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Coupled cross-sectional and longitudinal non-negative matrix factorization reveals dominant brain aging trajectories in 48,949 individuals.

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  1. [1] § Methods › Normative modeling for estimating the cross-sectional deviation map (C-map) ↔ ccl_nmf/aa.py, lines 150–201 · score 0.64 · cyclical learning rate, Adam, cycle, gradient, optimizer, batch

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The authors' code

Python · 403 lines · 15 KB · MIT · 1 match

  1. from __future__ import annotations
  3. import argparse
  4. import random
  5. from dataclasses import dataclass
  6. from pathlib import Path
  7. from typing import Tuple
  9. import numpy as np
  10. import pandas as pd
  11. import tensorflow as tf
  12. from tensorflow import keras
  14. import joblib
  15. from sklearn.model_selection import StratifiedShuffleSplit
  16. from sklearn.preprocessing import StandardScaler
  18. # Project-local imports (must exist in your repo)
  19. from models import (
  20. make_encoder_model_v1,
  21. make_decoder_model_v1,
  22. make_discriminator_model_v1,
  23. )
  25. # ------------------------- Minimal determinism helpers -------------------------
  26. def set_global_seeds(seed: int) -> None:
  27. """Seed Python, NumPy, and TensorFlow RNGs."""
  28. random.seed(seed)
  29. np.random.seed(seed)
  30. tf.keras.utils.set_random_seed(seed)
  33. def set_tf_verbosity(quiet: bool = True) -> None:
  34. if not quiet:
  35. return
  36. import logging, warnings # noqa
  37. warnings.simplefilter(action="ignore", category=FutureWarning)
  38. warnings.simplefilter(action="ignore", category=Warning)
  39. tf.get_logger().setLevel(logging.ERROR)
  42. def feature_cols_from_csv(path: Path) -> list[str]:
  43. cols = pd.read_csv(path, nrows=0).columns.tolist()
  44. return sorted(c for c in cols if c != "participant_id")
  47. def load_and_merge(features_csv: Path, covariates_csv: Path) -> pd.DataFrame:
  48. features = pd.read_csv(features_csv)
  49. covars = pd.read_csv(covariates_csv)
  50. df = covars.merge(features, on="participant_id").reset_index(drop=True)
  51. return df
  54. def stratify_key(df: pd.DataFrame, n_bins: int) -> pd.Series:
  55. """
  56. Equal-width age bins over the observed [min(Age), max(Age)].
  57. Assumes 'Age' has no NaNs (drop earlier if needed).
  58. """
  59. ages = df["Age"].to_numpy()
  60. min_age = float(np.nanmin(ages))
  61. max_age = float(np.nanmax(ages))
  62. if not np.isfinite(min_age) or not np.isfinite(max_age):
  63. raise ValueError("Age contains no finite values for stratification.")
  64. if max_age <= min_age:
  65. return pd.Series(["bin0"] * len(df), index=df.index)
  67. # Equal-width bins
  68. edges = np.linspace(min_age, max_age, num=n_bins + 1)
  69. labels = [f"bin{i}" for i in range(n_bins)]
  70. out = pd.cut(df["Age"], bins=edges, labels=labels,
  71. include_lowest=True, right=False, duplicates="drop")
  72. # If duplicates dropped (rare), fallback: label NaNs as last bin
  73. out = out.astype("object")
  74. mask_nan = pd.isna(out.values)
  75. if mask_nan.any():
  76. out[mask_nan] = labels[-1]
  77. return pd.Series(out)
  80. # ------------------------- Config -------------------------
  81. @dataclass
  82. class TrainConfig:
  83. project_root: Path
  84. features_csv: Path
  85. covariates_csv: Path
  86. outdir: Path
  87. # Splits
  88. valheldout_size: float = 0.35
  89. heldout_frac_within_val: float = 0.40
  90. age_bins: int = 5 # choose 4 or 5
  91. # Training
  92. batch_size: int = 200
  93. epochs: int = 1000
  94. patience: int = 50
  95. z_dim: int = 20
  96. h_dim: Tuple[int, int] = (110, 110)
  97. seed: int = 0
  98. # CLR
  99. base_lr: float = 1e-4
  100. max_lr: float = 5e-3
  101. gamma: float = 0.98
  102. step_size: int | None = None
  105. # ------------------------- Train -------------------------
  106. def train(cfg: TrainConfig) -> Path:
  107. set_global_seeds(cfg.seed)
  108. set_tf_verbosity(quiet=True)
  110. # Load & prepare
  111. df = load_and_merge(cfg.features_csv, cfg.covariates_csv)
