S-TREE: Self-Organizing Trees for Data Clustering and Online Vector Quantization

This paper introduces S-TREE (Self-Organizing Tree), a family of models that use unsupervised learning to construct hierarchical representations of data and online tree-structured vector quantizers. The S-TREE1 model, which features a new tree-building algorithm, can be implemented with various cost functions. An alternative implementation, S-TREE2, which uses a new double-path search procedure, is also developed. S-TREE2 implements an online procedure that approximates an optimal (unstructured) clustering solution while imposing a tree-structure constraint. The performance of the S-TREE algorithms is illustrated with data clustering and vector quantization examples, including a Gauss-Markov source benchmark and an image compression application. S-TREE performance on these tasks is compared with the standard tree-structured vector quantizer (TSVQ) and the generalized Lloyd algorithm (GLA). The image reconstruction quality with S-TREE2 approaches that of GLA while taking less than 10% of computer time. S-TREE1 and S-TREE2 also compare favorably with the standard TSVQ in both the time needed to create the codebook and the quality of image reconstruction.Office of Naval Research (N00014-95-10409, N00014-95-0G57

Vector quantization and clustering in presence of censoring

We consider the problem of optimal vector quantization for random vectors with one censored component and applications to clustering of censored observations. We introduce the definitions of the empirical distortion and of the empirically optimal quantizer in presence of censoring and we establish the almost sure consistency of empirical design. Moreover, we provide a non asymptotic exponential bound for the difference between the performance of the empirically optimal k-quantizer and the optimal performance over the class of all k-quantizers. As a natural application of the new quantization criterion, we propose an iterative two-step algorithm allowing for clustering of multivariate observations with one censored component. This method is investigated numerically through applications to real and simulated data

KOHONEN NEURAL NETWORK CLUSTERING FOR VOLTAGE CONTROL IN POWER SYSTEMS

Clustering a power system is very useful for the purpose of voltage stability control. However, the methods have developed usually have computational inefficiency. This paper presents a new cluster bus technique using Kohonen neural network for the purpose of forming bus clusters in power systems from the voltage stability viewpoint. This cluster formation will simplify voltage control in power system. With this proposed Kohonen algorithm, a large bus system will be partitioned into a small bus groups that have a coherence V, �, P and Q. The maximum number of area clusters will be formed need for voltage stability needed. The proposed technique was tested on IEEE 39 bus system by considering two contingency namely load increased and line outage by using voltage collapse analysis. This formation will be compared with the Learning Vector Quantization (LVQ) algorithm. The results showed the proposed technique produces four clusters on contingency load load increased and three clusters online outage contingency on IEEE 39 bus system as shown by the LVQ. Keywords: clustering, Kohonen, learning vector quantization, voltage stabilit

KOHONEN NEURAL NETWORK CLUSTERING FOR VOLTAGE CONTROL IN POWER SYSTEMS

Clustering a power system is very useful for the purpose of voltage stability control. However, the methods have developed usually have computational inefficiency. This paper presents a new cluster bus technique using Kohonen neural network for the purpose of forming bus clusters in power systems from the voltage stability viewpoint. This cluster formation will simplify voltage control in power system. With this proposed Kohonen algorithm, a large bus system will be partitioned into a small bus groups that have a coherence V, �, P and Q. The maximum number of area clusters will be formed need for voltage stability needed. The proposed technique was tested on IEEE 39 bus system by considering two contingency namely load increased and line outage by using voltage collapse analysis. This formation will be compared with the Learning Vector Quantization (LVQ) algorithm. The results showed the proposed technique produces four clusters on contingency load load increased and three clusters online outage contingency on IEEE 39 bus system as shown by the LVQ. Keywords: clustering, Kohonen, learning vector quantization, voltage stabilit

An Efficient Index for Visual Search in Appearance-based SLAM

Vector-quantization can be a computationally expensive step in visual bag-of-words (BoW) search when the vocabulary is large. A BoW-based appearance SLAM needs to tackle this problem for an efficient real-time operation. We propose an effective method to speed up the vector-quantization process in BoW-based visual SLAM. We employ a graph-based nearest neighbor search (GNNS) algorithm to this aim, and experimentally show that it can outperform the state-of-the-art. The graph-based search structure used in GNNS can efficiently be integrated into the BoW model and the SLAM framework. The graph-based index, which is a k-NN graph, is built over the vocabulary words and can be extracted from the BoW's vocabulary construction procedure, by adding one iteration to the k-means clustering, which adds small extra cost. Moreover, exploiting the fact that images acquired for appearance-based SLAM are sequential, GNNS search can be initiated judiciously which helps increase the speedup of the quantization process considerably