A variable scale approach for neighbor search in point cloud data

In this paper, the concepts of differential geometry traditionally applied to the segmentation of range maps is revisited in the context of implicit surface representation of unorganized point clouds. The paper shows that it is possible to combine covariance-based differential geometry and implicit surface representation methods to perform the segmentation of an unorganized point cloud (and not just a range map) into seven surface types. The acquisition of the point cloud data is achieved with handheld scanners used in metrology applications. The advantages of combining covariance-based differential geometry and implicit surface representation are that the segmentation does not require surface fitting nor does it require that all points be processed, thus reducing computational complexity. The segmentation approach is validated on synthetic data as well as point clouds borrowed from common datasets. Scans obtained from commercial metrologic handheld 3D sensors are also used for validation. The paper first presents the workflow commonly used for 3D scanning using handheld 3D scanners in the context of metrology. This is followed by a discussion on the different methods that are used for surface representation including the vector field, the implicit representation method exploited in this paper. Basic concepts of classical differential geometry for surface segmentation are presented. This is followed by the presentation of covariance-based differential geometry. The concepts of handheld 3D scanning, covariance-based differential geometry and implicit surface representation are then combined to achieve efficient segmentation of a point cloud into seven different surface types. Experimental results obtained on synthetic 3D data as well as real data demonstrate the segmentation approach.

K-d tree (k-dimensional tree) is a space partitioning data structure for organizing points in a k-dimensional space. K-d tree, or Multidimensional Binary Search Tree is a useful data structure for several applications such as searches involving a multidimensional search key (e.g., Range Search and Nearest Neighbour Search). K-d trees are a special case of binary space partitioning trees.KNN Search is a searching algorithm with complexity O(N log N) {N= no. of data points}. This search algorithm is relatively better than brute force search {Complexity= O(n*k); where k=No. of neighbours searched, N=No. of Data Points in Kd tree} for dimensions N>>2D {N=No. of Points, D=Dimensionality of Tree}.Furthermore, Parallel KNN Search is much more efficient and performs better than KNN Search, as it harnesses parallel processing capabilities of computers and thus, results in better search time.This paper tests the time performance of KNN Search and Parallel KNN Search and compares them by plotting it on a 3D graph. A more comprehensive comparison is done by use of 2D graphs for each dimension(from 2 to 20).

GPU 기반 병렬처리에서 대규모 데이터의 인접 정보 검색(nearest neighbor search)에서 Morton code의 역할이 점점 더 중요하게 부각되고 있으며 그 응용 사례도 점차 증가하고 있다. 본 논문에서는 Tero Karras가 제안한 float 형 변수에 기반한 <TEX>$[0,1</TEX><TEX>]</TEX><TEX>^3$</TEX> 공간 내의 3차원 기하 정보를 32비트 unsigned int형 Morton code로 변경하는 기존의 방법을 논의하고 그 기하학적인 의미를 분석함으로써, 보다 높은 해상도를 구현할 수 있는 64비트 unsigned long long형의 Morton code 변환 알고리듬을 제안한다. 제안하는 알고리듬은 GPU에서 구현되었을 때 CPU에서 실행하는 것보다 약 1000배 수준의 성능 향상을 달성한다. Morton codes play important roles in many parallel GPU applications for the nearest neighbor (NN) search in huge data and queries with its applications growing. This paper discusses and analyzes the meaning of Tero Karras's 32-bit 'unsigned int' Morton code algorithm for three-dimensional spatial information in <TEX>$[0,1</TEX><TEX>]</TEX><TEX>^3$</TEX> and its geometric implications. Based on this, this paper proposes 64-bit 'unsigned long long' version of Morton code and compares the results in both CPU vs. GPU and 32-bit vs. 64-bit versions. The proposed GPU algorithm runs around 1000 times faster than the CPU version.

