verify the proposed model and such model has an optimal evaluation index value compared to other contrast models after the model performance is evaluated as per the evaluation index such as RMSE, MAE, and mean absolute percentage error.

scholarly journals Refinement of the ice absorption spectrum in the visible using radiance profile measurements in Antarctic snow

2016 ◽  
Author(s):  
Ghislain Picard ◽  
Quentin Libois ◽  
Laurent Arnaud
Keyword(s):  
Absorption Coefficient ◽  
Fiber Optics ◽  
Estimation Method ◽  
Radiative Transfer Model ◽  
Transfer Model ◽  
Snow Layer ◽  
Antarctic Snow ◽  
Order Of Magnitude ◽  
The Difference ◽  
The Antarctic

Abstract. Ice is a highly transparent material in the visible. According to the most widely used database (Warren and Brandt, 2008; IA2008), the ice absorption coefficient reaches values lower than 10−3 m−1 around 400 nm. These values were obtained from a radiance profile measured in a single snow layer at Dome C in Antarctica. We reproduced this experiment using a fiber optics inserted in the snow to record 56 profiles from which 70 homogeneous layers were identified. Applying the same estimation method on every layer yields 70 ice absorption spectra with a significant variability and overall larger than IA2008 by one order of magnitude. We devise another estimation method based on Bayesian inference. It reduces the statistical variability and confirms the higher absorption, around 2 × 10−2 m−1 near the minimum at 440 nm. We explore potential instrumental artifacts by developing a 3D radiative transfer model able to explicitly account for the presence of the fiber in the snow. The simulation results show that the radiance profile is indeed perturbed by the fiber intrusion but the error on the ice absorption estimate is not larger than a factor 2. This is insufficient to explain the difference between our new estimate and IA2008. Nevertheless, considering the number of profiles acquired for this study and other estimates from the Antarctic Muon and Neutrino Detector Array (AMANDA), we estimate that ice absorption values around 10−2 m−1 at the minimum are more likely than under 10−3 m−1. We provide a new estimate in the range 400–600 nm for future modeling of snow, cloud, and sea-ice optical properties. Most importantly we recommend that modeling studies take into account the large uncertainty of the ice absorption coefficient in the visible.

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