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GSP Cochlea: A graph signal processing approach for studying sound encoding.

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The authors' code

MATLAB · 433 lines · 16 KB · GPL-3.0

  1. %% GRAPH SIGNAL PROCESSING ANALYSIS OF SOUND PROCESSING IN THE COCHLEA
  3. % Melia E. Bonomo, Santiago Segarra, Robert M. Raphael
  4. % Rice University, 2026
  6. % This code is freely distributed under the GNU General Public License.
  7. % http://www.gnu.org/licenses/gpl-3.0.html
  9. % PATIENT GROUPS
  10. % 32 patients spread across 7 levels of hearing loss severity
  12. % FOR EACH PATIENT GROUP
  13. % FOR EACH PATIENT (i.e., AUDIOGRAM)
  14. % 1. Input audiogram to UR_EAR model [1] to determine impairment
  15. % 2. Run UR_EAR model on N randomly sample stimuli
  16. % SAVE: voltage signals (VIHC) for each stimulus
  17. % 3. Run gsp on N signals for the 100 nodes
  18. % SAVE: graph adjacency matrix (W) for the patient
  20. % External scripts needed:
  21. % - UR_EAR toolbox [1]
  22. % - GSPBOX toolbox [2]
  24. % External data:
  25. % - full audiogram dataset [3]
  26. % - stimulus files [1,4,5]
  28. % Included files:
  29. % - stimulus_log_filenames.txt
  30. % - audiogram_%s.csv' (randomly sampled, each %s level of hearing loss)
  31. % - CF_position.mat (determined from [6])
  33. % References:
  34. %
  35. % [1] M. S. Zilany, I. C. Bruce, L. H. Carney, Updated parameters and
  36. % expanded simulation options for a model of the auditory periphery.
  37. % The Journal of the Acoustical Society of America, 135, (2014).
  38. % [2] N. Perraudin et al., GSPBOX: A toolbox for signal processing on
  39. % graphs. arXiv [Preprint] (2016). https://arxiv.org/abs/1408.5781
  40. % [3] J. A. Germiller et al., AudGenDB: A Public, Internet-Based,
  41. % Audiologic/Otologic/Genetic Database for Pediatric Hearing Research.
  42. % Otolaryngology–Head and Neck Surgery, 145, P235-P236 (2011).
  43. % [4] L. Fritts et al., Data from “Musical Instrument Samples.” University
  44. % of Iowa. Available at https://theremin.music.uiowa.edu/MIS.html.
  45. % [5] J. Hillenbrand, R. A. Houde, Vowel recognition: Formants, spectral
  46. % peaks, and spectral shape. The Journal of the Acoustical Society of
  47. % America, 98, 2949-2949 (1995).
  48. % [6] M. Pietsch et al., Spiral form of the human cochlea results from
  49. % spatial constraints. Scientific reports, 7, 7500 (2017).
  50. %
  52. %% Options
  54. clear
  56. start_date = 'DD-MM-YYY'; % For saving filename of GS and W
  58. general_model_mode = false;
  59. % true: Runs a perfect audiogram
  60. % false: Runs patient audiograms
  62. % Autosave options
  63. save_orig_signals = false; % GS-orig (raw signals)
  64. save_norm_signals = false; % GS (normalized signals)
  65. save_W_matrices = false; % W (connectivity matrix)
  67. % Plotting steps along the pipeline
  68. plot_patient = 1;
  69. plot_audiogram = false;
  70. plot_stim = false;
  71. plot_VIHC = false;
  72. plot_GS = false;
  73. plot_graph = false;
  75. % Network size
  76. CF_num = 100; % number of graph nodes
  77. total_stim = 1000; % number of graph signals to generate
  79. % Initialize random number generator (gsp)
  80. seed = 15;
  81. rng(seed)
  83. %% File Locations
  85. main_folder = '/LOCATION';
  86. data_folder = 'folder';
  88. %% Patient data information
  89. % Patient audiograms from AudGenDB
  91. if general_model_mode == true
  92. groups = {'gen'};
  93. else
  94. groups = {'1','2','3','4','5','6','7'};
  95. end
  96. num_groups = size(groups,2);
  97. data_type = '.csv';
