arXiv subjects

Pramod P Nair

Publications and source records attributed to Pramod P Nair.

6 recordsLinked to original sources

arXiv2026

Chaotic CNN for Limited Data Image Classification

Convolutional neural networks (CNNs) often exhibit poor generalisation in limited training data scenarios due to overfitting and insufficient feature diversity. In this work, a simple and effective chaos-based feature transformation is proposed to enhance CNN performance without increasing model complexity. The method applies nonlinear transformations using logistic, skew tent, and sine maps to normalised feature vectors before the classification layer, thereby reshaping the feature space and improving class separability. The approach is evaluated on greyscale datasets (MNIST and Fashion-MNIST) and an RGB dataset (CIFAR-10) using CNN architectures of varying depth under limited data conditions. The results show consistent improvement over the standalone (SA) CNN across all datasets. Notably, a maximum performance gain of 5.43% is achieved on MNIST using the skew tent map with a 3-layer CNN at 40 samples per class. A higher gain of 9.11% is observed on Fashion-MNIST using the sine map with a 3-layer CNN at 50 samples per class. Additionally, a strong gain of 7.47% is obtained on CIFAR-10 using the skew tent map at 200 samples per class. The consistent improvements across different chaotic maps indicate that the performance gain is driven by the shared nonlinear and dynamical properties of chaotic systems. The proposed method is computationally efficient, requires no additional trainable parameters, and can be easily integrated into existing CNN architectures, making it a practical solution for data-scarce image classification tasks.

cs.CV↗

arXiv2026

Self-Training the Neurochaos Learning Algorithm

In numerous practical applications, acquiring substantial quantities of labelled data is challenging and expensive, but unlabelled data is readily accessible. Conventional supervised learning methods frequently underperform in scenarios characterised by little labelled data or imbalanced datasets. This study introduces a hybrid semi-supervised learning (SSL) architecture that integrates Neurochaos Learning (NL) with a threshold-based Self-Training (ST) method to overcome this constraint. The NL architecture converts input characteristics into chaos-based ring-rate representations that encapsulate nonlinear relationships within the data, whereas ST progressively enlarges the labelled set utilising high-confidence pseudo-labelled samples. The model's performance is assessed using ten benchmark datasets and five machine learning classifiers, with 85% of the training data considered unlabelled and just 15% utilised as labelled data. The proposed Self-Training Neurochaos Learning (NL+ST) architecture consistently attains superior performance gain relative to standalone ST models, especially on limited, nonlinear and imbalanced datasets like Iris (188.66%), Wine (158.58%) and Glass Identification (110.48%). The results indicate that using chaos-based feature extraction with SSL improves generalisation, resilience, and classification accuracy in low-data contexts.

cs.LG↗

arXiv2023

Physics-informed Neural Networks approach to solve the Blasius function

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to solve the Blasius function. This method eliminates the process of changing the non-linear differential equation to an initial value problem. Also, it tackles the convergence issue arising in the conventional series solution. It is seen that this method produces results that are at par with the numerical and conventional methods. The solution is extended to the negative axis to show that PINNs capture the singularity of the function at $η=-5.69$

cs.LG↗

arXiv2023

Biologically inspired ChaosNet architecture for Hypothetical Protein Classification

ChaosNet is a type of artificial neural network framework developed for classification problems and is influenced by the chaotic property of the human brain. Each neuron of the ChaosNet architecture is the one-dimensional chaotic map called the Generalized Luroth Series (GLS). The addition of GLS as neurons in ChaosNet makes the computations straightforward while utilizing the advantageous elements of chaos. With substantially less data, ChaosNet has been demonstrated to do difficult classification problems on par with or better than traditional ANNs. In this paper, we use Chaosnet to perform a functional classification of Hypothetical proteins [HP], which is indeed a topic of great interest in bioinformatics. The results obtained with significantly lesser training data are compared with the standard machine learning techniques used in the literature.

cs.LG↗

arXiv2022

Upper Bounds to Genome Rearrangement Problem using Prefix Transpositions

A Genome rearrangement problem studies large-scale mutations on a set of DNAs in living organisms. Various rearrangements like reversals, transpositions, translocations, fissions, fusions, and combinations and different variations have been studied extensively by computational biologists and computer scientists over the past four decades. From a mathematical point of view, a genome is represented by a permutation. The genome rearrangement problem is interpreted as a problem that transforms one permutation into another in a minimum number of moves under certain constraints depending on the chosen rearrangements. Finding the minimum number of moves is equivalent to sorting the permutation with the given rearrangement. A transposition is an operation on a permutation that moves a sublist of a permutation to a different position in the same permutation. A \emph{Prefix Transposition}, as the name suggests, is a transposition that moves a sublist which is a prefix of the permutation. In this thesis, we study prefix transpositions on permutations and present a better upper bound for sorting permutations with prefix transpositions. A greedy algorithm called the \emph{generalised sequence length algorithm} is defined as an extension of the sequence length algorithm where suitable alternate moves are also considered. This algorithm is used to sequentially improve the upper bound to $n-\log_{3.3} n$ and $n-\log_3 n$. In the latter part of the thesis, we defined the concept of a \emph{block}. We used it along with the greedy moves of the generalised sequence length algorithm to get an upper bound of $n-\log_2 n$ to sort permutations by prefix transpositions.

cs.DM↗

arXiv2022

On The Diameter of Pancake Graphs

The Pancake graph($P_n$) represents the group of all permutations on n elements, namely $S_n$, with respect to the generating set containing all prefix reversals. The diameter of a graph is the maximum of all distances on the graph, where the distance between two vertices is the shortest path between them. In the case of the $P_n$, it is the maximum of the shortest generating sequence of each permutation in $S_n$. Here we propose a method to realise better upper bounds to the diameter of $P_n$ that has its focus on Graph Theoretical concepts rather than Algebra.

math.CO↗