Nearest neighbor search is a fundamental problem in computer vision and machine learning. The straightforward solution, linear scan, is both computationally and memory intensive in large scale high-dimensional cases, hence is not preferable in practice. Therefore, there have been a lot of interests in algorithms that perform approximate nearest neighbor (ANN) search. In this paper, we propose a novel addition-based vector quantization algorithm, Asymmetric Mapping Quantization (AMQ), to efficiently conduct ANN search. Unlike existing addition-based quantization methods that suffer from handling the problem caused by the norm of database vector, we map the query vector and database vector using different mapping functions to transform the computation of L-2 distance to inner product similarity, thus do not need to evaluate the norm of database vector. Moreover, we further propose Distributed Asymmetric Mapping Quantization (DAMQ) to enable AMQ to work on very large dataset by distributed learning. Extensive experiments on approximate nearest neighbor search and image retrieval validate the merits of the proposed AMQ and DAMQ.

Broadcasting data with an index is an effective way to disseminate public information to a large clients. For a server, using multiple channels to provide services (e.g., location-based services) makes the broadcast cycle shorter than using one channel. Among location-based services, the k nearest neighbors (k-NN) search is an important one and finds the fc closest objects to a query point in a multi-dimensional space. This paper considers k nearest neighbors search on a broadcast R-tree in a multi-channel environment. We assume that a mobile client can only tune into a specified channel at one time instance. We study how a server generates the broadcast schedules on multiple channels and explore how a client executes the k-NN search on the broadcast. Different broadcast schedules with the client k-NN search processing makes different k-NN search protocols. The objectives of the protocols is to minimize the latency (i.e., the time elapsed between issuing and termination of the query), tuning time (i.e., the amount of time spent on listening to the channel), and the memory usage for k-NN search processing. Last, we present our experiments and the experiment results validate that our mechanisms achieve the objectives.

Spatial interpolations are commonly used in geometric modeling for life science applications. In large-scale spatial interpolations, it is always needed to find a local set of data points for each interpolated point using the k Nearest Neighbor (kNN) search procedure. To improve the computational efficiency of kNN search, spatial decomposition structures such as grids and trees are employed to fastly locate the nearest neighbors. Among those spatial decomposition structures, the uniform grid is the simplest one, and the size of the grid cell could strongly affect the efficiency of kNN search. In this paper, we evaluate the effect of the size of uniform grid cell on the efficiency of kNN search. Our objective is to find the relatively optimal size of grid cell by considering the distribution of scattered points (i.e., the data points and the interpolated points). We employ the Standard Deviation of points’ coordinates to measure the spatial distribution of scattered points. For the irregularly distributed scattered points, we perform several series of kNN search procedures in two dimensions. Benchmark results indicate that: in two dimensions, with the increase of the Standard Deviation of points’ coordinates, the relatively optimal size of the grid cell decreases and eventually converges. The relationships between the Standard Deviation of scattered points’ coordinates and the relatively optimal size of grid cell are also fitted. The fitted relationships could be applied to determine the relatively optimal grid cell in kNN search, and further, improve the computational efficiency of spatial interpolations.

Here we report PPB2 as a target prediction tool assigning targets to a query molecule based on ChEMBL data. PPB2 computes ligand similarities using molecular fingerprints encoding composition (MQN), molecular shape and pharmacophores (Xfp), and substructures (ECfp4) and features an unprecedented combination of nearest neighbor (NN) searches and Naı̈ve Bayes (NB) machine learning, together with simple NN searches, NB and Deep Neural Network (DNN) machine learning models as further options. Although NN(ECfp4) gives the best results in terms of recall in a 10-fold cross-validation study, combining NN searches with NB machine learning provides superior precision statistics, as well as better results in a case study predicting off-targets of a recently reported TRPV6 calcium channel inhibitor, illustrating the value of this combined approach. PPB2 is available to assess possible off-targets of small molecule drug-like compounds by public access at http://gdb.unibe.ch .

Nearest Neighbor search is one of the simplest and most intuitive ideas in data mining. Due to it's simplicity and diverse utility, Nearest Neighbor search is often found to be the workhorse of a variety of data mining, machine learning, and computer vision algorithms. For very high dimensional data, the naive linear search tends to be optimal. This is due to the so called curse of dimensionality in database search. To accelerate the search time, may researchers have turned to the power and efficiency of GPGPU computing; mainly for computing the data intensive distance metrics. Though promising speedups are achieved through this method, it fails to capitalize on many of the recent advances in algorithms for bounded error approximate nearest neighbor searches. Approximate nearest neighbor methods give satisfactory results, especially in very large and possibly redundant datasets, while boasting sub-linear search complexities. In this paper we present a c-approximate r-nearest neighbor search algorithm for CUDA using Locality Sensitive Hash with Nearest Neighbor search (LSH-NN). We implement this system in CUDA and test it on real world image SIFT vector data. Our tests show that we are able to achieve significant speedup over the serial version, with good approximations on scalability, while achieving the near-optimal search complexity of LSH-NN.

