A reliable order-statistics-based approximate nearest neighbor search algorithm

We propose a new algorithm for fast approximate nearest neighbor search based on the properties of ordered vectors. Data vectors are classified based on the index and sign of their largest components, thereby partitioning the space in a number of cones centered in the origin. The query is itself classified, and the search starts from the selected cone and proceeds to neighboring ones. Overall, the proposed algorithm corresponds to locality sensitive hashing in the space of directions, with hashing based on the order of components. Thanks to the statistical features emerging through ordering, it deals very well with the challenging case of unstructured data, and is a valuable building block for more complex techniques dealing with structured data. Experiments on both simulated and real-world data prove the proposed algorithm to provide a state-of-the-art performance

Efficient and Scalable Listing of Four-Vertex Subgraph

Identifying four-vertex subgraphs has long been recognized as a fundamental technique in bioinformatics and social networks. However, listing these structures is a challenging task, especially for graphs that do not fit in RAM. To address this problem, we build a set of algorithms, models, and implementations that can handle massive graphs on commodity hardware. Our technique achieves 4 – 5 orders of magnitude speedup compared to the best prior methods on graphs with billions of edges, with external-memory operation equally efficient

Pb-Hash: Partitioned b-bit Hashing

Many hashing algorithms including minwise hashing (MinHash), one permutation hashing (OPH), and consistent weighted sampling (CWS) generate integers of $B$ bits. With $k$ hashes for each data vector, the storage would be $B\times k$ bits; and when used for large-scale learning, the model size would be $2^B\times k$, which can be expensive. A standard strategy is to use only the lowest $b$ bits out of the $B$ bits and somewhat increase $k$, the number of hashes. In this study, we propose to re-use the hashes by partitioning the $B$ bits into $m$ chunks, e.g., $b\times m =B$. Correspondingly, the model size becomes $m\times 2^b \times k$, which can be substantially smaller than the original $2^B\times k$. Our theoretical analysis reveals that by partitioning the hash values into $m$ chunks, the accuracy would drop. In other words, using $m$ chunks of $B/m$ bits would not be as accurate as directly using $B$ bits. This is due to the correlation from re-using the same hash. On the other hand, our analysis also shows that the accuracy would not drop much for (e.g.,) $m=2\sim 4$. In some regions, Pb-Hash still works well even for $m$ much larger than 4. We expect Pb-Hash would be a good addition to the family of hashing methods/applications and benefit industrial practitioners. We verify the effectiveness of Pb-Hash in machine learning tasks, for linear SVM models as well as deep learning models. Since the hashed data are essentially categorical (ID) features, we follow the standard practice of using embedding tables for each hash. With Pb-Hash, we need to design an effective strategy to combine $m$ embeddings. Our study provides an empirical evaluation on four pooling schemes: concatenation, max pooling, mean pooling, and product pooling. There is no definite answer which pooling would be always better and we leave that for future study

Large-scale image collection cleansing, summarization and exploration

A perennially interesting topic in the research field of large scale image collection organization is how to effectively and efficiently conduct the tasks of image cleansing, summarization and exploration. The primary objective of such an image organization system is to enhance user exploration experience with redundancy removal and summarization operations on large-scale image collection. An ideal system is to discover and utilize the visual correlation among the images, to reduce the redundancy in large-scale image collection, to organize and visualize the structure of large-scale image collection, and to facilitate exploration and knowledge discovery. In this dissertation, a novel system is developed for exploiting and navigating large-scale image collection. Our system consists of the following key components: (a) junk image filtering by incorporating bilingual search results; (b) near duplicate image detection by using a coarse-to-fine framework; (c) concept network generation and visualization; (d) image collection summarization via dictionary learning for sparse representation; and (e) a multimedia practice of graffiti image retrieval and exploration. For junk image filtering, bilingual image search results, which are adopted for the same keyword-based query, are integrated to automatically identify the clusters for the junk images and the clusters for the relevant images. Within relevant image clusters, the results are further refined by removing the duplications under a coarse-to-fine structure. The duplicate pairs are detected with both global feature (partition based color histogram) and local feature (CPAM and SIFT Bag-of-Word model). The duplications are detected and removed from the data collection to facilitate further exploration and visual correlation analysis. After junk image filtering and duplication removal, the visual concepts are further organized and visualized by the proposed concept network. An automatic algorithm is developed to generate such visual concept network which characterizes the visual correlation between image concept pairs. Multiple kernels are combined and a kernel canonical correlation analysis algorithm is used to characterize the diverse visual similarity contexts between the image concepts. The FishEye visualization technique is implemented to facilitate the navigation of image concepts through our image concept network. To better assist the exploration of large scale data collection, we design an efficient summarization algorithm to extract representative examplars. For this collection summarization task, a sparse dictionary (a small set of the most representative images) is learned to represent all the images in the given set, e.g., such sparse dictionary is treated as the summary for the given image set. The simulated annealing algorithm is adopted to learn such sparse dictionary (image summary) by minimizing an explicit optimization function. In order to handle large scale image collection, we have evaluated both the accuracy performance of the proposed algorithms and their computation efficiency. For each of the above tasks, we have conducted experiments on multiple public available image collections, such as ImageNet, NUS-WIDE, LabelMe, etc. We have observed very promising results compared to existing frameworks. The computation performance is also satisfiable for large-scale image collection applications. The original intention to design such a large-scale image collection exploration and organization system is to better service the tasks of information retrieval and knowledge discovery. For this purpose, we utilize the proposed system to a graffiti retrieval and exploration application and receive positive feedback

Differentially Private One Permutation Hashing and Bin-wise Consistent Weighted Sampling

Minwise hashing (MinHash) is a standard algorithm widely used in the industry, for large-scale search and learning applications with the binary (0/1) Jaccard similarity. One common use of MinHash is for processing massive n-gram text representations so that practitioners do not have to materialize the original data (which would be prohibitive). Another popular use of MinHash is for building hash tables to enable sub-linear time approximate near neighbor (ANN) search. MinHash has also been used as a tool for building large-scale machine learning systems. The standard implementation of MinHash requires applying $K$ random permutations. In comparison, the method of one permutation hashing (OPH), is an efficient alternative of MinHash which splits the data vectors into $K$ bins and generates hash values within each bin. OPH is substantially more efficient and also more convenient to use. In this paper, we combine the differential privacy (DP) with OPH (as well as MinHash), to propose the DP-OPH framework with three variants: DP-OPH-fix, DP-OPH-re and DP-OPH-rand, depending on which densification strategy is adopted to deal with empty bins in OPH. A detailed roadmap to the algorithm design is presented along with the privacy analysis. An analytical comparison of our proposed DP-OPH methods with the DP minwise hashing (DP-MH) is provided to justify the advantage of DP-OPH. Experiments on similarity search confirm the merits of DP-OPH, and guide the choice of the proper variant in different practical scenarios. Our technique is also extended to bin-wise consistent weighted sampling (BCWS) to develop a new DP algorithm called DP-BCWS for non-binary data. Experiments on classification tasks demonstrate that DP-BCWS is able to achieve excellent utility at around $\epsilon = 5\sim 10$, where $\epsilon$ is the standard parameter in the language of $(\epsilon, \delta)$-DP