ResNet-50 & Faiss Clustering

• ResNet-50 and Faiss-based clustering is a framework that extracts 2048-D image features and applies efficient ANN search and clustering algorithms.
• It integrates k-means, hierarchical clustering, and conditional pairwise clustering (ConPaC) to balance trade-offs between speed, accuracy, and memory use.
• The pipeline supports applications in face clustering, fine-grained retrieval, and vector database engineering using GPU acceleration and optimized indices.

ResNet-50 and Faiss-based Clustering refers to a class of image representation and large-scale vector clustering workflows that leverage deep convolutional neural network embeddings and highly optimized approximate nearest neighbor (ANN) and clustering algorithms. This integration enables scalable clustering, retrieval, and indexing for millions of high-dimensional image descriptors, with pronounced applications in face clustering, fine-grained retrieval, and vector database engineering. The technical landscape is characterized by standardized ResNet-50 feature pipelines, k-means and hierarchical clustering implementations within Faiss, and precise evaluation of speed, accuracy, memory, and scalability trade-offs.

1. ResNet-50 Feature Extraction and Fine-Tuning

ResNet-50, a 50-layer CNN architecture, is extensively used for extracting discriminative, fixed-length (2048-dimensional) feature vectors from images. In face clustering (Shi et al., 2017), a modified ResNet-50 replaces the 1000-way classifier with a 2048-dim bottleneck, followed by ReLU, and is trained via softmax cross-entropy on a combined dataset of CASIA-WebFace and VGG-Face (~2.1M images, 11,326 subjects) using SGD (lr=0.1, momentum=0.9, batch=256, 37 epochs). At inference, 10-crop features (five crops and flips) are averaged, and ℓ₂-normalization is applied ($\|x\|_2 = 1$).

For domain-specific retrieval and clustering (Rahman et al., 2 Dec 2024), the pipeline involves fine-tuning ResNet-50 on private datasets (e.g., 44,446 fashion images, consolidated into 32 balanced classes, with a 90/10/10 split). Adam optimizer ($\beta_1 = 0.9$, $\beta_2 = 0.999$, $\epsilon = 1e{-8}$), cross-entropy loss, learning rate $\alpha_0 = 1e{-3}$, ReduceLROnPlateau scheduling (factor=0.1, patience=3), gradient clipping (max norm=1.0), and early stopping complete the protocol. Final embeddings (extracted from the penultimate layer) are used as raw 2048-D vectors, typically L2-normalized for inner-product similarity metrics.

2. Faiss Clustering Algorithms and Index Structures

Faiss (Douze et al., 16 Jan 2024) is a vector similarity and ANN search library optimized for billion-scale vector collections and GPU acceleration. Clustering ResNet-50 embeddings with Faiss is founded on Lloyd’s k-means and hierarchical k-means algorithms:

• Flat k-means: Minimizes within-cluster sum of squared L2 distances:

$$\min_{C_1,\dots,C_k}\;\sum_{i=1}^n\;\min_{1\le j\le k}\;\|x_i - C_j\|_2^2$$

Assignment: $j_i = \arg\min_j \|x_i - C_j\|^2$; centroids updated as $$C_j \leftarrow \frac{1}{|S_j|}\sum_{i\,:\,j_i=j}x_i$$; convergence via centroid shift thresholds or fixed iterations.

• Hierarchical k-means (multi-level): For large $k$ or $n$, employs a two-level coarse-to-fine clustering (often in IVF): coarse centroids $\{D_\ell\}$, followed by clustering residuals $x_i - D_\ell$ into fine centroids $C_{\ell, j}$.

Cluster assignment, centroid updates, and objective minimization are accelerated via batched GEMM (BLAS), multi-threading (OpenMP) on CPU, and parallel CUDA kernels on GPU. Centroid storage uses contiguous float32 arrays; data can be streamed and shuffled for memory and convergence control. GPU support is exposed through faiss.Clustering.use_gpu=True.

3. Computational Complexity and Scalability

Resource requirements for k-means on $n$ 2048-D embeddings scale as follows (Douze et al., 16 Jan 2024):

Operation	Complexity per Iteration	Memory Footprint
Assignment	$O(nkd)$ BLAS	$n\times d\times 4$ bytes (raw embeddings); $1M \times 2048 \times 4B \approx 8.19$ GB
Update	$O(nd)$ accumulation	$k\times d\times 4$ bytes (centroids) minimal
Buffers	—	labels: $n\times 4$ bytes; scratch: $k \times 4$ bytes

For $n\leq2$ million and $k=10,000$, multi-core CPU (16 threads) completes in tens of minutes; A100 GPU reduces to minutes. Benchmarks: 1M vectors, 2048-D, $k=5000$, results in estimated CPU time (16 h) and GPU time (2 h), practically reduced to 30–60 min per 1M×2k run (Douze et al., 16 Jan 2024).