Nearest neighbor (NN) searches represent an important class of queries in geographic information systems (GIS). Most nearest neighbor algorithms rely on static distance information to compute NN queries (e.g., Euclidean distance or spatial network distance). However, the final goal of a user when performing an NN search is often to travel to one of the points of the search result. In this case, finding the nearest neighbors in terms of travel time is more important than the actual distance. In the existing NN algorithms dynamic real-time events (e.g., traffic congestions, detours, etc.) are usually not considered and hence the pre-computed nearest neighbor objects may not accurately reflect the shortest travel time. In this paper we propose a novel travel time network that integrates both spatial networks and real-time traffic event information. Based on this foundation of the travel time network, we develop a local-based greedy nearest neighbor algorithm and a global-based adaptive nearest neighbor algorithm that both utilize real-time traffic information to provide adaptive nearest neighbor search results. We have performed a theoretical analysis and simulations to verify our methods. The results indicate that our algorithms remarkably reduce the travel time compared with previous nearest neighbor solutions.

The Iterative Closest Point (ICP) algorithm is one of the most popular methods for geometric alignment of 3-dimensional data points. We focus on how to make it faster for 3D range scanner in intelligent vehicle. The ICP algorithm mainly consists of two parts: nearest neighbor search and estimation of transformation between two data sets. The former is the most time consuming process. Many variants of the k-d trees have been introduced to accelerate the search. This paper presents a remarkably efficient search procedure, exploiting two concepts of approximate nearest neighbor and local search. Consequently, the proposed algorithm is about 24 times faster than the standard k-d tree.

Nearest neighbor (NN) search computations are at the core of many applications such as few-shot learning, classification, and hyperdimensional computing. As such, efficient hardware support for NN search is highly desired. In-memory computing using emerging devices offers attractive solutions for NN search. Solutions based on ternary content-addressable memories (TCAMs) offer high energy and latency improvements for NN search at the expense of accuracy. In this work, we propose a novel distance function that can be natively evaluated with multi-bit content-addressable memories (MCAMs) based on ferroelectric FETs (FeFETs) to perform a single-step, in-memory NN search. We evaluate the efficacy of FeFET MCAMs in the context of few-shot learning applications with different datasets. As an example, we achieve a 78.54% accuracy for a 5-way, 5-shot classification task for the mini-ImageNet dataset (only 1.5% lower than software-based implementations) when using a 3-bit MCAM for NN search. We consider the effects of FeFET threshold voltage variations on the application accuracy and analyze the area and search energy requirements of FeFET MCAMs for accurate operations. Our results indicate that MCAMs require 2× lower area and search energy than TCAMs to achieve the same accuracy. Furthermore, we experimentally demonstrate a 2-bit implementation of FeFET MCAM using AND arrays from GLOBALFOUNDRIES to further validate the design concept.

Currently, Nearest-Neighbor approaches (NN) have been widely applied to real world image data mining. These approaches have the following three disadvantages: (i) the performance is inferior on small datasets; (ii) the performance of approximated nearest neighbor search will degrade for data with high dimensions; (iii) they are heavily dependent on the chosen feature and distance measure. To overcome these intrinsic weaknesses, we propose a novel Nearest-Neighbor method, which improves the original NN approaches from three aspects. Firstly, we propose a novel neighborhood similarity measure, where the similarity between test images and labeled images in the database is calculated jointly by the original image-to-image similarity and the average similarity of their neighboring unlabeled data. Secondly, we adopt the kernelized locality sensitive hashing to effectively conduct the nearest neighbor search for high dimensional data. Finally, to enhance the robustness of the method on different genres of images, we propose to fuse the discrimination power of different features by considering all the retrieved nearest neighbors via hashing systems using different features/kernels. Experimental result shows the advantage over traditional Nearest-Neighbor methods using the labeled data only. Even when the ratio of labeled data is very small, our method could also achieve remarkable results, thanks to the help of unlabeled data and multiple features.

