Visually Synthesizing the Genotype-Phenotype Distinction in Cannabis sativa

Year: 2019 Authors: Martin D. Pham

Core claim

CGR reveals fractal genomic structure, and neural style transfer can visually merge genotypic and phenotypic representations of Cannabis sativa.

Topics

genotype-phenotype distinction, chaos game representation, neural style transfer, algorithmic art

Domains

DNA sequence visualization, fractal structure, Maximum Mean Discrepancy, convolutional neural networks, generative art, image synthesis, computational aesthetics, biological visualization

Methods

chaos game representation, neural style transfer, ResNet, FractalNet

Media

whole chloroplast genome, Cannabis sativa photograph, DNA sequence data, rendered images

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Bridges 2019 Conference Proceedings

Visually Synthesizing the Genotype-Phenotype Distinction in Cannabis sativa

Martin D. Pham

Brampton, Ontario, Canada; martindopham@gmail.com

Abstract

Presented are results of two numerical experiments: the whole chloroplast genome chaos game representation of Cannabis sativa and the comparison of two state-of-the-art neural network architectures applied to the neural style transfer problem. A brief explanation of the chaos game representation is given followed by results illustrating that the whole chloroplast genome has global structure. An explication of neural style transfer and the ResNet and FractalNet neural network architectures is then given followed by results when both networks are trained to learn the underlying feature representation of an image of Cannabis sativa. Finally, the artistic motivation of these numerical experiments is presented in the context of the genotype-phenotype distinction.

Chaos Game Representation

Chaos game representation (CGR) [4] is a method for visualizing global structure in DNA sequences by uniquely representing the sequence as a set of points on the unit square. The CGR of a sequence is given by plotting the set $S$ computed using the following steps:

1. Associate each vertex $\{(0,0),(1,0),(1,1),(0,1)\}$ with the nucleotides $\{A,G,T,C\}$ , respectively.
2. Initialize a set $S=\{(0,0)\}$ .
3. Read off the sequence. For each element in the sequence, add to the set $S$ the midpoint between the most previous point added to the set and the vertex associated with the current element.

Analysis of many sample sequences taken from several taxonomic subsets done by [6] demonstrated that the CGRs of DNA sequences have fractal, self-similar structure. However, the CGR of Cannabis sativa was not included in this analysis, as it did not fall under the taxonomic subsets of interest, and so is reported below. Figure 1 shows the CGR of four complete chloroplast genomes taken from Cannabis sativa [10, 11]. Prior work in using genomic information for algorithmic art can be found in [2, 8].

Dagestani, Russia

Yoruba, Nigeria

Carmagnola, Italy Figure 1: Chaos game representations of Cannabis sativa from different regions around the world.

Cheungsam, Korea

Neural Style Transfer

The neural style transfer (NST) problem, popularized by the technique of [1], is an image processing task where neural networks are trained to learn the ‘style’ of a target image such that this style may be applied (i.e. ‘transferred’) to the ’content’ of a source image in order to render an aesthetically similar result while preserving semantic content. Work done by [9] demonstrated that NST may be considered as a domain adaptation problem where the objective is to minimize the Maximum Mean Discrepancy. That is, NST may be thought of as learning the convolutional kernels such that the source image pixel distribution shifts towards the target image.

As in [5], a bottleneck (downsample, feature representation, upsampling) neural network was trained to approximate a solution to the problem presented in [1] by learning the feature representation of the target image and stylizing the source image by a feedforward pass. Feature layers encode the lower dimensional representation of the target image and thus it is of interest to compare style transfer results given either ResNet [3] or FractalNet [7] encoding. ResNet is a popular architecture introducing a skip connection between convolutions. Let $R$ be a feature layer:

R(x):=\sigma\bigg{(}\big{(}f_{C}\circ\sigma\circ f_{B}\circ\sigma\circ f_{A}\big{)}(x)+x\bigg{)}

where $\{A,B,C\}$ are learnable kernels for the convolution operator $f$, $\sigma (x)=\max (0,x)$ the rectified linear unit (ReLU) activation function applied element-wise, and $x$ an (image) function ${\mathbb{R}}^2\to {\mathbb{R}}^3$. FractalNet is an architecture based on the repeated application of an expansion rule to generate deep neural networks whose structure is a truncated fractal. Let $F$ be a feature layer generated on one application of the expansion rule:

F(x):=\sigma\bigg{(}\frac{\big{(}\sigma\circ f_{C}\circ\sigma\circ f_{B}\big{)}(x)+(\sigma\circ f_{A})(x)}{2}\bigg{)}

where, similarly, $\{A,B,C\}$ are learnable convolutional kernels and $\sigma$ is the ReLU activation function. Note that both ResNet and FractalNet have three convolution operations arranged (layered) differently.

