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title = {Analysis of genomic sequences by {Chaos} {Game} {Representation}},
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volume = {17},
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issn = {1367-4803},
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doi = {10.1093/bioinformatics/17.5.429},
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abstract = {MOTIVATION: Chaos Game Representation (CGR) is an iterative mapping technique that processes sequences of units, such as nucleotides in a DNA sequence or amino acids in a protein, in order to find the coordinates for their position in a continuous space. This distribution of positions has two properties: it is unique, and the source sequence can be recovered from the coordinates such that distance between positions measures similarity between the corresponding sequences. The possibility of using the latter property to identify succession schemes have been entirely overlooked in previous studies which raises the possibility that CGR may be upgraded from a mere representation technique to a sequence modeling tool.
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RESULTS: The distribution of positions in the CGR plane were shown to be a generalization of Markov chain probability tables that accommodates non-integer orders. Therefore, Markov models are particular cases of CGR models rather than the reverse, as currently accepted. In addition, the CGR generalization has both practical (computational efficiency) and fundamental (scale independence) advantages. These results are illustrated by using Escherichia coli K-12 as a test data-set, in particular, the genes thrA, thrB and thrC of the threonine operon.},
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language = {eng},
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number = {5},
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journal = {Bioinformatics (Oxford, England)},
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author = {Almeida, J. S. and Carriço, J. A. and Maretzek, A. and Noble, P. A. and Fletcher, M.},
file = {Full Text:/home/ediman/Zotero/storage/VESM4PR8/Almeida et al. - 2001 - Analysis of genomic sequences by Chaos Game Representation.pdf:application/pdf},
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}
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@article{chicco_ten_2017,
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title = {Ten quick tips for machine learning in computational biology},
abstract = {Machine learning has become a pivotal tool for many projects in computational biology, bioinformatics, and health informatics. Nevertheless, beginners and biomedical researchers often do not have enough experience to run a data mining project effectively, and therefore can follow incorrect practices, that may lead to common mistakes or over-optimistic results. With this review, we present ten quick tips to take advantage of machine learning in any computational biology context, by avoiding some common errors that we observed hundreds of times in multiple bioinformatics projects. We believe our ten suggestions can strongly help any machine learning practitioner to carry on a successful project in computational biology and related sciences.},
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language = {en},
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number = {1},
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urldate = {2020-10-14},
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journal = {BioData Mining},
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author = {Chicco, Davide},
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month = dec,
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year = {2017},
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pages = {35},
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file = {Chicco - 2017 - Ten quick tips for machine learning in computation.pdf:/home/ediman/Zotero/storage/TLEC5K7L/Chicco - 2017 - Ten quick tips for machine learning in computation.pdf:application/pdf;Chicco - 2017 - Ten quick tips for machine learning in computation.pdf:/home/ediman/Zotero/storage/XD5SCMV9/Chicco - 2017 - Ten quick tips for machine learning in computation.pdf:application/pdf},
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# Summary
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Computational analysis of DNA sequences underpins numerous bioinformatics applications, including sequence classification, genome comparison, mutation detection, and evolutionary studies. These tasks often require transforming symbolic nucleotide sequences (A, T, C, G) into numerical representations suitable for mathematical processing or machine learning [@greener_guide_2022].
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Computational analysis of DNA sequences underpins numerous bioinformatics applications, including sequence classification, genome comparison, mutation detection, and evolutionary studies. These tasks often require transforming symbolic nucleotide sequences (A, T, C, G) into numerical representations suitable for mathematical processing or machine learning [@greener_guide_2022]. Chaos Game Representation (CGR) is a well-established method that encodes DNA sequences as points in a 2D space, revealing motifs and structural patterns [@jeffrey_chaos_1990]. However, traditional CGR depends on floating-point arithmetic, leading to rounding errors and imprecision, especially when applied to long sequences or tasks that require exact sequence reconstruction. `chaoscoder` implements the Integer Chaos Game Representation (iCGR), a variant that operates entirely in integer space to provide lossless encoding and decoding [@yin_encoding_2018]. To address the exponential scaling limitation of iCGR, the software introduces a block-based variant that divides sequences into overlapping segments, enabling scalable and parallelizable encoding of genome-length sequences. The software provides a command-line interface for encoding, decoding, visualizing CGRs, and comparing sequence structure via image-based SSIM (Structural Similarity Index Measure) [@wang_image_2004]. It supports standardized storage of encoded data in a custom `.bicgr` file format, designed for efficient downstream use.
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Chaos Game Representation (CGR) is a well-established method that encodes DNA sequences as points in a 2D space, revealing motifs and structural patterns [@jeffrey_chaos_1990]. However, traditional CGR depends on floating-point arithmetic, leading to rounding errors and imprecision, especially when applied to long sequences or tasks that require exact sequence reconstruction.
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# Statement of need
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`chaoscoder` implements the Integer Chaos Game Representation (iCGR), a variant that operates entirely in integer space to provide lossless encoding and decoding [@yin_encoding_2018]. To address the exponential scaling limitation of iCGR, the software introduces a block-based variant that divides sequences into overlapping segments, enabling scalable and parallelizable encoding of genome-length sequences.
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The software provides a command-line interface for encoding, decoding, visualizing CGRs, and comparing sequence structure via image-based SSIM (Structural Similarity Index Measure) [@wang_image_2004]. It supports standardized storage of encoded data in a custom `.bicgr` file format, designed for efficient downstream use.
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The exponential growth of genomic datasets necessitates robust, scalable, and reversible methods for DNA sequence encoding that can support downstream computational workflows. Among existing approaches, CGR has been widely adopted for its ability to visualize and analyze nucleotide composition in a geometric framework [@almeida_analysis_2001]. However, CGR suffers from inherent limitations: it relies on floating-point arithmetic, which introduces precision errors, lacks scalability to large sequences, and is not reversible, making exact sequence reconstruction impossible. The Integer Chaos Game Representation introduced by Yin *et al.* [@yin_encoding_2018], addresses these shortcomings by providing a mathematically rigorous and fully reversible encoding scheme based on integer arithmetic. Despite its theoretical advantages, iCGR remains underutilized due to the absence of a comprehensive, open-source implementation suitable for genome-scale applications. Apart from the illustrative prototype provided by the original authors, no available software supports full encoding, decoding, and standardized storage of iCGR coordinates in a format adapted to large-scale, reproducible workflows.
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This software fills that gap by offering a modular, high-performance implementation of iCGR. It introduces a block-based strategy capable of handling arbitrarily long sequences through segmented and overlapping encoding, ensuring both scalability and reversibility. The toolset includes efficient utilities for encoding, decoding, and storing sequences in a compressed, structured format that is suitable for integration into bioinformatics pipelines. By enabling reproducible, high-throughput analyses, this implementation makes iCGR practically accessible to researchers working in genome classification, alignment-free comparison, compression, evolutionary genomics, and machine learning applications [@chicco_ten_2017]. It combines computational efficiency with mathematical rigor to support exact sequence recovery and interpretable analyses at scale.
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