A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps

• URL: http://arxiv.org/abs/2508.02330v2
• Date: Tue, 05 Aug 2025 03:35:41 GMT
• Title: A Compression Based Classification Framework Using Symbolic Dynamics of Chaotic Maps
• Authors: Parth Naik, Harikrishnan N B,
• Abstract summary: We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps.<n>The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are then evolved through a one-dimensional chaotic map.<n>We evaluate the proposed method: emphChaosComp on both synthetic and real-world datasets, demonstrating competitive performance compared to traditional machine learning algorithms.
• Score: 1.534667887016089
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel classification framework grounded in symbolic dynamics and data compression using chaotic maps. The core idea is to model each class by generating symbolic sequences from thresholded real-valued training data, which are then evolved through a one-dimensional chaotic map. For each class, we compute the transition probabilities of symbolic patterns (e.g., `00', `01', `10', and `11' for the second return map) and aggregate these statistics to form a class-specific probabilistic model. During testing phase, the test data are thresholded and symbolized, and then encoded using the class-wise symbolic statistics via back iteration, a dynamical reconstruction technique. The predicted label corresponds to the class yielding the shortest compressed representation, signifying the most efficient symbolic encoding under its respective chaotic model. This approach fuses concepts from dynamical systems, symbolic representations, and compression-based learning. We evaluate the proposed method: \emph{ChaosComp} on both synthetic and real-world datasets, demonstrating competitive performance compared to traditional machine learning algorithms (e.g., macro F1-scores for the proposed method on Breast Cancer Wisconsin = 0.9531, Seeds = 0.9475, Iris = 0.8469 etc.). Rather than aiming for state-of-the-art performance, the goal of this research is to reinterpret the classification problem through the lens of dynamical systems and compression, which are foundational perspectives in learning theory and information processing.

Related papers

• Chaotic Map based Compression Approach to Classification [3.3573756702816495]
  Modern machine learning approaches prioritize performance at the cost of increased complexity, computational demands, and reduced interpretability.<n>This paper introduces a novel framework that challenges this trend by reinterpreting learning from an information-theoretic perspective.<n>Rather than following the conventional approach of fitting data to complex models, we propose a fundamentally different method that maps data to intervals of initial conditions in a dynamical system.
  arXiv  Detail & Related papers  (2025-02-17T20:22:49Z)
• Accurate Explanation Model for Image Classifiers using Class Association Embedding [5.378105759529487]
  We propose a generative explanation model that combines the advantages of global and local knowledge.<n>Class association embedding (CAE) encodes each sample into a pair of separated class-associated and individual codes.<n>Building-block coherency feature extraction algorithm is proposed that efficiently separates class-associated features from individual ones.
  arXiv  Detail & Related papers  (2024-06-12T07:41:00Z)
• A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data [77.34726150561087]
  This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. The model is able to produce fairly rich yet human-readable conceptual representations without training.
  arXiv  Detail & Related papers  (2023-07-16T15:59:13Z)
• Efficient Generator of Mathematical Expressions for Symbolic Regression [0.0]
  We propose an approach to symbolic regression based on a novel variational autoencoder for generating hierarchical structures, HVAE. HVAE can be trained efficiently with small corpora of mathematical expressions and can accurately encode expressions into a smooth low-dimensional latent space. Finally, EDHiE system for symbolic regression, which applies an evolutionary algorithm to the latent space of HVAE, reconstructs equations from a standard symbolic regression benchmark better than a state-of-the-art system based on a similar combination of deep learning and evolutionary algorithms.
  arXiv  Detail & Related papers  (2023-02-20T10:40:29Z)
• Learning with Neighbor Consistency for Noisy Labels [69.83857578836769]
  We present a method for learning from noisy labels that leverages similarities between training examples in feature space. We evaluate our method on datasets evaluating both synthetic (CIFAR-10, CIFAR-100) and realistic (mini-WebVision, Clothing1M, mini-ImageNet-Red) noise.
  arXiv  Detail & Related papers  (2022-02-04T15:46:27Z)
• Application of Hierarchical Temporal Memory Theory for Document Categorization [4.506399699599753]
  The study aims to provide an alternative framework for document categorization using the Spatial Pooler learning algorithm in the HTM Theory. The results prove that HTM theory, although is in its nascent stages, performs at par with most of the popular machine learning based classifiers.
  arXiv  Detail & Related papers  (2021-12-29T20:34:03Z)
• Temporally-Consistent Surface Reconstruction using Metrically-Consistent Atlases [131.50372468579067]
  We propose a method for unsupervised reconstruction of a temporally-consistent sequence of surfaces from a sequence of time-evolving point clouds. We represent the reconstructed surfaces as atlases computed by a neural network, which enables us to establish correspondences between frames. Our approach outperforms state-of-the-art ones on several challenging datasets.
  arXiv  Detail & Related papers  (2021-11-12T17:48:25Z)
• Improving Deep Learning Sound Events Classifiers using Gram Matrix Feature-wise Correlations [1.2891210250935146]
  In our method, we analyse all the activations of a generic CNN in order to produce feature representations using Gram Matrices. The proposed approach can be applied to any CNN and our experimental evaluation of four different architectures on two datasets demonstrated that our method consistently improves the baseline models.
  arXiv  Detail & Related papers  (2021-02-23T16:08:02Z)
• Structured Graph Learning for Clustering and Semi-supervised Classification [74.35376212789132]
  We propose a graph learning framework to preserve both the local and global structure of data. Our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Our model is equivalent to a combination of kernel k-means and k-means methods under certain condition.
  arXiv  Detail & Related papers  (2020-08-31T08:41:20Z)
• Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoning [134.77207192945053]
  Prior methods learn the neural-symbolic models using reinforcement learning approaches. We introduce the textbfgrammar model as a textitsymbolic prior to bridge neural perception and symbolic reasoning. We propose a novel textbfback-search algorithm which mimics the top-down human-like learning procedure to propagate the error.
  arXiv  Detail & Related papers  (2020-06-11T17:42:49Z)
• Latent Embedding Feedback and Discriminative Features for Zero-Shot Classification [139.44681304276]
  zero-shot learning aims to classify unseen categories for which no data is available during training. Generative Adrial Networks synthesize unseen class features by leveraging class-specific semantic embeddings. We propose to enforce semantic consistency at all stages of zero-shot learning: training, feature synthesis and classification.
  arXiv  Detail & Related papers  (2020-03-17T17:34:16Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.