  99. if general_model_mode == true
  100. num_patients_each_group = [1];
  101. else
  102. num_patients_each_group = [32,32,32,32,32,32,32];
  103. end
  104. total_patients = sum(num_patients_each_group);
  106. %% UR_EAR model parameters
  108. species = 2; % 1 for cat (2 for human with Shera et al. tuning; 3 for human with Glasberg & Moore tuning)
  110. % Characteristic Frequency Range (Hz)
  111. % Must be between 125 Hz and 20 kHz for human model
  112. minCF = 125; % original range 200 Hz
  113. maxCF = 8000; % original range 3000 Hz
  115. CF_range = [minCF, maxCF];
  116. CFs = logspace(log10(CF_range(1)),log10(CF_range(2)),CF_num); % set range and resolution of CFs here
  117. CFs([1 end]) = CF_range; % force end points to be exact
  118. num_iters = length(CFs);
  120. % Hearing loss in dB, to determine Cohc and Cihc for model using
  121. % function from Bruce and Zilany models, as in Bruce et al 2018 code.
  122. %ag_fs = [250 500 1e3 2e3 4e3]; % audiometric frequencies
  123. ag_fs_ALL = [125 250 500 750 1e3 1.5e3 2e3 3e3 4e3 6e3 8e3]; % audiometric frequencies
  125. % Stimulus Parameters
  126. spl = 65; % Sound Level (dB SPL)
  127. Pref = 20e-6; % reference pressure in pascals
  128. %from UR_EAR, line 226
  129. % Model sampling rate (must be 100k, 200k or 500k for AN model):
  130. Fs = 100e3; % samples/sec
  131. RsFs = 10e3; % resample rate for time_freq surface plots
  132. nrep = 1;
  134. % Load in stimulus randomly sampled list
  135. input_stim_name = sprintf('%s/results/%s/stimulus_log_filenames.txt',main_folder,data_folder);
  136. stimulus_log_filenames = readtable(input_stim_name,'Delimiter','tab','ReadVariableNames', false, 'TextType','string'); % dummy delimeter
  138. %% GSP BOX Parameters
  140. params.maxit = 50000;
  141. params.step_size = 0.1;
  142. params.verbosity = 1;
  143. params.tol = 1e-5;
  144. gsp_reset_seed(0);
  146. % GSP method
  147. method = 1; %1 = logarithmic prior, 2 = L-2 prior
  149. % Optimization model
  150. if method == 1
  151. % Learn weighted adjacency matrix from pairwise distances using
  152. % negative log prior on nodes degrees
  153. s = sqrt(2*(CF_num-1))/2 / 3;
  154. else
  155. % Learn weighted adjacency matrix from pairwise distances using
  156. % l2 prior on nodes degrees
  157. s = 1/2/sqrt(2);
  158. end
  160. %% Running the model
  162. iPatient_overall = 0;
  163. for iGroup = 1:num_groups
  164. nPatient = num_patients_each_group(iGroup);
  166. if general_model_mode == false
  168. input_data_name = sprintf('%s/data/audiogram_%s%s',main_folder,groups{iGroup},data_type);
  170. % Specify variable data types before import
  171. types = {'uint16','categorical','categorical','categorical','categorical','uint32','categorical','categorical','double','double','double','double','double','double','double','double','double','double','double','uint32','logical','logical','uint32','uint32','datetime','double','uint32','string','uint8','categorical'};
  173. opts = detectImportOptions(input_data_name);
  174. opts = setvartype(opts,types);
  176. data_audiograms = readtable(input_data_name,opts);
  177. data_audiograms = renamevars(data_audiograms,'Var1','index');
  179. % Extract patient identifiers & audiograms
  180. patient_index = data_audiograms.index;
  181. patient_id = data_audiograms.patient_id;
  182. audiograms = table2array(data_audiograms(:,9:19));
  183. else
  184. % Generic cochlea graph
  185. patient_index = [000];
  186. patient_id = [000];
  187. audiograms = zeros(nPatient,size(ag_fs_ALL,2));
  188. end
  190. tic
  191. for iPatient = 1:nPatient
