Kernel learning over the manifold of symmetric positive definite matrices for dimensionality reduction in a BCI application

In this paper, we propose a kernel for nonlinear dimensionality reduction over the manifold of Symmetric Positive Definite (SPD) matrices in a Motor Imagery (MI)-based Brain Computer Interface (BCI) application. The proposed kernel, which is based on Riemannian geometry, tries to preserve the topology of data points in the feature space. Topology preservation is the main challenge in nonlinear dimensionality reduction (NLDR). Our main idea is to decrease the non-Euclidean characteristics of the manifold by modifying the volume elements. We apply a conformal transform over data-dependent isometric mapping to reduce the negative eigen fraction to learn a data dependent kernel over the Riemannian manifolds. Multiple experiments were carried out using the proposed kernel for a dimensionality reduction of SPD matrices that describe the EEG signals of dataset IIa from BCI competition IV. The experiments show that this kernel adapts to the input data and leads to promising results in comparison with the most popular manifold learning methods and the Common Spatial Pattern (CSP) technique as a reference algorithm in BCI competitions. The proposed kernel is strong, particularly in the cases where data points have a complex and nonlinear separable distribution

Self-supervised Vector-Quantization in Visual SLAM using Deep Convolutional Autoencoders

In this paper, we introduce AE-FABMAP, a new self-supervised bag of words-based SLAM method. We also present AE-ORB-SLAM, a modified version of the current state of the art BoW-based path planning algorithm. That is, we have used a deep convolutional autoencoder to find loop closures. In the context of bag of words visual SLAM, vector quantization (VQ) is considered as the most time-consuming part of the SLAM procedure, which is usually performed in the offline phase of the SLAM algorithm using unsupervised algorithms such as Kmeans++. We have addressed the loop closure detection part of the BoW-based SLAM methods in a self-supervised manner, by integrating an autoencoder for doing vector quantization. This approach can increase the accuracy of large-scale SLAM, where plenty of unlabeled data is available. The main advantage of using a self-supervised is that it can help reducing the amount of labeling. Furthermore, experiments show that autoencoders are far more efficient than semi-supervised methods like graph convolutional neural networks, in terms of speed and memory consumption. We integrated this method into the state of the art long range appearance based visual bag of word SLAM, FABMAP2, also in ORB-SLAM. Experiments demonstrate the superiority of this approach in indoor and outdoor datasets over regular FABMAP2 in all cases, and it achieves higher accuracy in loop closure detection and trajectory generation

Adaptive spectrum transformation by topology preserving on indefinite proximity data

Similarity-based representation generates indefinite matrices, which are inconsistent with classical kernel-based learning frameworks. In this paper, we present an adaptive spectrum transformation method that provides a positive semidefinite ( psd ) kernel consistent with the intrinsic geometry of proximity data. In the proposed method, an indefinite similarity matrix is rectified by maximizing the Euclidian fac- tor ( EF ) criterion, which represents the similarity of the resulting feature space to Euclidean space. This maximization is achieved by modifying volume elements through applying a conformal transform over the similarity matrix. We performed several experiments to evaluate the performance of the proposed method in comparison with flip, clip, shift , and square spectrum transformation techniques on similarity matrices. Applying the resulting psd matrices as kernels in dimensionality reduction and clustering problems confirms the success of the proposed approach in adapting to data and preserving its topological information. Our experiments show that in classification applications, the superiority of the proposed method is considerable when the negative eigenfraction of the similarity matrix is significant

CUDA and OpenMp Implementation of Boolean Matrix Product with Applications in Visual SLAM

In this paper, the concept of ultrametric structure is intertwined with the SLAM procedure. A set of pre-existing transformations has been used to create a new simultaneous localization and mapping (SLAM) algorithm. We have developed two new parallel algorithms that implement the time-consuming Boolean transformations of the space dissimilarity matrix. The resulting matrix is an important input to the vector quantization (VQ) step in SLAM processes. These algorithms, written in Compute Unified Device Architecture (CUDA) and Open Multi-Processing (OpenMP) pseudo-codes, make the Boolean transformation computationally feasible on a real-world-size dataset. We expect our newly introduced SLAM algorithm, ultrametric Fast Appearance Based Mapping (FABMAP), to outperform regular FABMAP2 since ultrametric spaces are more clusterable than regular Euclidean spaces. Another scope of the presented research is the development of a novel measure of ultrametricity, along with creation of Ultrametric-PAM clustering algorithm. Since current measures have computational time complexity order, O(n3) a new measure with lower time complexity, O(n2) , has a potential significance

Machine Learning Modelling for Compressive Strength Prediction of Superplasticizer-Based Concrete

Superplasticizers (SPs), also known as naturally high-water reducers, are substances used to create high-strength concrete. Due to the system’s complexity, predicting concrete’s compressive strength can be difficult. In this study, a prediction model for the compressive strength with SP was developed to handle the high-dimensional complex non-linear relationship between the mixing design of SP and the compressive strength of concrete. After performing a statistical analysis of the dataset, a correlation analysis was performed and then 16 supervised machine learning regression techniques were used. Finally, by using the Extra Trees method and creating the SP variable values, it was shown that the compressive strength values of concrete increased with the addition of SP in the optimal dose. The results indicate that superplasticizers can often reduce the water content of concrete by 25 to 35 per cent and consequently resistivity increased by 50 to 75 per cent and the optimum amount of superplasticizers was up to 12 kg per cubic meter as well. From one point, the increase in superplasticizers does not lead to a rise in the concrete compressive strength, and it remains constant. According to the findings, SP additive has the most impact on concrete’s compressive strength after cement. Given the scant information now available on concrete-including superplasticizer, it is prudent to design a concrete mixing plan for future studies. It is also conceivable to investigate how concrete’s compressive strength is impacted by water reduction