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Saikat Chatterjee

Publications and source records attributed to Saikat Chatterjee.

At least 37 records · Page 2Linked to original sources
arXiv2023

Connections on Lie groupoids and Chern-Weil theory

Let $\mathbb{X}=[X_1\rightrightarrows X_0]$ be a Lie groupoid equipped with a connection, given by a smooth distribution $\mathcal{H} \subset T X_1$ transversal to the fibers of the source map. Under the assumption that the distribution $\mathcal{H}$is integrable, we define a version of de Rham cohomology for the pair $(\mathbb{X}, \mathcal{H})$, and we study connections on principal $G$-bundles over $(\mathbb{X}, \mathcal{H})$ in terms of the associated Atiyah sequence of vector bundles. We also discuss associated constructions for differentiable stacks. Finally, we develop the corresponding Chern-Weil theory and describe characteristic classes of principal G-bundles over a pair $(\mathbb{X}, \mathcal{H})$.

math.DG↗
arXiv2023

Identifying and analysing toxic actors and communities on Facebook by employing network analysis

There has been an increasingly widespread agreement among both academic circles and the general public that the Social Media Platforms (SMPs) play a central role in the dissemination of harmful and negative sentiment content in a coordinated manner. A substantial body of recent scholarly research has demonstrated the ways in which hateful content, political propaganda, and targeted messaging on SMPs have contributed to serious real-world consequences. Adopting inspirations from graph theory, in this paper we apply novel network and community finding algorithms over a representative Facebook dataset (n=608,417) which we have scrapped through 630 pages. By applying Girvan-Newman algorithm over the historical dataset our analysis finds five communities of coordinated networks of actors, within the contexts of Indian far-right Hindutva discourse. This work further paves the path for future potentials of applying such novel network analysis algorithms to SMPs, in order to automatically identify toxic coordinated communities and sub-communities, and to possibly resist real-world threats emerging from information dissemination in the SMPs.

cs.SI↗
arXiv2023

IMU-based Online Multi-lidar Calibration

Modern autonomous systems typically use several sensors for perception. For best performance, accurate and reliable extrinsic calibration is necessary. In this research, we propose a reliable technique for the extrinsic calibration of several lidars on a vehicle without the need for odometry estimation or fiducial markers. First, our method generates an initial guess of the extrinsics by matching the raw signals of IMUs co-located with each lidar. This initial guess is then used in ICP and point cloud feature matching which refines and verifies this estimate. Furthermore, we can use observability criteria to choose a subset of the IMU measurements that have the highest mutual information -- rather than comparing all the readings. We have successfully validated our methodology using data gathered from Scania test vehicles.

cs.RO↗
arXiv2023

Parallel transport on a Lie 2-group bundle over a Lie groupoid along Haefliger paths

We prove a Lie 2-group torsor version of the well-known one-one correspondence between fibered categories and pseudofunctors. Consequently, we obtain a weak version of the principal Lie group bundle over a Lie groupoid. The correspondence also enables us to extend a particular class of principal 2-bundles to be defined over differentiable stacks. We show that the differential geometric connection structures introduced in the authors' previous work, combine nicely with the underlying fibration structure of a principal 2-bundle over a Lie groupoid. This interrelation allows us to derive a notion of parallel transport in the framework of principal 2-bundles over Lie groupoids along a particular class of Haefliger paths. The corresponding parallel transport functor is shown to be smooth. We apply our results to examine the parallel transport on an associated VB-groupoid.

math.DG↗
arXiv2023

Automated Sentiment and Hate Speech Analysis of Facebook Data by Employing Multilingual Transformer Models

In recent years, there has been a heightened consensus within academia and in the public discourse that Social Media Platforms (SMPs), amplify the spread of hateful and negative sentiment content. Researchers have identified how hateful content, political propaganda, and targeted messaging contributed to real-world harms including insurrections against democratically elected governments, genocide, and breakdown of social cohesion due to heightened negative discourse towards certain communities in parts of the world. To counter these issues, SMPs have created semi-automated systems that can help identify toxic speech. In this paper we analyse the statistical distribution of hateful and negative sentiment contents within a representative Facebook dataset (n= 604,703) scrapped through 648 public Facebook pages which identify themselves as proponents (and followers) of far-right Hindutva actors. These pages were identified manually using keyword searches on Facebook and on CrowdTangleand classified as far-right Hindutva pages based on page names, page descriptions, and discourses shared on these pages. We employ state-of-the-art, open-source XLM-T multilingual transformer-based language models to perform sentiment and hate speech analysis of the textual contents shared on these pages over a period of 5.5 years. The result shows the statistical distributions of the predicted sentiment and the hate speech labels; top actors, and top page categories. We further discuss the benchmark performances and limitations of these pre-trained language models.