The great advances in deep learning enable human beings to extract the semantic information in ubiquitous unstructured data into high-dimensional vectors, leading to an urgent priority of managing vector data. Nearest neighbor (NN) query is a pivotal question in vector data management. Unfortunately, the NN query has been proved to be intrinsically hard. Researchers, thus, turn to approximate nearest neighbor (ANN) query which targets better efficiency by slightly compromising accuracy. Despite this, existing ANN methods still incur high time and space costs, which are mainly due to the high dimensionality. Specifically, in most in-memory ANN algorithms, the time cost is dominated by the time for comparing the distances among vectors. Each distance comparison operation (DCO) involves hundreds of arithmetic operations as each vector has hundreds of dimensions. Similarly, the space cost is dominated by the space for storing the vectors. Towards the goal of reducing the time and space costs, we present three methods in this thesis. First, we observe that, for a DCO, if an approximate distance can confirm that a vector is not a NN, then it can be discarded without computing exact distances. Based on this observation, we propose a method named ADSampling. For a DCO, it iteratively and incrementally samples a few dimensions and computes an approximate distance. When this distance is accurate enough to decide the result of the DCO, it terminates sampling. Second, to further improve the efficiency of DCOs, we design an efficient distance estimator. We propose a new quantization method named RaBitQ, which maps $D$-dimensional vectors into $D$-bit strings. RaBitQ provides an unbiased and asymptotically optimal estimator with good empirical accuracy. In addition, we introduce efficient implementations of RaBitQ based on bitwise operations or SIMD-based operations. Third, by extending the RaBitQ method, we develop an algorithm which compresses a floating-point vector into a $B$-bit unsigned integer vector. We prove that our algorithm is asymptotically optimal in terms of the space-accuracy trade-off.

Case Based Reasoning (CBR) is a method that aims to resolve a new case by adapting the solutions contained in previous cases that are similar to the new case. The system built in this study is the CBR system to make recommendations on the topic of student thesis concentration. This study used data from undergraduate students of Informatics Engineering IST AKPRIND Yogyakarta with a total of 115 data consisting of 80 training data and 35 test data. This study aims to design and build a Case Based Reasoning system using the Nearest Neighbor and Manhattan Distance Similarity Methods, and to compare the results of the accuracy value using the Nearest Neighbor Similarity and Manhattan Distance Similarity methods. The recommendation process is carried out by calculating the value of closeness or similarity between new cases and old cases stored on a case basis using the Nearest Neighbor Method and Manhattan Distance. The features used in this study consisted of GPA and course grades. The case taken is the case with the highest similarity value. If a case doesnt get a topic recommendation or is less than the trashold value of 0.8, a case revision will be carried out by an expert. Successfully revised cases are stored in the system to be made new knowledge. The test results using the Nearest Neighbor Method get an accuracy value of 97.14% and Manhattan Distance Method 94.29%.

Approximate nearest neighbor (ANN) search is a fundamental search in multi-dimensional databases, which has numerous real-world applications, such as image retrieval, recommendation, entity resolution, and sequence matching. Proximity graph (PG) has been the state-of-the-art index for ANN search. However, the search on existing PGs either suffers from a high time complexity or has no performance guarantee on the search result. In this paper, we propose a novel τ-monotonic graph (τ- MG) to address the limitations. The novelty of τ-MG lies in a τ-monotonic property. Based on this property, we prove that if the distance between a query q and its nearest neighbor is less than a constant τ, the search on τ-MG guarantees to find the exact nearest neighbor of q and the time complexity of the search is smaller than all existing PG-based methods. For index construction efficiency, we propose an approximate variant of τ-MG, namely τ-monotonic neighborhood graph (τ- MNG), which only requires the neighborhood of each node to be τ-monotonic. We further propose an optimization to reduce the number of distance computations in search. Our extensive experiments show that our techniques outperform all existing methods on well-known real-world datasets.