2014 Theses Doctoral

# Large Scale Nearest Neighbor Search - Theories, Algorithms, and Applications

We are witnessing a data explosion era, in which huge data sets of billions or more samples represented by high-dimensional feature vectors can be easily found on the Web, enterprise data centers, surveillance sensor systems, and so on. On these large scale data sets, nearest neighbor search is fundamental for lots of applications including content based search/retrieval, recommendation, clustering, graph and social network research, as well as many other machine learning and data mining problems.

Exhaustive search is the simplest and most straightforward way for nearest neighbor search, but it can not scale up to huge data set at the sizes as mentioned above. To make large scale nearest neighbor search practical, we need the online search step to be sublinear in terms of the database size, which means offline indexing is necessary. Moreover, to achieve sublinear search time, we usually need to make some sacrifice on the search accuracy, and hence we can often only obtain approximate nearest neighbor instead of exact nearest neighbor. In other words, by large scale nearest neighbor search, we aim at approximate nearest neighbor search methods with sublinear online search time via offline indexing.

To some extent, indexing a vector dataset for (sublinear time) approximate search can be achieved by partitioning the feature space to different regions, and mapping each point to its closet regions. There are different kinds of partition structures, for example, tree based partition, hashing based partition, clustering/quantization based partition, etc. From the viewpoint of how the data partition function is generated, the partition methods can be grouped into two main categories: 1. data independent (random) partition such as locality sensitive hashing, randomized trees/forests methods, etc.; 2. data dependent (optimized) partition, such as compact hashing, quantization based indexing methods, and some tree based methods like kd-tree, pca tree, etc.

With the offline indexing/partitioning, online approximate nearest neighbor search usually consists of three steps: locate the query region that the query point falls in, obtain candidates which are the database points in the regions near the query region, and rerank/return candidates. For large scale nearest neighbor search, the key question is: how to design the optimal offline indexing, such that the online search performance is the best, or more specifically, the online search can be as fast as possible, while meeting a required accuracy?

In this thesis, we have studied theories, algorithms, systems and applications for (approximate) nearest neighbor search on large scale data sets, for both indexing with random partition and indexing with learning based partition.

Our specific main contributions are:

1. We unify various nearest neighbor search methods into the data partition framework, and provide a general formulation of optimal data partition, which supports fastest search speed while satisfying a required search accuracy. The formulation is general, and can be used to explain most existing (sublinear) large scale approximate nearest neighbor search methods.

2. For indexing with data-independent partitions, we have developed theories on their lower and upper bounds of time and space complexity, based on the optimal data partition formulation. The bounds are applicable for a general group of methods called Nearest Neighbor Preferred Hashing and Nearest Neighbor Preferred Partition, including, locality sensitive hashing, random forest, and many other random hashing methods, etc. Moreover, we also extend the theory to study how to choose the parameters for indexing methods with random partitions.

3. For indexing with data-dependent partitions, I have applied the same formulation to develop a joint optimization approach with two important criteria: nearest neighbor preserving and region size balancing. we have applied the joint optimization to different partition structures such as hashing and clustering, and achieved several new nearest neighbor search methods, outperforming (or at least comparable) to state-of-the-art solutions for large scale nearest neighbor search.

4. we have further studied fundamental problems for nearest neighbor search beyond search methods, for example, what is the difficulty of nearest neighbor search on a given data set (independent of search methods)? What data properties affect the difficulty and how? How will the theoretical analysis and algorithm design of large scale nearest neighbor search problem be affected by the data set difficulty?

5. Finally, we have applied our nearest neighbor search methods for practical applications. We focus on the development of large visual search engines using new indexing methods developed in this thesis. The techniques can be applied to other domains with data-intensive applications, and moreover, be extended to other applications beyond visual search engine, such as large scale machine learning, data mining, and social network analysis, etc.

## Subjects

## Files

- He_columbia_0054D_11723.pdf application/pdf 8.8 MB Download File

## More About This Work

- Academic Units
- Electrical Engineering
- Thesis Advisors
- Chang, Shih-Fu
- Degree
- Ph.D., Columbia University
- Published Here
- January 6, 2014