ADS: Approximate Densest Subgraph for Novel Image Discovery

TL;DR

The paper tackles the problem of discovering visually novel images in large repositories without requiring training data. It models a collection as a perceptual distance-weighted complete graph and relaxes the NP-hard $K$-densest subgraph problem into a sparse continuous objective $\mathbf{s}^T D \mathbf{s}$ solved by SGD with Monte Carlo gradient estimates and sparsity clipping, avoiding full distance matrix storage. The approach, ADS, is training-free and scalable, demonstrated to be faster and more memory-efficient than state-of-the-art methods while accurately identifying novel images on synthetic data and the Tiny-ImageNet dataset. This yields a practical on-device capability for real-time novelty mining in large image collections, with potential for broad adoption in content management and retrieval tasks.

Abstract

The volume of image repositories continues to grow. Despite the availability of content-based addressing, we still lack a lightweight tool that allows us to discover images of distinct characteristics from a large collection. In this paper, we propose a fast and training-free algorithm for novel image discovery. The key of our algorithm is formulating a collection of images as a perceptual distance-weighted graph, within which our task is to locate the K-densest subgraph that corresponds to a subset of the most unique images. While solving this problem is not just NP-hard but also requires a full computation of the potentially huge distance matrix, we propose to relax it into a K-sparse eigenvector problem that we can efficiently solve using stochastic gradient descent (SGD) without explicitly computing the distance matrix. We compare our algorithm against state-of-the-arts on both synthetic and real datasets, showing that it is considerably faster to run with a smaller memory footprint while able to mine novel images more accurately.

Figures (4)

• Figure 1: A 2-dimensional synthetic dataset. The dataset contains 100 uniformly generated 2D points with a few of them perturbed to become anomalies. The colour of each data point is from cold to warm indicating the corresponding value of the sparse eigenvector computed by our algorithm (\ref{['alg:ads']}). The sparsity parameter $K$ is set to 9 (the exact number of anomaly points). The epoch size $E$ is displayed under each sub figure from (a) to (h). The remaining parameters are set to their default values.
• Figure 2: A 50-dimensional synthetic dataset. This dataset has 1,000 points generated from a mixture of two 50-dimensional Gaussian distributions (we only plot the first two features for visualization). The colour of each data point is from cold to warm indicating the corresponding value of the sparse eigenvector computed by our algorithm (\ref{['alg:ads']}). The sparsity parameter $K$ is set to 120 (the exact number of anomaly points). The epoch size $E$ is displayed under each sub figure from (a) to (h). The remaining parameters are set to their default values.
• Figure 3: Tiny-ImageNet train set (500 images from the class Egyptian cat-n02124075 and 1 randomly chosen image from each of the remaining 119 classes) results. (a) shows the accuracy of our computed sparse eigenvector used for differentiating normal and novel images with respect to each value of $K$ - an image is classified to be novel if its computed weight is non-zero. (b) shows the weight of each image along with its t-SNE embeddings derived from the MobileNet-V2 extracted 1,000-dimensional features when $K$ is set to 119 as the ground-truth number of anomalies.
• Figure 4: Tiny-ImageNet test set (10,000 images) results. (a) and (b) visualize our computed novelty weight for each image along with its PCA and t-SNE embeddings derived from the MobileNet-V2 extracted 1,000-dimensional features. (c)-(h) show the 6 images with the highest weight (displayed under each corresponding sub figure) found by our algorithm with the sparsity $K=100$.