  192. iPatient_overall = iPatient_overall + 1;
  194. %% Run UR_EAR
  196. % Audiogram Processing
  197. ag_dbloss_ALL = audiograms(iPatient,:);
  199. freqs = ~isnan(ag_dbloss_ALL);
  200. ag_dbloss = ag_dbloss_ALL(freqs);
  201. ag_fs = ag_fs_ALL(freqs);
  203. if plot_audiogram == true
  204. if iPatient == plot_patient
  205. figure
  206. plot(ag_fs,ag_dbloss,'o-k','LineWidth',1.75)
  207. set(gca, 'YDir','reverse')
  208. set(gca, 'FontSize', 20)
  209. ylim([-10,90])
  210. ylabel('Hearing Level in Decibels (dB)')
  211. xlabel('Frequency (Hz)')
  212. title('Audiogram')
  213. end
  214. end
  216. dbloss = interp1(ag_fs,ag_dbloss,CFs,'linear','extrap');
  217. [cohc_vals,cihc_vals] = fitaudiogram2(CFs,dbloss,species);
  218. if cohc_vals(1) == 0
  219. % Only set to 1 if coch_vals(2) == 1
  220. if cohc_vals(2) == 1
  221. % For a very low CF, a 0 may be returned by Bruce et al. fit
  222. % audiogram, but this is a bad default. Set it to 1 here.
  223. cohc_vals(1) = 1;
  224. end
  225. end
  226. if cihc_vals(1) == 0
  227. % Only set to 1 if coch_vals(2) == 1
  228. if cihc_vals(2) == 1
  229. % For a very low CF, a 0 may be returned, but this is a bad default.
  230. % Set it to 1 here.
  231. cihc_vals(1) = 1;
  232. end
  233. end
  235. VIHC_signals = nan(CF_num,total_stim);
  236. VIHC_signals_orig = nan(CF_num,total_stim);
  238. % Run stimulus
  239. for iStim = 1:total_stim
  240. in_stim_name = sprintf('%s/stimuli_all/%s',main_folder,stimulus_log_filenames{iPatient_overall,iStim});
  242. info = audioinfo(in_stim_name);
  243. dur1 = info.Duration;
  244. stim_length_RsFs = round(RsFs * dur1);
  245. VIHC_population = nan(CF_num,stim_length_RsFs);
  247. % Load stimulus
  248. [stimulus,~] = audioread(in_stim_name);
  250. if plot_stim == true
  251. if iStim == plot_stim
  252. % plot the FFT of the stimulus
  254. % Get length of stimulus.
  255. N = length(stimulus);
  257. % Plot FFT
  258. figure
  259. f = (0:N-1)*(Fs/N); % frequency range
  260. power = abs(fft(stimulus)).^2/N;
  261. plot(f,power,'k-','LineWidth',1.75)
  262. xlabel('Frequency (Hz)')
  263. ylabel('Power')
  264. title(sprintf('%s',stimulus_log_filenames{iPatient,iStim}))
  265. xlim([0 4000])
  267. set(gca,'FontSize',15,'FontWeight','bold')
  268. ax = gca;
  269. ax.LineWidth = 1;
  270. end
  271. end
  273. % duration of waveform in sec
  274. dur2 = dur1 + 0.04;
  276. % Loop through CFs (within nconditions loop) in reverse order so
  277. % matrices don't have to be resized.
  278. for iCF = length(CFs):-1:1
  280. % Get iCF element of each array.
  281. CF = CFs(iCF); % CF in Hz;
  282. cohc = cohc_vals(iCF);
  283. cihc = cihc_vals(iCF);
  285. % Using ANModel_2014 (2-step process)
  286. vihc = model_IHC(stimulus',CF,nrep,1/Fs,dur2,cohc,cihc,species);
  287. % Save output waveform into matrices.
  288. vihc_resampled = resample(vihc,RsFs,Fs);
  289. resampled_length = size(vihc_resampled,2);
  291. VIHC_population(iCF,1:resampled_length) = vihc_resampled(1:resampled_length);
  293. end % end of CF loop
  295. if plot_VIHC == true
  296. if iPatient == plot_patient
  297. if iStim == plot_stim
  298. % plot the inner hair cell voltages
  299. end
  300. end
  301. end
  303. % Average VIHC time series to get the graph signals
  304. X_orig = squeeze(nanmean(VIHC_population,2));
  306. % Normalize
  307. X = normalize(X_orig,'range',[0 1]); %for 1000 signals
  309. % Save into graph signal variable
  310. VIHC_signals(:,iStim) = X;
  311. VIHC_signals_orig(:,iStim) = X_orig;
  313. if plot_GS == true
  314. if iPatient == plot_patient
  315. if iStim == plot_stim
