DeepCEE: Deep Learning for Galaxy Cluster Detection

• DeepCEE is a deep learning framework that identifies galaxy clusters directly from wide-field, three-band optical images without relying on photometric catalogues.
• The system employs a modular Faster R-CNN architecture, integrating Inception-v2 for feature extraction, a region proposal network, and a detection network with refined loss functions for precise localization.
• It demonstrates scalability to large surveys such as LSST and Euclid by achieving high precision and recall in cluster detection, enabling rapid, real-time catalog production for cosmological studies.

Deep-CEE (Deep Learning for Galaxy Cluster Extraction and Evaluation) is a deep learning framework designed for the identification and localization of galaxy clusters directly from wide-field color images, without reliance on photometric catalogues or simulated data. Conceived as a proof of concept, Deep-CEE operates on optical imaging from surveys such as SDSS, and is architected around state-of-the-art object detection methodologies. It represents a shift in astronomical cluster finding, leveraging publicly available cluster labels to maximize training data realism and enable generalization to new data domains. The system is explicitly intended for scalability to large surveys, including LSST and Euclid, with the goal of producing real-time cluster catalogues for studies of galaxy evolution and cosmology (Chan et al., 2019).

1. System Architecture

Deep-CEE employs a modular adaptation of the Faster-R-CNN object-detection framework, discriminating between "foreground" (cluster candidates) and "background" (all other content). The detection/classification pipeline consists of three jointly trained modules:

• Feature Network (FN): Utilizes Inception-v2, truncated at the Mixed_4e layer, pretrained on COCO. The FN takes 1000×1000×3 RGB inputs—prepared by stacking SDSS i, r, g bands mapped via a square-root stretch—and outputs a lower-resolution feature map. The configuration ensures a 16 px input stride aligns with one spatial position on the feature map.
• Region Proposal Network (RPN): Slides a 3×3 window across the FN feature map with a stride of 1. At each anchor point, K=12 bounding boxes (4 scales × 3 aspect ratios, size range 0.25×256 px to 2×256 px) are generated. The RPN applies (1) a 3×3 convolution+ReLU to extract shared features, (2) 1×1 convolutions to predict objectness scores ($p_i$) via softmax (foreground/background) and box-regression offsets ($t_i$) via smooth L1 loss. Anchors with $\text{IoU}\geq0.7$ with ground truth are positive, $\text{IoU}\leq0.3$ negative, and remaining are ignored; up to 128 of each per image are used in training. Proposals are filtered by Non-Maximum Suppression (NMS, threshold 0.7) to a maximum of 300 per image.
• Detection Network (DN): Surviving proposals are mapped back onto the feature map via ROI pooling, cropped/rescaled, and then processed by two parallel fully-connected heads: one for foreground/background classification, one for box refinement. In training, up to 16 positive (IoU$\geq$0.5) and 48 negative proposals are used per image, with softmax and smooth L1 losses, followed by NMS (threshold 0.6) to yield up to 100 final detections.

2. Loss Functions and Probabilistic Inference

The Deep-CEE framework adopts a probabilistic treatment of localization and classification:

• In every module, the predicted score $p_i$ is interpreted as the posterior probability that box $i$ contains a cluster: $P(\text{cluster}|\,\text{box}_i)$.
• The RPN employs a binary cross-entropy (objectness) loss:

$$L_{\text{cls}}(p_i,p_i^*) = -p_i^*\log{p_i} - (1-p_i^*)\log{(1-p_i)},$$

where $p_i^*\in\{0,1\}$ is the ground-truth label.

• Localization is penalized using the smooth L1 loss:

$t_i$0

where $t_i$1 are the four box parameters.

• Joint optimization employs the combined multi-task loss:

$t_i$2

with $t_i$3, $t_i$4.

• During inference, softmax scores are directly interpreted as posterior cluster probabilities, and detections are thresholded by a user-specified $t_i$5 (e.g. $t_i$6) for candidate selection.