  112. feature_cols = feature_cols_from_csv(cfg.features_csv)
  114. # Drop rows with missing Age before stratification
  115. if df["Age"].isna().any():
  116. dropped = int(df["Age"].isna().sum())
  117. print(f"[INFO] Dropping {dropped} rows with missing Age before stratified split.")
  118. df = df[df["Age"].notna()].reset_index(drop=True)
  120. df_split = pd.DataFrame({"participant_id": df["participant_id"], "Age": df["Age"]})
  121. strat = stratify_key(df_split, cfg.age_bins)
  123. # Split TRAIN vs (VAL+HELDOUT)
  124. sss = StratifiedShuffleSplit(
  125. n_splits=1, test_size=cfg.valheldout_size, random_state=cfg.seed)
  126. train_idx, valheld_idx = next(sss.split(df_split["participant_id"], strat))
  127. df_train = df.iloc[train_idx].copy()
  128. df_valheld = df.iloc[valheld_idx].copy()
  130. # Split (VAL+HELDOUT) into VAL and HELDOUT
  131. sss2 = StratifiedShuffleSplit(
  132. n_splits=1, test_size=cfg.heldout_frac_within_val, random_state=cfg.seed)
  133. strat2 = stratify_key(df_valheld[["Age"]].assign(participant_id=df_valheld["participant_id"]), cfg.age_bins)
  134. val_idx, held_idx = next(sss2.split(df_valheld["participant_id"], strat2))
  135. # Smaller subset becomes validation, remainder heldout (consistent naming)
  136. df_val = df_valheld.iloc[held_idx].copy()
  137. df_held = df_valheld.iloc[val_idx].copy()
  139. # Save split manifests
  140. cfg.outdir.mkdir(parents=True, exist_ok=True)
  141. df_train[["participant_id"]].to_csv(cfg.outdir / "train_participants.csv", index=False)
  142. df_val[["participant_id"]].to_csv(cfg.outdir / "val_participants.csv", index=False)
  143. df_held[["participant_id"]].to_csv(cfg.outdir / "heldout_participants.csv", index=False)
  145. df_train[["participant_id"] + feature_cols].to_csv(cfg.outdir / "train_features.csv", index=False)
  146. df_val [["participant_id"] + feature_cols].to_csv(cfg.outdir / "val_features.csv", index=False)
  147. df_held [["participant_id"] + feature_cols].to_csv(cfg.outdir / "heldout_features.csv", index=False)
  150. # Scale
  151. scaler = StandardScaler()
  152. X_train = scaler.fit_transform(df_train[feature_cols].values).astype("float32")
  153. X_val = scaler.transform(df_val[feature_cols].values).astype("float32")
  155. # Build models
  156. n_features = X_train.shape[1]
  157. encoder = make_encoder_model_v1(n_features, list(cfg.h_dim), cfg.z_dim)
  158. decoder = make_decoder_model_v1(cfg.z_dim, n_features, list(cfg.h_dim)[::-1])
  159. discriminator = make_discriminator_model_v1(cfg.z_dim, list(cfg.h_dim)[::-1])
  161. # Losses
  162. bce = tf.keras.losses.BinaryCrossentropy(from_logits=True)
  163. mse = tf.keras.losses.MeanSquaredError()
  165. def d_loss(real_out, fake_out):
  166. return bce(tf.ones_like(real_out), real_out) + bce(tf.zeros_like(fake_out), fake_out)
  168. def g_loss(fake_out):
  169. return bce(tf.ones_like(fake_out), fake_out)
  171. # Optimizers (CLR-updated per step)
  172. ae_opt = keras.optimizers.Adam(learning_rate=cfg.base_lr)
  173. d_opt = keras.optimizers.Adam(learning_rate=cfg.base_lr)
  174. g_opt = keras.optimizers.Adam(learning_rate=cfg.base_lr)
  176. # tf.data pipeline (deterministic ordering and seeded shuffle)
  177. ds = tf.data.Dataset.from_tensor_slices(X_train)
  178. ds = ds.shuffle(buffer_size=len(df_train), seed=cfg.seed, reshuffle_each_iteration=True).batch(cfg.batch_size)
  179. options = tf.data.Options()
  180. options.experimental_deterministic = True
  181. ds = ds.with_options(options)
  183. # ---- Cyclical Learning Rate (CLR) setup ----
  184. n_samples = X_train.shape[0]
  185. step_size = cfg.step_size if cfg.step_size is not None else int(2 * np.ceil(n_samples / cfg.batch_size))
  186. def scale_fn(cycle):
  187. return cfg.gamma ** cycle
  188. global_step = 0
  190. @tf.function
  191. def train_step(xb, ae_lr, d_lr, g_lr):
  192. ae_opt.learning_rate.assign(tf.cast(ae_lr, tf.float32))
  193. d_opt.learning_rate.assign(tf.cast(d_lr, tf.float32))
  194. g_opt.learning_rate.assign(tf.cast(g_lr, tf.float32))
  195. # Autoencoder
  196. with tf.GradientTape() as t_ae:
  197. z = encoder(xb, training=True)
  198. xhat = decoder(z, training=True)
