Support Vector Machines
A new trigonometric kernel function for support vector machine
Hafshejani, Sajad Fathi, Moberfard, Zahra
In the last few years, various types of machine learning algorithms, such as Support Vector Machine (SVM), Support Vector Regression (SVR), and Non-negative Matrix Factorization (NMF) have been introduced. The kernel approach is an effective method for increasing the classification accuracy of machine learning algorithms. This paper introduces a family of one-parameter kernel functions for improving the accuracy of SVM classification. The proposed kernel function consists of a trigonometric term and differs from all existing kernel functions. We show this function is a positive definite kernel function. Finally, we evaluate the SVM method based on the new trigonometric kernel, the Gaussian kernel, the polynomial kernel, and a convex combination of the new kernel function and the Gaussian kernel function on various types of datasets. Empirical results show that the SVM based on the new trigonometric kernel function and the mixed kernel function achieve the best classification accuracy. Moreover, some numerical results of performing the SVR based on the new trigonometric kernel function and the mixed kernel function are presented.
Learning 3D Representations from 2D Pre-trained Models via Image-to-Point Masked Autoencoders
Zhang, Renrui, Wang, Liuhui, Qiao, Yu, Gao, Peng, Li, Hongsheng
Pre-training by numerous image data has become de-facto for robust 2D representations. In contrast, due to the expensive data acquisition and annotation, a paucity of large-scale 3D datasets severely hinders the learning for high-quality 3D features. In this paper, we propose an alternative to obtain superior 3D representations from 2D pre-trained models via Image-to-Point Masked Autoencoders, named as I2P-MAE. By self-supervised pre-training, we leverage the well learned 2D knowledge to guide 3D masked autoencoding, which reconstructs the masked point tokens with an encoder-decoder architecture. Specifically, we first utilize off-the-shelf 2D models to extract the multi-view visual features of the input point cloud, and then conduct two types of image-to-point learning schemes on top. For one, we introduce a 2D-guided masking strategy that maintains semantically important point tokens to be visible for the encoder. Compared to random masking, the network can better concentrate on significant 3D structures and recover the masked tokens from key spatial cues. For another, we enforce these visible tokens to reconstruct the corresponding multi-view 2D features after the decoder. This enables the network to effectively inherit high-level 2D semantics learned from rich image data for discriminative 3D modeling. Aided by our image-to-point pre-training, the frozen I2P-MAE, without any fine-tuning, achieves 93.4% accuracy for linear SVM on ModelNet40, competitive to the fully trained results of existing methods. By further fine-tuning on on ScanObjectNN's hardest split, I2P-MAE attains the state-of-the-art 90.11% accuracy, +3.68% to the second-best, demonstrating superior transferable capacity. Code will be available at https://github.com/ZrrSkywalker/I2P-MAE.
Hand-breathe: Non-Contact Monitoring of Breathing Abnormalities from Hand Palm
Pervez, Kawish, Aman, Waqas, Rahman, M. Mahboob Ur, Nawaz, M. Wasim, Abbasi, Qammer H.
In post-covid19 world, radio frequency (RF)-based non-contact methods, e.g., software-defined radios (SDR)-based methods have emerged as promising candidates for intelligent remote sensing of human vitals, and could help in containment of contagious viruses like covid19. To this end, this work utilizes the universal software radio peripherals (USRP)-based SDRs along with classical machine learning (ML) methods to design a non-contact method to monitor different breathing abnormalities. Under our proposed method, a subject rests his/her hand on a table in between the transmit and receive antennas, while an orthogonal frequency division multiplexing (OFDM) signal passes through the hand. Subsequently, the receiver extracts the channel frequency response (basically, fine-grained wireless channel state information), and feeds it to various ML algorithms which eventually classify between different breathing abnormalities. Among all classifiers, linear SVM classifier resulted in a maximum accuracy of 88.1\%. To train the ML classifiers in a supervised manner, data was collected by doing real-time experiments on 4 subjects in a lab environment. For label generation purpose, the breathing of the subjects was classified into three classes: normal, fast, and slow breathing. Furthermore, in addition to our proposed method (where only a hand is exposed to RF signals), we also implemented and tested the state-of-the-art method (where full chest is exposed to RF radiation). The performance comparison of the two methods reveals a trade-off, i.e., the accuracy of our proposed method is slightly inferior but our method results in minimal body exposure to RF radiation, compared to the benchmark method.