4. Faiss Index Types and Clustering Techniques

Faiss provides several ANN and clustering indices, each with quantization, speed and resource characteristics (Rahman et al., 2 Dec 2024):

Index Type	Precision	Memory (N=40K, D=2048)	Query Time (CPU)
Exact Flat-L2	98.4%	1.67 MB	1.7 s / query
PQ	98.4%	0.24 MB	240 ms / query
IVF-PQ	98.0%	<0.24 MB	358 ms / query
HNSW	98.5%	≈12 MB	5.2 s / query

• Product Quantization (PQ): Divides vectors into $m$ subspaces, runs k-means ($k=2^b$) per subspace. Typical parameters: $m=16$ subquantizers, $b=8$ bits.
• IVF-PQ: Clusters full space into $nlist$ coarse clusters (e.g., $nlist=100$), within each, stores PQ codes.
• IVFSQ: Scalar quantization, dimension-wise.
• HNSW: Graph-based, multi-layer proximity (M=32 neighbors, efConstruction=40).
• LSH: Hash-bucket projections.

Selection and tuning depend on trade-offs between memory, speed, and accuracy. For 2048-D ResNet-50 embeddings, $m=16$, $b=8$ strikes high precision and compact memory footprint.

5. k-NN Accelerated Conditional Pairwise Clustering (ConPaC)

Conditional Pairwise Clustering (ConPaC) (Shi et al., 2017) formulates clustering as inference over an $N\times N$ binary adjacency matrix $Y$ specifying cluster membership, leveraging deep features and pairwise similarity:

• Similarity: Cosine similarity $s(x_i,x_j) = x_i^\top x_j$ (with $\|x\|_2=1$), thresholded at $\tau=0.7$ into unary potentials.
• CRF Model: Posterior $$p(Y|X) \propto \prod_{i<j} \psi_u(Y_{ij}) \prod_{i<j<k} \psi_t(Y_{ij}, Y_{ik}, Y_{jk})$$; triplet potentials force clustering transitivity.
• Inference: Loopy Belief Propagation (LBP), min-sum over edge messages; post-processing with transitive closure.
• Complexity: Full graph $O(T N^3)$; linear in $N$ for k-NN (O($T N k^2$)).

Faiss enables constructing the k-NN graph efficiently: IVF4096+PQ64 indices, $k=200$ neighbors per point, millions/sec throughput on GPU. Experimental results show near-parity in F-measure (0.960 k-NN vs. 0.965 full graph) on LFW, with runtime increases (1 min k-NN vs. 39 s full graph) and substantial scalability to millions.

6. Performance Evaluation and Trade-offs

Clustering quality and resource consumption are evaluated via inertia (sum of squared distances), silhouette score, F-measure, and memory/latency profiling (Douze et al., 16 Jan 2024, Rahman et al., 2 Dec 2024):

• Inertia: Available as clustering.obj[-1] in Faiss; lower values indicate tighter clusters.
• Silhouette Score: $O(n^2)$ naïvely; practical via 100K subsampling.
• Retrieval Metrics: Precision, recall, F₁-score (e.g., PQ and Flat both achieve 98.4% precision at k=5).
• Empirical Scaling: Flat-L2 yields highest accuracy but is memory/CPU intensive; PQ and IVF-PQ approach Flat performance at vastly reduced memory with moderate latency; HNSW attains highest recall at increased memory and build time.

Recommendations:

• Use $k\sim\sqrt{n}$ for clusters.
• PQ with $m=16, b=8$ for compact yet precise indices.
• Stream batches ≤100K points if RAM-constrained.
• Tune $nprobe$ in IVF-PQ ($10$–$50$) for speed/recall balance.

7. Practical Pipeline and Applications

The established pipeline (Douze et al., 16 Jan 2024, Rahman et al., 2 Dec 2024) is suitable for production environments and offline/interactive use:

1. Fine-tune ResNet-50 using 90/10/10 train/val/test splits, Adam optimizer, cross-entropy, and early stopping.
2. Extract and normalize 2048-D embeddings.
3. Build Faiss index: Flat-L2 (exact), PQ (memory/accuracy), or IVF-PQ (speed/memory/accuracy trade-off).
4. Optionally, perform clustering (k-means, hierarchical, ConPaC) using Faiss for efficient centroid search and update.
5. Assign cluster labels via nearest-centroid ANN search.
6. Evaluate clustering or retrieval with inertia, silhouette, F-measure, Recall@k; adjust parameters to optimize along the memory-accuracy-latency frontier.

In large-scale face clustering, Faiss-accelerated k-NN ConPaC outperforms k-means, spectral clustering, and rank-order algorithms with nuanced handling of semantic constraints. In image retrieval, PQ and IVF-PQ offer operational precision with significant gains in resource efficiency, validated across contemporary benchmarks. The confluence of ResNet-50 and Faiss thus anchors scalable, high-precision clustering regimes within academic and industrial pipelines (Douze et al., 16 Jan 2024, Shi et al., 2017, Rahman et al., 2 Dec 2024).