  199. ae_loss = mse(xb, xhat)
  200. ae_grads = t_ae.gradient(ae_loss, encoder.trainable_variables + decoder.trainable_variables)
  201. ae_opt.apply_gradients(zip(ae_grads, encoder.trainable_variables + decoder.trainable_variables))
  203. # Discriminator
  204. with tf.GradientTape() as t_d:
  205. z_real = tf.random.normal([tf.shape(xb)[0], cfg.z_dim])
  206. z_fake = encoder(xb, training=True)
  207. d_real = discriminator(z_real, training=True)
  208. d_fake = discriminator(z_fake, training=True)
  209. loss_d = d_loss(d_real, d_fake)
  210. d_grads = t_d.gradient(loss_d, discriminator.trainable_variables)
  211. d_opt.apply_gradients(zip(d_grads, discriminator.trainable_variables))
  213. # Generator/Encoder
  214. with tf.GradientTape() as t_g:
  215. z_fake = encoder(xb, training=True)
  216. d_fake = discriminator(z_fake, training=True)
  217. loss_g = g_loss(d_fake)
  218. g_grads = t_g.gradient(loss_g, encoder.trainable_variables)
  219. g_opt.apply_gradients(zip(g_grads, encoder.trainable_variables))
  221. return ae_loss, loss_d, loss_g
  223. # Training loop with EarlyStopping on val AE loss
  224. best_val = np.inf
  225. best_epoch = -1
  226. history = {"ae_loss": [], "d_loss": [], "g_loss": [], "val_ae_loss": []}
  228. for epoch in range(cfg.epochs):
  229. ae_epoch, d_epoch, g_epoch = [], [], []
  230. for xb in ds:
  231. global_step += 1
  232. cycle = np.floor(1 + global_step / (2 * step_size))
  233. x_lr = np.abs(global_step / step_size - 2 * cycle + 1)
  234. clr = cfg.base_lr + (cfg.max_lr - cfg.base_lr) * max(0.0, 1.0 - x_lr) * scale_fn(cycle)
  235. clr32 = tf.constant(clr, dtype=tf.float32)
  236. ae_l, d_l, g_l = train_step(xb, clr32, clr32, clr32)
  237. ae_epoch.append(float(ae_l.numpy()))
  238. d_epoch.append(float(d_l.numpy()))
  239. g_epoch.append(float(g_l.numpy()))
  241. # Validation AE loss
  242. z_val = encoder(X_val, training=False)
  243. xhat_val = decoder(z_val, training=False)
  244. val_loss = float(mse(X_val, xhat_val).numpy())
  246. history["ae_loss"].append(np.mean(ae_epoch))
  247. history["d_loss"].append(np.mean(d_epoch))
  248. history["g_loss"].append(np.mean(g_epoch))
  249. history["val_ae_loss"].append(val_loss)
  251. print(f"Epoch {epoch:04d} | AE {np.mean(ae_epoch):.4f} | D {np.mean(d_epoch):.4f} "
  252. f"| G {np.mean(g_epoch):.4f} | VAL {val_loss:.4f} | BEST {best_val:.4f} @ {best_epoch}")
  254. # Save best
  255. if val_loss < best_val:
  256. best_val = val_loss
  257. best_epoch = epoch
  258. encoder.save(cfg.outdir / "best_encoder.h5")
  259. decoder.save(cfg.outdir / "best_decoder.h5")
  260. discriminator.save(cfg.outdir / "best_discriminator.h5")
  262. if epoch - best_epoch >= cfg.patience:
  263. break
  265. # Save final artifacts
  266. encoder.save(cfg.outdir / "encoder.h5")
  267. decoder.save(cfg.outdir / "decoder.h5")
  268. discriminator.save(cfg.outdir / "discriminator.h5")
  270. joblib.dump(scaler, cfg.outdir / "scaler.joblib")
  271. pd.DataFrame(history).to_csv(cfg.outdir / "training_history.csv", index=False)
  273. print(f"Best VAL AE loss: {best_val:.6f} @ epoch {best_epoch}")
  274. return cfg.outdir
  277. # ------------------------- Inference -------------------------
  278. def infer(models_dir: Path, features_csv: Path, covariates_csv: Path, dataset_name: str = "test", seed: int = 0) -> Path:
  279. set_global_seeds(seed)
  280. set_tf_verbosity(quiet=True)
  282. outdir = Path(models_dir) / dataset_name
  283. outdir.mkdir(parents=True, exist_ok=True)
  285. df = load_and_merge(features_csv, covariates_csv)
  286. feature_cols = feature_cols_from_csv(features_csv)
  288. # Optional safety check:
  289. missing = [c for c in feature_cols if c not in df.columns]
  290. if missing:
  291. raise ValueError(f"Missing expected feature columns: {missing}")
  292. X = df[feature_cols].values.astype("float32")
  294. encoder = keras.models.load_model(Path(models_dir) / "best_encoder.h5", compile=False)
  295. decoder = keras.models.load_model(Path(models_dir) / "best_decoder.h5", compile=False)
  296. scaler = joblib.load(Path(models_dir) / "scaler.joblib")
  298. Xn = scaler.transform(X).astype("float32")