  316. % plot the graph signals of nodes (IHC)
  317. end
  318. end
  319. end
  321. stat = sprintf('Finished running iStim = %d',iStim);
  322. disp(stat)
  323. end
  325. %% Save graph signals for patient
  326. if save_norm_signals == true
  327. out_GSnorm_data_name = sprintf('%s/results/%s/%s_%d_%d_GS_%s.txt',main_folder,data_folder,groups{iGroup},patient_index(iPatient),patient_id(iPatient),start_date);
  328. writematrix(VIHC_signals,out_GSnorm_data_name,'Delimiter','tab')
  329. end
  331. if save_orig_signals == true
  332. out_GS_data_name = sprintf('%s/results/%s/%s_%d_%d_GS-orig_%s.txt',main_folder,data_folder,groups{iGroup},patient_index(iPatient),patient_id(iPatient),start_date);
  333. writematrix(VIHC_signals_orig,out_GS_data_name,'Delimiter','tab')
  334. end
  336. toc % time to run UR_EAR
  338. %% Run GSP BOX
  340. % Compute the pairwise distances of the features of each signal
  341. % and learn a graph using them:
  343. Z = gsp_distanz(VIHC_signals').^2;
  344. if method == 1
  345. W = gsp_learn_graph_log_degrees(Z, s*2, s*1, params);
  346. else
  347. W = gsp_learn_graph_l2_degrees(Z, s*1, params);
  348. end
  349. W(W<1e-5) = 0;
  351. if plot_graph == true
  352. if iPatient == plot_patient
  353. %% Plot graph
  355. % Cochlea 3D coordinates determined from reference [6] for
  356. % 100 nodes spaced at given characteristic frequencies (CF)
  357. load('CF_position.mat')
  358. CF_position_rev = flip(CF_position,2);
  360. fprintf('Graph of %d signals: %d edges\n', total_stim,nnz(W)/2);
  361. G = gsp_graph(W / sum(W(:)) * CF_num, [CF_position_rev(1,:)', CF_position_rev(2,:)', CF_position_rev(3,:)']);
  363. params_plot.edge_size = 1;
  364. params_plot.show_edges = 1;
  365. G.plotting.vertex_size = 30;%5;
  367. investigate_boundary_effect = false;
  368. if investigate_boundary_effect == true
  370. box1 = 17;
  371. box2 = 71;
  373. bound_colors = ones(CF_num,3);
  374. for iNode = [1:box1,box2:CF_num]
  375. bound_colors(iNode,:) = [0 0 0];
  376. end
  378. [ki,kj] = find(G.W);
  379. num_edges = size(ki,1);
  381. % Variable containing the color assigned to each edge
  382. bound_edge_colors = nan(num_edges,3);
  383. for iEdge = 1:num_edges
  384. iNode = ki(iEdge);
  385. jNode = kj(iEdge);
  387. if iNode <= box1 && jNode >= box2
  388. % Edge between boundary nodes
  389. c = [0.8 0 0];
  390. elseif iNode >= box2 && jNode <= box1
  391. % Edge between boundary nodes
  392. c = [0.8 0 0];
  393. else
  394. % Edge between non-boundary nodes
  395. c = [0.6 0.6 0.6];
  396. end
  397. bound_edge_colors(iEdge,:) = c;
  399. end
  401. G.plotting.vertex_color = bound_colors;
  402. G.plotting.edge_color = bound_edge_colors;
  404. figure
  405. imagesc(W)
  406. colorbar
  407. set(gca,'FontSize',15,'FontWeight','bold')
  408. ax = gca;
  409. ax.XTick = [1 18 34 51 67 84 93 100]; %CF number
  410. ax.XTickLabel = {'125' '250' '500' '1k' '2k' '4k' '6k' '8k'}; %CF freq
  411. ax.YTick = [1 18 34 51 67 84 93 100];
  412. ax.YTickLabel = {'125' '250' '500' '1k' '2k' '4k' '6k' '8k'};
  413. ax.XAxisLocation='top';
  414. ax.Position = [0.1220 0.1100 0.7272 0.8150];
  416. end
  418. figure;
  419. gsp_plot_graph(G, params_plot);
  420. axis equal
  421. view([-90 90])
  423. end
  424. end
  426. %% Save W data for patient
  427. if save_W_matrices == true
  428. out_W_data_name = sprintf('%s/results/%s/%s_%d_%d_W_%s.txt',main_folder,data_folder,groups{iGroup},patient_index(iPatient),patient_id(iPatient),start_date);
  429. writematrix(W,out_W_data_name,'Delimiter','tab')
  430. end
  432. end
  433. end

