Unsupervised Anomaly Detection in Low-Resolution Spectra: A Self-Supervised Autoencoder with Isolation-Forest Latent Scoring

1. Introduction

Supervised classification can only recover the classes it was trained on. For discovery — rare transients, blends, mis-calibrated sources, or genuinely new spectral types — the interesting objects are precisely those absent from any label set, so a classifier cannot surface them. Unsupervised anomaly detection takes the opposite stance: it models the empirical distribution of "typical" spectra and quantifies deviation from it, an approach that has repeatedly proven productive on spectroscopic surveys ^[4][3][7]. This is especially timely for SPHEREx, which measures a low-resolution spectrum ($0.75$–$5\,\mu$m, 102 channels) at every point on the sky and whose source catalogues are not yet released — untouched ground for a representation-learning / anomaly layer ^[1].

2. Data

The final sample is drawn from SDSS DR17 ^[5] SpecObj requiring zWarning=0, snMedian>5, sciencePrimary=1; a modular-hash ordering scatters the selection across plates and sub-surveys. Each spectrum is resampled by linear interpolation onto a common grid of 512 points uniform in $\log_{10}\lambda$ over 3850–9000 Å. The cached sample (data/spectra.npz) contains 4,990 spectra spanning $z\in[-0.002, 6.9]$:

3. Methods

Let a spectrum be a flux vector $x\in\mathbb{R}^{D}$ with $D=512$.

3.1 Preprocessing

To separate spectral shape from brightness, each spectrum is divided by its mean flux, $\tilde{x}=x/\bar{x}$; each wavelength bin is then standardised across the sample,

3.2 Self-supervised autoencoder

An autoencoder $f_\theta=g\circ h$ compresses each standardised spectrum to a latent code $z=h(x)\in\mathbb{R}^{d}$ with $d=16$ and reconstructs $\hat{x}=g(z)$, trained purely self-supervised (no labels) to minimise the mean-squared reconstruction loss

The encoder is $512\to256\to128\to16$ and the decoder its mirror, with ReLU activations; Adam ($\text{lr}=10^{-3}$, weight decay $10^{-5}$), 200 epochs, batch size 256, on the Apple-MPS backend (seconds of wall-clock). Final train / validation MSE: 0.127 / 0.196 (standardised units).

3.3 Anomaly scores

Reconstruction error. $e_i=\tfrac{1}{D}\lVert x_i-\hat{x}_i\rVert_2^2$ — large $e_i$ means the model, trained on the typical population, cannot represent this spectrum (an outlier in data space).

Isolation Forest in latent space ^[2]. 300 random trees are fit to $\{z_i\}$; anomalies are isolated in fewer splits, i.e. shorter expected path length. The score is

with $H$ the harmonic number; $s\to1$ indicates a strong anomaly.

Combined ranking. The two independent signals are converted to robust median/MAD $z$-scores and summed, $C_i=Z(e_i)+Z(s(z_i))$ with $Z(v)=(v-\mathrm{median}(v))/(1.4826\,\mathrm{MAD}(v))$. Using one detector in data space and one in latent space makes the ranking robust to the failure modes of either alone.

4. Results

Emergent class structure (unsupervised). Although no labels were used in training, a t-SNE ^[6] projection of the 16-D latent space cleanly separates stars, galaxies, and quasars into distinct regions — direct evidence that the autoencoder learned a physically meaningful representation. The flagged anomalies concentrate in the sparse, peripheral regions (the outskirts of the quasar locus and the galaxy–quasar transition), exactly where an anomaly detector should place them.

What the anomalies are. Of the 100 top-ranked anomalies, 68 are galaxies and 32 are quasars, with no ordinary stars; 96 of 100 carry an emission-line or broad-line subclass (STARBURST, STARFORMING, BROADLINE, AGN), versus 30.9% of the full sample — a $3.1\times$ enrichment. This is physically sensible: the bulk population is dominated by smooth absorption/continuum spectra, so the objects most unlike the bulk are those with towering [O III], H$\alpha$, [O II] or broad quasar lines.

4.1 Top-ranked anomalies

Full ranking of all 4,990 sources in outputs/anomaly_ranking.csv.

5. Caveats

• "Anomaly" means rare, not new. The top anomalies are recognisably extreme-emission-line galaxies and quasars — real, known types that are under-represented and spectrally distinctive. The method ranks the unusual; it does not certify novelty.
• Most anomalies in a real survey are artefacts (flux-calibration residuals, blends, sky-subtraction, edges). This is a triage / ranking tool; human vetting and active learning ^[4] are required to convert a ranked list into discoveries.
• Stand-in data. The specific anomalies are SDSS optical objects, not SPHEREx NIR sources. The results validate the method; applying it to SPHEREx requires the forced-spectrophotometry extraction step (§2).
• Normalisation dependence. The outlier set depends on the chosen normalisation; unit-mean + per-bin standardisation emphasises spectral shape.

6. Reproducibility

cd projects/p2-spherex-anomaly
python3 src/fetch_sdss.py            # query + download + resample -> data/spectra.npz
python3 src/anomaly_detect_local.py  # autoencoder + isolation forest -> figures + ranking

Deterministic (seeded); runs locally on Apple M2 / MPS.

References