  300. Z = encoder(Xn, training=False)
  301. Xhat = decoder(Z, training=False)
  303. # normalized inputs
  304. norm_df = pd.DataFrame({"participant_id": df["participant_id"]})
  305. for i, c in enumerate(feature_cols):
  306. norm_df[c] = Xn[:, i]
  307. norm_df.to_csv(outdir / "normalized.csv", index=False)
  309. # reconstructions
  310. recon_df = pd.DataFrame({"participant_id": df["participant_id"]})
  311. xhat_np = Xhat.numpy()
  312. for i, c in enumerate(feature_cols):
  313. recon_df[c] = xhat_np[:, i]
  314. recon_df.to_csv(outdir / "reconstruction.csv", index=False)
  316. # latent codes
  317. enc_df = pd.DataFrame({"participant_id": df["participant_id"]})
  318. z_np = Z.numpy()
  319. for i in range(z_np.shape[1]):
  320. enc_df[f"z{i:02d}"] = z_np[:, i]
  321. enc_df.to_csv(outdir / "encoded.csv", index=False)
  323. # reconstruction error (per-subject MSE)
  324. rec_err = np.mean((Xn - xhat_np) ** 2, axis=1)
  325. pd.DataFrame({
  326. "participant_id": df["participant_id"],
  327. "Reconstruction error": rec_err}).to_csv(outdir / "reconstruction_error.csv", index=False)
  329. print(f"Wrote outputs to {outdir}")
  330. return outdir
  333. # ------------------------- CLI -------------------------
  334. def build_parser() -> argparse.ArgumentParser:
  335. p = argparse.ArgumentParser(description="AAE pipeline (train + infer) — NO-SEX condition (minimal deterministic)")
  336. sub = p.add_subparsers(dest="cmd", required=True)
  338. pt = sub.add_parser("train", help="Train models")
  339. pt.add_argument("--features_csv", required=True, type=Path)
  340. pt.add_argument("--covariates_csv", required=True, type=Path)
  341. pt.add_argument("--outdir", required=True, type=Path)
  342. pt.add_argument("--z_dim", type=int, default=20)
  343. pt.add_argument("--h_dim", type=int, nargs=2, default=[110, 110])
  344. pt.add_argument("--epochs", type=int, default=1000)
  345. pt.add_argument("--patience", type=int, default=50)
  346. pt.add_argument("--batch_size", type=int, default=200)
  347. pt.add_argument("--seed", type=int, default=0)
  348. pt.add_argument("--valheldout_size", type=float, default=0.35)
  349. pt.add_argument("--heldout_frac_within_val", type=float, default=0.40)
  350. # CLR
  351. pt.add_argument("--base_lr", type=float, default=1e-4)
  352. pt.add_argument("--max_lr", type=float, default=5e-3)
  353. pt.add_argument("--gamma", type=float, default=0.98)
  354. pt.add_argument("--step_size", type=int, default=0, help="0=auto (2 * ceil(N/batch))")
  355. # Age-bin choice
  356. pt.add_argument("--age_bins", type=int, choices=[4, 5], default=5)
  357. pi = sub.add_parser("infer", help="Run inference with trained models")
  358. pi.add_argument("--models_dir", required=True, type=Path)
  359. pi.add_argument("--features_csv", required=True, type=Path)
  360. pi.add_argument("--covariates_csv", required=True, type=Path)
  361. pi.add_argument("--name", default="test", help="Output subfolder name (e.g., val/heldout/test)")
  362. pi.add_argument("--seed", type=int, default=0, help="Seed for deterministic inference")
  364. return p
  367. def main():
  368. parser = build_parser()
  369. args = parser.parse_args()
  371. if args.cmd == "train":
  372. cfg = TrainConfig(
  373. project_root=Path.cwd(),
  374. features_csv=args.features_csv,
  375. covariates_csv=args.covariates_csv,
  376. outdir=args.outdir,
  377. z_dim=args.z_dim,
  378. h_dim=(args.h_dim[0], args.h_dim[1]),
  379. epochs=args.epochs,
  380. patience=args.patience,
  381. batch_size=args.batch_size,
  382. seed=args.seed,
  383. valheldout_size=args.valheldout_size,
  384. heldout_frac_within_val=args.heldout_frac_within_val,
  385. base_lr=args.base_lr,
  386. max_lr=args.max_lr,
  387. gamma=args.gamma,
  388. step_size=(None if args.step_size == 0 else args.step_size),
  389. age_bins=args.age_bins)
  390. train(cfg)
  392. elif args.cmd == "infer":
  393. infer(
  394. models_dir=args.models_dir,
  395. features_csv=args.features_csv,
  396. covariates_csv=args.covariates_csv,
  397. dataset_name=args.name,
  398. seed=args.seed)
  401. if __name__ == "__main__":
  402. main()