cs.CL↗
arXiv2022

Observability-aware online multi-lidar extrinsic calibration

Accurate and robust extrinsic calibration is necessary for deploying autonomous systems which need multiple sensors for perception. In this paper, we present a robust system for real-time extrinsic calibration of multiple lidars in vehicle base frame without the need for any fiducial markers or features. We base our approach on matching absolute GNSS and estimated lidar poses in real-time. Comparing rotation components allows us to improve the robustness of the solution than traditional least-square approach comparing translation components only. Additionally, instead of comparing all corresponding poses, we select poses comprising maximum mutual information based on our novel observability criteria. This allows us to identify a subset of the poses helpful for real-time calibration. We also provide stopping criteria for ensuring calibration completion. To validate our approach extensive tests were carried out on data collected using Scania test vehicles (7 sequences for a total of ~ 6.5 Km). The results presented in this paper show that our approach is able to accurately determine the extrinsic calibration for various combinations of sensor setups.

cs.RO↗
arXiv2022

A Comparative Analysis of Machine-learning Models for Solar Flare Forecasting: Identifying High-performing Active Region Flare Indicators

Solar flares create adverse space weather impacting space and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k-nearest neighbor, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of $0.967 \pm 0.018$, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that the magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity.

astro-ph.SR↗
arXiv2022

M-LIO: Multi-lidar, multi-IMU odometry with sensor dropout tolerance

We present a robust system for state estimation that fuses measurements from multiple lidars and inertial sensors with GNSS data. To initiate the method, we use the prior GNSS pose information. We then perform incremental motion in real-time, which produces robust motion estimates in a global frame by fusing lidar and IMU signals with GNSS translation components using a factor graph framework. We also propose methods to account for signal loss with a novel synchronization and fusion mechanism. To validate our approach extensive tests were carried out on data collected using Scania test vehicles (5 sequences for a total of ~ 7 Km). From our evaluations, we show an average improvement of 61% in relative translation and 42% rotational error compared to a state-of-the-art estimator fusing a single lidar/inertial sensor pair.

cs.RO↗
arXiv2022

Neural Greedy Pursuit for Feature Selection

We propose a greedy algorithm to select $N$ important features among $P$ input features for a non-linear prediction problem. The features are selected one by one sequentially, in an iterative loss minimization procedure. We use neural networks as predictors in the algorithm to compute the loss and hence, we refer to our method as neural greedy pursuit (NGP). NGP is efficient in selecting $N$ features when $N \ll P$, and it provides a notion of feature importance in a descending order following the sequential selection procedure. We experimentally show that NGP provides better performance than several feature selection methods such as DeepLIFT and Drop-one-out loss. In addition, we experimentally show a phase transition behavior in which perfect selection of all $N$ features without false positives is possible when the training data size exceeds a threshold.

cs.LG↗
arXiv2022

Multi-modal curb detection and filtering

Reliable knowledge of road boundaries is critical for autonomous vehicle navigation. We propose a robust curb detection and filtering technique based on the fusion of camera semantics and dense lidar point clouds. The lidar point clouds are collected by fusing multiple lidars for robust feature detection. The camera semantics are based on a modified EfficientNet architecture which is trained with labeled data collected from onboard fisheye cameras. The point clouds are associated with the closest curb segment with $L_2$-norm analysis after projecting into the image space with the fisheye model projection. Next, the selected points are clustered using unsupervised density-based spatial clustering to detect different curb regions. As new curb points are detected in consecutive frames they are associated with the existing curb clusters using temporal reachability constraints. If no reachability constraints are found a new curb cluster is formed from these new points. This ensures we can detect multiple curbs present in road segments consisting of multiple lanes if they are in the sensors' field of view. Finally, Delaunay filtering is applied for outlier removal and its performance is compared to traditional RANSAC-based filtering. An objective evaluation of the proposed solution is done using a high-definition map containing ground truth curb points obtained from a commercial map supplier. The proposed system has proven capable of detecting curbs of any orientation in complex urban road scenarios comprising straight roads, curved roads, and intersections with traffic isles.

cs.CV↗
arXiv2022

Extrinsic Calibration and Verification of Multiple Non-overlapping Field of View Lidar Sensors

We demonstrate a multi-lidar calibration framework for large mobile platforms that jointly calibrate the extrinsic parameters of non-overlapping Field-of-View (FoV) lidar sensors, without the need for any external calibration aid. The method starts by estimating the pose of each lidar in its corresponding sensor frame in between subsequent timestamps. Since the pose estimates from the lidars are not necessarily synchronous, we first align the poses using a Dual Quaternion (DQ) based Screw Linear Interpolation. Afterward, a Hand-Eye based calibration problem is solved using the DQ-based formulation to recover the extrinsics. Furthermore, we verify the extrinsics by matching chosen lidar semantic features, obtained by projecting the lidar data into the camera perspective after time alignment using vehicle kinematics. Experimental results on the data collected from a Scania vehicle [$\sim$ 1 Km sequence] demonstrate the ability of our approach to obtain better calibration parameters than the provided vehicle CAD model calibration parameters. This setup can also be scaled to any combination of multiple lidars.

cs.RO↗
arXiv2022

DeepBayes -- an estimator for parameter estimation in stochastic nonlinear dynamical models