GSPcochlea.m at commit d517533, under GPL-3.0 · at the source

Overview

Authors: Melia E Bonomo1, Santiago Segarra2, Robert M Raphael3
ORCID iDs: Melia E Bonomo, Santiago Segarra, Robert M Raphael
  1. Department of Physics and Astronomy, Rice University, Houston, TX 77005, USA
  2. Department of Electrical and Computer Engineering, Rice University, Houston, TX 77005, USA
  3. Department of Bioengineering, Rice University, Houston, TX 77005, USA
Institutions: Rice University (United States)
Journal: PNAS nexus, volume 5, issue 5, article pgag134
Dates: received 22 August 2025; accepted 1 April 2026; published online 21 April 2026
Type: Brief report · Language: English
License: CC BY
Identifiers: DOI 10.1093/pnasnexus/pgag134 · PMID 42099576 · PMCID PMC13148644 · OpenAlex W7155086423
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: other condition (population), computational (subfield)
Keywords: cochlea, complex systems, graph signal processing, graph theory, hearing loss
Topic: Hearing, Cochlea, Tinnitus, Genetics (Sensory Systems, Neuroscience), according to OpenAlex
Funding: Rice University; U.S. National Library of Medicine (T15LM007093)
Citations: not cited yet (Europe PMC); 15 references in the paper

Abstract

Humans are able to hear in a variety of complicated acoustic environments. This feat begins in the peripheral auditory system, where the cochlea collects and transmits thousands of individual bits of sound data to the brain. Here, we introduce GSP Cochlea: a graph signal processing-based framework to investigate and visualize sound encoding. We show that a cochlea graph with a mesh topology provides a mechanism of denoising, efficient information transfer, and modular processing. We demonstrate an application to assess hearing loss as more than just a decibel loss at particular frequencies of sound but also a significant change to the cochlea graph architecture. GSP Cochlea is a generalized approach that provides new insight into the higher-level functional activity of the inner ear.