aa.py at commit 76d8801, under MIT · at the source

Overview

Authors: Ioanna Skampardoni1,2, Guray Erus1, Ilya M. Nasrallah1,3, Zhijian Yang1, Michael R. Duggan4, Keenan A. Walker4, Alexander Getka1, Kyunglok Baik1, Randa Melhem1, Sindhuja T. Govindarajan1, Susan M. Resnick4, Haochang Shou1,5, Konstantina Nikita2, Christos Davatzikos1
ORCID iDs: Ioanna Skampardoni, Guray Erus, Ilya M. Nasrallah, Michael R. Duggan, Keenan A. Walker, Alexander Getka, Kyunglok Baik, Sindhuja T. Govindarajan, Susan M. Resnick, Haochang Shou, Christos Davatzikos
  1. AI2D Center for AI and Data Science for Integrated Diagnostics, University of Pennsylvania,Philadelphia, PA USA
  2. School of Electrical and Computer Engineering, National Technical University of Athens,Athens, Greece
  3. Department of Radiology, University of Pennsylvania,Philadelphia, PA USA
  4. Laboratory of Behavioral Neuroscience, National Institute on Aging,Baltimore, MD USA
  5. Department of Biostatistics, Epidemiology, & Informatics, University of Pennsylvania,Philadelphia, PA USA
Institutions: University of Pennsylvania (United States); National Technical University of Athens (Greece); National Institute on Aging (United States)
Journal: Nature communications, volume 17, issue 1, article 5709
Dates: received 21 April 2025; accepted 6 April 2026; published online 25 April 2026
Type: Research article · Language: English
License: CC BY-NC-ND
Identifiers: DOI 10.1038/s41467-026-72091-7 · PMID 42034902 · PMCID PMC13319776 · OpenAlex W7155606518
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: structural MRI / diffusion (modality), human (organism), Alzheimer's / dementia (population)
Methods: Connectivity, Statistics, Machine learning, Preprocessing, fMRI & imaging
Keywords: Prognostic markers, Magnetic resonance imaging, Machine learning, Alzheimer's disease, Neurodegeneration
MeSH: Aging*, Brain*, Aged, Cognition, Cross-Sectional Studies, Female, Humans, Longitudinal Studies, Machine Learning, Magnetic Resonance Imaging, Male, Middle Aged, Neuroimaging (* major topic)
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: National Institute on Aging
Citations: not cited yet (Europe PMC); 64 references in the paper