Stochastic nonlinear dynamical systems are ubiquitous in modern, real-world applications. Yet, estimating the unknown parameters of stochastic, nonlinear dynamical models remains a challenging problem. The majority of existing methods employ maximum likelihood or Bayesian estimation. However, these methods suffer from some limitations, most notably the substantial computational time for inference coupled with limited flexibility in application. In this work, we propose DeepBayes estimators that leverage the power of deep recurrent neural networks in learning an estimator. The method consists of first training a recurrent neural network to minimize the mean-squared estimation error over a set of synthetically generated data using models drawn from the model set of interest. The a priori trained estimator can then be used directly for inference by evaluating the network with the estimation data. The deep recurrent neural network architectures can be trained offline and ensure significant time savings during inference. We experiment with two popular recurrent neural networks -- long short term memory network (LSTM) and gated recurrent unit (GRU). We demonstrate the applicability of our proposed method on different example models and perform detailed comparisons with state-of-the-art approaches. We also provide a study on a real-world nonlinear benchmark problem. The experimental evaluations show that the proposed approach is asymptotically as good as the Bayes estimator.

stat.ML↗
arXiv2021

Use of Deterministic Transforms to Design Weight Matrices of a Neural Network

Self size-estimating feedforward network (SSFN) is a feedforward multilayer network. For the existing SSFN, a part of each weight matrix is trained using a layer-wise convex optimization approach (a supervised training), while the other part is chosen as a random matrix instance (an unsupervised training). In this article, the use of deterministic transforms instead of random matrix instances for the SSFN weight matrices is explored. The use of deterministic transforms provides a reduction in computational complexity. The use of several deterministic transforms is investigated, such as discrete cosine transform, Hadamard transform, Hartley transform, and wavelet transforms. The choice of a deterministic transform among a set of transforms is made in an unsupervised manner. To this end, two methods based on features' statistical parameters are developed. The proposed methods help to design a neural net where deterministic transforms can vary across its layers' weight matrices. The effectiveness of the proposed approach vis-a-vis the SSFN is illustrated for object classification tasks using several benchmark datasets.

cs.LG↗
arXiv2021

Atiyah sequence and Gauge transformations of a principal $2$-bundle over a Lie groupoid

In this paper, a notion of a principal $2$-bundle over a Lie groupoid has been introduced. For such principal $2$-bundles, we produced a short exact sequence of VB-groupoids, namely, the Atiyah sequence. Two notions of connection structures viz. strict connections and semi-strict connections on a principal $2$-bundle arising respectively, from a retraction of the Atiyah sequence and a retraction up to a natural isomorphism have been introduced. We constructed a class of principal $\mathbb{G}=[G_1\rightrightarrows G_0]$-bundles and connections from a given principal $G_0$-bundle $E_0\rightarrow X_0$ over $[X_1\rightrightarrows X_0]$ with connection. An existence criterion for the connections on a principal $2$-bundle over a proper, étale Lie groupoid is proposed. The action of the $2$-group of gauge transformations on the category of strict and semi-strict connections has been studied. Finally we noted an extended symmetry of the category of semi-strict connections.

math.DG↗
arXiv2021

Normalizing Flow based Hidden Markov Models for Classification of Speech Phones with Explainability

In pursuit of explainability, we develop generative models for sequential data. The proposed models provide state-of-the-art classification results and robust performance for speech phone classification. We combine modern neural networks (normalizing flows) and traditional generative models (hidden Markov models - HMMs). Normalizing flow-based mixture models (NMMs) are used to model the conditional probability distribution given the hidden state in the HMMs. Model parameters are learned through judicious combinations of time-tested Bayesian learning methods and contemporary neural network learning methods. We mainly combine expectation-maximization (EM) and mini-batch gradient descent. The proposed generative models can compute likelihood of a data and hence directly suitable for maximum-likelihood (ML) classification approach. Due to structural flexibility of HMMs, we can use different normalizing flow models. This leads to different types of HMMs providing diversity in data modeling capacity. The diversity provides an opportunity for easy decision fusion from different models. For a standard speech phone classification setup involving 39 phones (classes) and the TIMIT dataset, we show that the use of standard features called mel-frequency-cepstral-coeffcients (MFCCs), the proposed generative models, and the decision fusion together can achieve $86.6\%$ accuracy by generative training only. This result is close to state-of-the-art results, for examples, $86.2\%$ accuracy of PyTorch-Kaldi toolkit [1], and $85.1\%$ accuracy using light gated recurrent units [2]. We do not use any discriminative learning approach and related sophisticated features in this article.

cs.LG↗
arXiv2021

Robust Classification using Hidden Markov Models and Mixtures of Normalizing Flows

We test the robustness of a maximum-likelihood (ML) based classifier where sequential data as observation is corrupted by noise. The hypothesis is that a generative model, that combines the state transitions of a hidden Markov model (HMM) and the neural network based probability distributions for the hidden states of the HMM, can provide a robust classification performance. The combined model is called normalizing-flow mixture model based HMM (NMM-HMM). It can be trained using a combination of expectation-maximization (EM) and backpropagation. We verify the improved robustness of NMM-HMM classifiers in an application to speech recognition.

cs.LG↗