On Generalization and Regularization via Wasserstein Distributionally Robust Optimization
Wu, Qinyu, Li, Jonathan Yu-Meng, Mao, Tiantian
Wasserstein distributionally robust optimization (DRO) has found success in operations research and machine learning applications as a powerful means to obtain solutions with favourable out-of-sample performances. Two compelling explanations for the success are the generalization bounds derived from Wasserstein DRO and the equivalency between Wasserstein DRO and the regularization scheme commonly applied in machine learning. Existing results on generalization bounds and the equivalency to regularization are largely limited to the setting where the Wasserstein ball is of a certain type and the decision criterion takes certain forms of an expected function. In this paper, we show that by focusing on Wasserstein DRO problems with affine decision rules, it is possible to obtain generalization bounds and the equivalency to regularization in a significantly broader setting where the Wasserstein ball can be of a general type and the decision criterion can be a general measure of risk, i.e., nonlinear in distributions. This allows for accommodating many important classification, regression, and risk minimization applications that have not been addressed to date using Wasserstein DRO. Our results are strong in that the generalization bounds do not suffer from the curse of dimensionality and the equivalency to regularization is exact. As a byproduct, our regularization results broaden considerably the class of Wasserstein DRO models that can be solved efficiently via regularization formulations.
SUPPORT VECTOR MACHINES โ Towards AI
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Mining Explainable Predictive Features for Water Quality Management
Muldoon, Conor, Gรถrgรผ, Levent, O'Sullivan, John J., Meijer, Wim G., O'Hare, Gregory M. P.
Process mining is a family of techniques that support the analysis of operational processes, in terms of key performance indicators, using event data Van Der Aalst (2012). Process mining can be used in number of ways, such as in identifying insights into current processes or in identifying actions or places within workflows where interventions should be made to improve performance. Although processing mining is typically used in the context of commercial business environments, there is crossover to other areas where processes play an important role, such as in water quality management processes administered by local government authorities or citizen science projects that use the Business Process Model and Notation (BPMN) Higgins, Williams, Leibovici, Simonis, Davis, Muldoon, van Genuchten, O'Hare and Wiemann (2016). In the case of water quality management, traditional event log data from information technology systems is often lacking in that many tasks, such as the manual sampling of water and the microbial culturing by biologists and laboratory technicians to identify faecal coliforms, are not performed using computers and are not logged. Nevertheless, it is likely that techniques developed to aid explainability and in the evaluation of machine learning algorithms in such cases will prove using in traditional process mining systems where similar problems must be addressed. This paper focuses on mining suitable features to perform inference for the level of bacteria, and specifically Enterococci and Escherichia coli (E.
Regularized ERM on random subspaces
Della Vecchia, Andrea, De Vito, Ernesto, Rosasco, Lorenzo
We study a natural extension of classical empirical risk minimization, where the hypothesis space is a random subspace of a given space. In particular, we consider possibly data dependent subspaces spanned by a random subset of the data, recovering as a special case Nystrom approaches for kernel methods. Considering random subspaces naturally leads to computational savings, but the question is whether the corresponding learning accuracy is degraded. These statistical-computational tradeoffs have been recently explored for the least squares loss and self-concordant loss functions, such as the logistic loss. Here, we work to extend these results to convex Lipschitz loss functions, that might not be smooth, such as the hinge loss used in support vector machines. This unified analysis requires developing new proofs, that use different technical tools, such as sub-gaussian inputs, to achieve fast rates. Our main results show the existence of different settings, depending on how hard the learning problem is, for which computational efficiency can be improved with no loss in performance.
Support Vector Machine for Determining Euler Angles in an Inertial Navigation System
Grekov, Aleksandr N., Kabanov, Aleksei A., Alekseev, Sergei Yu.
The paper discusses the improvement of the accuracy of an inertial navigation system created on the basis of MEMS sensors using machine learning (ML) methods. As input data for the classifier, we used infor-mation obtained from a developed laboratory setup with MEMS sensors on a sealed platform with the ability to adjust its tilt angles. To assess the effectiveness of the models, test curves were constructed with different values of the parameters of these models for each core in the case of a linear, polynomial radial basis function. The inverse regularization parameter was used as a parameter. The proposed algorithm based on MO has demonstrated its ability to correctly classify in the presence of noise typical for MEMS sensors, where good classification results were obtained when choosing the optimal values of hyperpa-rameters.