A recurrent neural network for classification of unevenly sampled variable stars

Contributions

• B.N. implemented and trained the networks, assembled the machine-learning results, and drafted the paper and figures.J.S.B. conceived the project, assembled the astronomical light curves, and oversaw supervised training; F.P. provided theoretical input, and S.vdW. discussed results and commented on the manuscript.Source: Contributions · p. 5

Affiliations

• The authors are affiliated with UC Berkeley's Department of Astronomy, Department of Statistics, and Berkeley Institute for Data Science.The Department of Astronomy affiliation lists B. Naul and J. S. Bloom; Statistics lists F. Pérez; the Institute lists S. van der Walt.Source: Affiliations · p. 6

Corresponding author

• Correspondence is directed to B. Naul.Source: Corresponding author · p. 6

Comparison with other neural network approaches

• Interpolation-based networks replace uneven sampling with interpolated data, which can introduce algorithm-dependent biases and artifacts as sampling becomes less even.The approach instead uses recurrent networks that take the sampling times into account directly.Source: Comparison with other neural network… · pp. 6–7, Figure 1 · p. 7

Methods

• The encoder maps measurements and sampling-time differences to a fixed-length embedding, which the decoder combines with time differences to generate an output sequence.The illustrated architecture uses recurrent layers in both components; sampling times are supplied to both because the embedding represents signal form while times determine evaluation points.Source: Figure 1 · p. 7

Comparison with other neural network approaches

• Figure 2 presents example reconstructions from 64-dimensional features for raw and period-folded ASAS light curves, showing 25th- and 75th-percentile reconstruction errors.The plotted magnitudes are approximately V-band magnitudes in the Vega system.Source: Figure 2 · p. 8

• The models minimize weighted mean squared reconstruction error, weighting each time-step error according to its measurement uncertainty.Errors at measurements with larger uncertainty receive less penalty, while errors at more precise measurements receive more.Source: Loss function for known measurement… · p. 8
• The loss is defined over sequences and light curves, with nT denoting sequence length and N the number of light curves.Source: Loss function for known measurement… · p. 8
• At each indexed time step, the loss compares a measurement with its reconstruction and uses the measurement error in the weighting.The passage identifies these quantities as the measurement, reconstruction value, and measurement error for a light curve.Source: Loss function for known measurement… · p. 8

• The ASAS and LINEAR classification autoencoders use two encoder and two decoder GRU layers of size 96 and an embedding size of 64.They are trained with Adam at learning rate λ = 5 × 10^-4 to minimize the weighted mean squared reconstruction error.Source: Neural network parameters · p. 9

• Random forests predict each labeled light curve’s class from either unsupervised autoencoder features or baseline features.Source: Random forest classifier parameters · p. 9
• A five-fold cross-validation grid search selects forest hyperparameters from the specified tree-count, criterion, feature-count, and leaf-size options.The grid includes 50, 100, or 250 trees; Gini or entropy; 3, 6, 12, or 18 maximum features; and 1, 2, or 3 minimum leaf samples.Source: Random forest classifier parameters · p. 10
• Each comparison uses the same five 80/20 train/test splits for autoencoder and Richards et al. features, with tuning restricted to training data.Source: Random forest classifier parameters · p. 10

All Sky Automated Survey (ASAS) data

• ASAS contributes five selected variable-star classes, with labels manually identified or assigned at greater than 99% probability by its machine-learned catalog.The catalog contains 50,124 mostly unlabeled light curves; selected classes include Beta Persei, Classical Cepheids, RR Lyrae (FM), Semiregular PV, and W Ursae Major.Source: All Sky Automated Survey (ASAS) data · p. 10

Lincoln Near-Earth Asteroid Research (LINEAR) data

• LINEAR contributes 5,204 manually classified light curves across five stellar classes, with periods manually validated.Source: Lincoln Near-Earth Asteroid Research… · p. 10

Massive Compact Halo Object (MACHO) Project data

• MACHO contributes 21,474 light curves across eight classes, using red-band brightness and error values; labels and periods were determined semi-automatically.Non-variable sources in the full MACHO dataset were excluded from autoencoder and random-forest training.Source: Massive Compact Halo Object (MACHO)… · p. 10

• Raw survey data are filtered to remove grade C-or-lower measurements, then each light curve is centered and scaled to mean zero and standard deviation one.Source: Data preprocessing · p. 10
• A super-smoother fit at the estimated period screens out light curves with residuals greater than 0.7 because including aperiodic sources tended to degrade reconstruction quality.Source: Data preprocessing · p. 10
• The processed curves are partitioned into length-200 subsequences, an optional choice that reduces training time and is computationally advantageous.The resulting dataset contains 33,103 sequences.Source: Data preprocessing · p. 11