Reproduced under the paper's license (CC BY), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

meliabonomo/GSPcochlea

License: GPL-3.0
State: the link answers, verified on 29 September 2026
Evidence: files inventoried
Commit: d517533f31d166e162a55745fe8ad12ebf43c1d9, 15 April 2026
Languages: MATLAB (1)
Size: 5 files, 1 script
Software Heritage: not archived
Found in: “Data availability”
Holds: README, license file
Not found: CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (1 file)
Availability: 1 check, the latest on 29 September 2026: the link answers
  • 29 September 2026: the link answers
3 files
At the source: github.com/meliabonomo/GSPcochlea

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

What the map holds:

  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 1 script, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

No dataset and no data link were found in the paper.

Data availability

Computer codes written for the GSP Cochlea formulation presented here are available at https://github.com/meliabonomo/GSPcochlea.

Reproduced under the paper's license (CC BY), from the paper cited above.

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 29 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 3 authors, 5 keywords, 2 funders, 8 references.

Cite

This paper

Bonomo, M. E., Segarra, S., & Raphael, R. M. (2026). GSP Cochlea: A graph signal processing approach for studying sound encoding. PNAS nexus, 5(5), pgag134. https://doi.org/10.1093/pnasnexus/pgag134

BibTeX

@article{bonomo2026gsp,
author = {Bonomo, Melia E and Segarra, Santiago and Raphael, Robert M},
title = {{GSP Cochlea: A graph signal processing approach for studying sound encoding}},
journal = {PNAS nexus},
year = {2026},
month = apr,
volume = {5},
number = {5},
pages = {pgag134},
publisher = {Oxford University Press},
issn = {2752-6542},
doi = {10.1093/pnasnexus/pgag134},
url = {https://doi.org/10.1093/pnasnexus/pgag134},
pmid = {42099576},
pmcid = {PMC13148644}
}

RIS

TY - JOUR
AU - Bonomo, Melia E
AU - Segarra, Santiago
AU - Raphael, Robert M
TI - GSP Cochlea: A graph signal processing approach for studying sound encoding
T2 - PNAS nexus
J2 - PNAS Nexus
PY - 2026
DA - 2026/04/21
VL - 5
IS - 5
SP - pgag134
SN - 2752-6542
PB - Oxford University Press
DO - 10.1093/pnasnexus/pgag134
UR - https://doi.org/10.1093/pnasnexus/pgag134
LA - en
ER -

CSL-JSON

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"id": "10.1093/pnasnexus/pgag134",
"type": "article-journal",
"title": "GSP Cochlea: A graph signal processing approach for studying sound encoding",
"container-title": "PNAS nexus",
"author": [
{
"family": "Bonomo",
"given": "Melia E"
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{
"family": "Segarra",
"given": "Santiago"
},
{
"family": "Raphael",
"given": "Robert M"
}
],
"container-title-short": "PNAS Nexus",
"volume": "5",
"issue": "5",
"page": "pgag134",
"DOI": "10.1093/pnasnexus/pgag134",
"PMID": "42099576",
"PMCID": "PMC13148644",
"ISSN": "2752-6542",
"publisher": "Oxford University Press",
"URL": "https://doi.org/10.1093/pnasnexus/pgag134",
"language": "en",
"issued": {
"date-parts": [
[
2026,
4,
21
]
]
}
}

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Brain structural and functional connectivity converge prenatally but diverge after birth.
Journal: PLoS biology
In common: Statistics and Machine Learning Toolbox, 1 reference
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A conserved node degree-based backbone and flexible hub organization of brain connectome during naturalistic movie watching.
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In common: Statistics and Machine Learning Toolbox, 1 reference
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Journal: Nature communications
In common: Statistics and Machine Learning Toolbox, 1 reference
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In common: Statistics and Machine Learning Toolbox, 1 reference
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Shared genetic architecture between the topology of brain white matter structural connectome and fluid intelligence.
Journal: Communications biology
In common: Statistics and Machine Learning Toolbox, 1 reference

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