3. Data Selection and Preprocessing

Training and evaluation are carried out using real data from SDSS:

• Catalogue: The Wen et al. (2012) Friends-of-Friends SDSS DR8 cluster catalogue provides the labelling reference, focusing on 497 Abell clusters with $t_i$7 and at least 20 members within $t_i$8.
• Image Preparation: For each cluster, a 2000×2000 px i/r/g triplet is extracted, registered, and stacked; a square-root stretch equalizes galaxy and sky contrast. The images are then downsampled to 1000×1000 px for model input.
• Augmentation: To mitigate positional bias, random uniform offsets (up to $t_i$9270 arcsec, $\text{IoU}\geq0.7$0270 kpc at $\text{IoU}\geq0.7$1) are applied in RA and Dec before cropping, each image is thus translated 4 times, and 50% of images undergo random horizontal flips. This yields 1,988 examples.
• Split: 10% (204 images) are held out for testing, while the remaining 1,784 form the training set.

4. Training Regimen and Optimization

• Joint Training: RPN and DN are jointly optimized by stochastic gradient descent with momentum 0.9, fixed learning rate $\text{IoU}\geq0.7$2, and gradient clipping at 10.
• Batch Handling: Each mini-batch consists of one image (batch size 1).
• Initialization: RPN convolutional layers are initialized from a normal distribution $\text{IoU}\geq0.7$3; DN fully-connected layers use variance-scaled uniform initialization (Xavier).
• Training Duration: Up to 25,000 steps are run, with convergence reported at approximately 7,458 steps.

5. Evaluation Metrics and Empirical Performance

Performance is assessed on the held-out SDSS test set and external cluster samples:

• Detection Criteria: A true positive (TP) is recorded if the predicted box (confidence $\text{IoU}\geq0.7$4) is centered within 100 kpc of the ground truth Brightest Cluster Galaxy (BCG). False positives (FP) occur when detections are outside this radius; false negatives (FN) are missed detections.
• Statistics:
  • Precision: TP/(TP+FP)
  • Recall: TP/(TP+FN)
  • F1: $\text{IoU}\geq0.7$5
• SDSS Test Set Results: Scanning $\text{IoU}\geq0.7$6, maximum F1 is at $\text{IoU}\geq0.7$7: Precision = 0.696, Recall = 0.809.
• Localization Accuracy: Standard error of estimated center position, $\text{IoU}\geq0.7$8, is 17.4 kpc (95% CI $\text{IoU}\geq0.7$9 kpc) for true positives.
• Generalization: On 31 unseen redMaPPer clusters ($\text{IoU}\leq0.3$0), optimal $\text{IoU}\leq0.3$1 yields Precision=0.77, Recall=0.87, $\text{IoU}\leq0.3$2 kpc. No significant bias was detected in predicted versus true redshift, BCG $\text{IoU}\leq0.3$3-band magnitude, or cluster richness (Kolmogorov–Smirnov test $\text{IoU}\leq0.3$4 at $\text{IoU}\leq0.3$5).

6. Scalability, Applications, and Limitations

Deep-CEE is designed for immediate deployment on any optical survey featuring three-band imaging. Ingest capabilities extend to LSST’s coadded $\text{IoU}\leq0.3$6 and analogous channels; the pipeline scales to 1000×1000 px inputs and supports multi-scale tiling for higher-resolution operation. Integration with X-ray or SZ imaging is feasible by extending the FN for additional channels.

Applications include rapid galaxy cluster identification, construction of candidate catalogs for multi-wavelength confirmation, and advanced cosmological studies in future large-area surveys. Reported limitations include dependence on existing catalogue labels (Wen+12 catalogue false-detection rate $\text{IoU}\leq0.3$76%), fixed preprocessing protocols, and the computational burden of hyperparameter optimization.

Planned enhancements encompass further image augmentation (rotations, vertical flips) and k-fold cross-validation, joint regression of cluster redshift and richness, and the use of lighter-weight backbone architectures (e.g., MobileNet) for increased throughput.

7. Significance and Future Prospects

Deep-CEE establishes a framework for galaxy cluster detection that combines established machine learning techniques (Faster-R-CNN, Inception-v2, transfer learning) with the demands of astronomical imaging and catalog construction. The system demonstrates high completeness and purity for cluster localization and classification tasks, with empirical evidence of generalization across different cluster catalogs. Given its scalability and flexibility, Deep-CEE offers a template for automated cluster finding as astronomical surveys enter the petabyte-scale data regime (Chan et al., 2019). A plausible implication is that such deep-learning-based science pipelines will become central to next-generation survey analysis, especially as their capacity for high-throughput, multi-wavelength candidate selection and cross-validation with other detection modalities is further enhanced.