The target style image to be learned was chosen to be an image of Cannabis sativa [12]. The source content image was chosen to be the CGR of the Dagestani Cannabis sativa. Results are shown in Figure 2.

Summary and Conclusions

Presented are numerical experiments in both chaos game representations and neural style transfer. The CGRs of previously unanalyzed Cannabis sativa DNA sequences are reported, demonstrating a fractal structure, as expected. A comparison between two state-of-the-art neural network architectures trained to stylize an image of Cannabis sativa is then reported, using the aforementioned CGR as a content image. The artistic motivation of this experiment is as a synthesis of two distinct, obverse representations of Cannabis sativa. CGR uniquely represents the genotypic information of the whole chloroplast genome while the target image contains phenotypic information (i.e. the leaves and blooming of a plant). The style transfer process superimposes these two representations into a synthesized image of Cannabis sativa where, in a reversal of biology, the genotypic has been expressed in the texture of the phenotypic.

Acknowledgements

A great deal of gratitude is owed to Vivian Chen for her enduring support in all creative endeavours.

Visually Synthesizing the Genotype-Phenotype Distinction in Cannabis sativa

Source image, CGR of Cannabis sativa FractalNet style transfer Figure 2: Neural style transfer applied to genotypic and phenotypic representations of Cannabis sativa. The chaos game representation of whole chloroplast genome is used as content for the neural style transfer of an image of hemp.

Target image, Cannabis sativa ResNet style transfer

Pham

References

• [1] L.A. Gatys, A.S. Ecker, and M. Bethge. “Image Style Transfer Using Convolutional Neural Networks.” The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, United States, Jun. 26–Jul. 1, 2016, pp. 2414–2423. http://openaccess.thecvf.com/content_cvpr_2016//Gatys_Image_Style_Transfer_CVPR_2016_paper.
• [2] G. Greenfield. “Evolved look-up tables for simulated DNA controlled robots.” Simulated Evolution and Learning Conference Proceedings, Melbourne, Australia, Dec. 7–10, 2008, pp. 51–60.
• [3] K. He, X. Zhang, S. Ren, and J. Sun. “Deep residual learning for image recognition.” The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), Las Vegas, United States, Jun. 26–Jul. 1, 2016, pp. 770–778.
• [4] H.J. Jeffrey. “Chaos game representation of gene structure.” Nucleic Acids Research, vol. 18, no. 8, 1990, pp. 2163–2170.
• [5] J. Johnson, A. Alahi, and L. Fei-Fei. “Perceptual losses for real-time style transfer and super-resolution.” European Conference on Computer Vision, Amsterdam, The Netherlands, Oct. 8–16, 2016, pp. 694–711. https://cs.stanford.edu/people/jcjohns/papers/eccv16/JohnsonECCV16.pdf
• [6] L. Kari, K.A. Hill, A.S. Sayem, R. Karamichalis, N. Bryans, K. Davis, and N.S. Dattani. “Mapping the space of genomic signatures.” PLOS ONE, vol. 10, no. 5, 2015, e0119815.
• [7] G. Larsson, M. Maire, and G. Shakhnarovich. “FractalNet: Ultra-Deep Neural Networks without Residuals.” International Conference on Learning Representations, Toulon, France, Apr. 24–26, 2017. http://people.cs.uchicago.edu/~larsson/fractalnet/
• [8] W. Latham, M. Shaw, S. Todd, F. Leymarie, B. Jefferys, and L. Kelly. “Using DNA to generate 3D organic art forms.” Lecture Notes in Computer Science, vol. 4974, 2008, pp. 433-442.
• [9] Y. Li, N. Wang, J. Liu, and X. Hou. “Demystifying neural style transfer.” Proceedings of the 26th International Joint Conference on Artificial Intelligence, Melbourne, Australia, Aug. 19–25, 2017. https://www.ijcai.org/proceedings/2017/0310.pdf
• [10] H. Oh, B. Seo, S. Lee, D.H. Ahn, E. Jo, J.K. Park, and G.S. Min. “Two complete chloroplast genome sequences of Cannabis sativa varieties.” Mitochondrial DNA Part A: DNA mapping, sequencing, and analysis, vol. 27, no. 4, 2016, pp. 2835–2837.
• [11] D. Vergara, K.H. White, K.G. Keepers, and N.C. Kane. “The complete chloroplast genomes of Cannabis sativa and Humulus lupulus.” Mitochondrial DNA Part A: DNA mapping, sequencing, and analysis, vol. 27, no. 4, 2016, pp. 3793–3794.
• [12] Photograph by ‘Hendrike’, distributed under a CC BY-SA 2.5 license. https://commons.wikimedia.org/wiki/Cannabis_sativa#/media/File:Hanf.jpg