Abstract

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cbica/ccl_nmf_prediction

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Languages: Python (4), Shell (1)
Size: 41 files, 5 scripts
Software Heritage: archived
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Holds: README, license file, environment (requirements.txt, setup.cfg, setup.py), tests
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Availability: 1 check, the latest on 30 September 2026: the link answers
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At the source: github.com/CBICA/CCL_NMF_Prediction/tree/main

IoannaSkampardoni/CCL-NMF

License: MIT
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Commit: 76d8801e3f9bf821e8a46ebf5f4c6d05349cc487, 19 September 2025
Languages: Python (6)
Size: 22 files, 6 scripts
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Found in: “Code availability”
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Tools: NumPy (5 files), pandas (4 files), Keras (2 files), scikit-learn (2 files), TensorFlow (2 files), statsmodels (1 file)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
8 files
At the source: github.com/IoannaSkampardoni/CCL-NMF

Code availability statement

The paper has a code availability statement. Its license (CC BY-NC-ND) does not allow reproducing it here; in short, from what the harvester recognized in it:

Read it in the paper: doi.org/10.1038/s41467-026-72091-7.

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  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
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Data

Datasets cited

Data availability statement

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Read it in the paper: doi.org/10.1038/s41467-026-72091-7.

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 14 authors, 5 keywords, 13 MeSH terms, 1 funder, 58 references.

Cite

This paper

Skampardoni, I., Erus, G., Nasrallah, I. M., Yang, Z., Duggan, M. R., Walker, K. A., Getka, A., Baik, K., Melhem, R., Govindarajan, S. T., Resnick, S. M., Shou, H., Nikita, K., & Davatzikos, C. (2026). Coupled cross-sectional and longitudinal non-negative matrix factorization reveals dominant brain aging trajectories in 48,949 individuals. Nature communications, 17(1), 5709. https://doi.org/10.1038/s41467-026-72091-7

BibTeX

@article{skampardoni2026coupled,
author = {Skampardoni, Ioanna and Erus, Guray and Nasrallah, Ilya M. and Yang, Zhijian and Duggan, Michael R. and Walker, Keenan A. and Getka, Alexander and Baik, Kyunglok and Melhem, Randa and Govindarajan, Sindhuja T. and Resnick, Susan M. and Shou, Haochang and Nikita, Konstantina and Davatzikos, Christos},
title = {{Coupled cross-sectional and longitudinal non-negative matrix factorization reveals dominant brain aging trajectories in 48,949 individuals}},
journal = {Nature communications},
year = {2026},
month = apr,
volume = {17},
number = {1},
pages = {5709},
publisher = {Nature Publishing Group},
issn = {2041-1723},
doi = {10.1038/s41467-026-72091-7},
url = {https://doi.org/10.1038/s41467-026-72091-7},
pmid = {42034902},
pmcid = {PMC13319776}
}

RIS

TY - JOUR
AU - Skampardoni, Ioanna
AU - Erus, Guray
AU - Nasrallah, Ilya M.
AU - Yang, Zhijian
AU - Duggan, Michael R.
AU - Walker, Keenan A.
AU - Getka, Alexander
AU - Baik, Kyunglok
AU - Melhem, Randa
AU - Govindarajan, Sindhuja T.
AU - Resnick, Susan M.
AU - Shou, Haochang
AU - Nikita, Konstantina
AU - Davatzikos, Christos
TI - Coupled cross-sectional and longitudinal non-negative matrix factorization reveals dominant brain aging trajectories in 48,949 individuals
T2 - Nature communications
J2 - Nat Commun
PY - 2026
DA - 2026/04/25
VL - 17
IS - 1
SP - 5709
SN - 2041-1723
PB - Nature Publishing Group
DO - 10.1038/s41467-026-72091-7
UR - https://doi.org/10.1038/s41467-026-72091-7
LA - en
ER -

CSL-JSON

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"type": "article-journal",
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"container-title": "Nature communications",
"author": [
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{
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{
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{
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{
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},
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"family": "Baik",
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"container-title-short": "Nat Commun",
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"issue": "1",
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"DOI": "10.1038/s41467-026-72091-7",
"PMID": "42034902",
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"ISSN": "2041-1723",
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"language": "en",
"issued": {
"date-parts": [
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}

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