• Conventional time-series workflows map each sequence to scalar features, but building, selecting, and computing effective features can require expertise and iterative tuning.Source: §1 · p. 11
• Most neural-network applications to time series assume evenly spaced samples, despite the importance of temporal structure in sequences.Source: §1 · p. 11
• Fully connected networks treat observations independently and ignore local temporal structure, whereas convolutional networks recognize local patterns and are less suited to irregular, unequal-length sequences.Convolutional networks also tend to be faster and easier to train than recurrent networks.Source: §1 · pp. 11–12
• Recurrent networks handle sequences of arbitrary length but are harder to train and can lose information over time; LSTMs and GRUs were developed to help retain longer-term information.Source: §1 · p. 12

2 Frequency-domain characteristics of unevenly sampled time series

• Frequency-domain features, including periods and power spectra, are commonly used in time-series inference.Source: §2 · p. 12
• The standard DFT assumes uniform sampling, while uneven data may require interpolation or methods such as the Lomb-Scargle periodogram.The periodogram estimates frequency properties by least-squares fitting sinusoids.Source: §2 · p. 12
• The proposed neural network infers periodic behavior directly from irregularly sampled time series without constructing an explicit full power-spectrum estimate.Source: §2 · p. 12

3 Simulation study: sinusoidal data

• Simulated data comprise periodic functions with randomly selected frequency, amplitude, phase, and offset, sampled at uneven times and perturbed with white Gaussian noise (σ = 0.5).The training dataset contains 50,000 periodic functions and sampling time sequences.Source: §3 · pp. 12–13

3.1 Estimating period, phase, amplitude, offset

• Across architectures, multilayer networks achieve somewhat higher maximum accuracy than one-layer networks, while all recover periodic characteristics despite noise and irregular sampling; Lomb–Scargle performs slightly better in the period comparison.The Lomb–Scargle comparison is for this particular case.Source: §3.1 · pp. 14–15

3.2 Inferring periodic parameters from autoencoding features

• Increasing embedding size improves reconstruction accuracy up to a point, although longer training or a different learning rate might let a four-value embedding match larger ones.The reconstruction target is the original de-noised periodic function, not the raw measurements.Source: §3.2 · pp. 15–16
• A random forest can infer period, phase, amplitude, and offset from autoencoder features, showing that useful aggregate sequence properties are encoded in the learned representation.The reported inference accuracy depends on embedding size and other modeling choices, as well as the simulated-data distribution.Source: §3.2 · pp. 16–17

4.1 Validation accuracy

• Larger embeddings than for simulated sinusoidal data were needed, yet relatively parsimonious representations modeled light curves accurately; withheld-curve reconstruction was comparable to training reconstruction.Validation losses used curves withheld during training; after reconstruction performance was checked, the autoencoder was retrained on all available data.Source: §4.1 · p. 17
• Simulated irregular periodic inputs yielded encodings with frequency-domain and global information, while observed features varied nonlinearly with period and phase.The period and phase relationships were visualized for the eight-dimensional autoencoding features.Source: §4.1 · pp. 17, 19, Figure 9 · p. 18

4.2 Sequence length

• Constant-length subsequences of 200 points avoid padding or masking and empirically speed training; variable-length sequences reached roughly the same reconstruction quality but took significantly longer.The authors note that sufficiently large length differences may become problematic, suggesting length-grouped batches or separate models.Source: §4.2 · pp. 19, 21

4.3 Data augmentation using noise properties

• Validation accuracy rose from 72.6% to 78.1% with added samples for non-period-folded LINEAR, but fell from 97.1% to 96.7% for period-folded curves.The authors suggest period-folded curves were already reconstructed accurately, while raw curves were less well modeled; ASAS classifier accuracy changed negligibly.Source: §4.3 · p. 21

4.4 Direct supervised classification

• 98.6% average validation accuracy for ASAS and 96.7% for LINEAR were achieved by direct supervised classification on period-folded data and sampling times.This approach requires a large amount of labeled training data, whereas the autoencoder can use labeled or unlabeled data.Source: §4.4 · p. 22

4.5 Transfer learning

• Less than 1% reduction in each case was found when ASAS- or LINEAR-trained autoencoder features classified light curves from the other survey.The autoencoder and random-forest stages are decoupled, allowing unsupervised training data to come from a different source.Source: §4.5 · p. 22