Informative labeling schemes for graphs

AbstractThis paper introduces the notion of informative labeling schemes for arbitrary graphs. Let f(W) be a function on subsets of vertices W. An f labeling scheme labels the vertices of a weighted graph G in such a way that f(W) can be inferred (or at least approximated) efficiently for any vertex subset W of G by merely inspecting the labels of the vertices of W, without having to use any additional information sources.A number of results illustrating this notion are presented in the paper. We begin by developing f labeling schemes for three functions f over the class of n-vertex trees. The first function, SepLevel, gives the separation level of any two vertices in the tree, namely, the depth of their least common ancestor. The second, LCA, provides the least common ancestor of any two vertices. The third, Center, yields the center of any three given vertices v1,v2,v3 in the tree, namely, the unique vertex z connected to them by three edge-disjoint paths. All of these three labeling schemes use O(log2n)-bit labels, which is shown to be asymptotically optimal.Our main results concern the function Steiner(W), defined for weighted graphs. For any vertex subset W in the weighted graph G, Steiner(W) represents the weight of the Steiner tree spanning the vertices of W in G. Considering the class of n-vertex trees with M-bit edge weights, it is shown that for this class there exists a Steiner labeling scheme using O((M+logn)logn) bit labels, which is asymptotically optimal. It is then shown that for the class of arbitrary n-vertex graphs with M-bit edge weights, there exists an approximate-Steiner labeling scheme, providing an estimate (up to a factor of O(logn)) for the Steiner weight Steiner(W) of a given set of vertices W, using O((M+logn)log2n) bit labels

Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction

Motivated by applications to sensor networks, as well as to many other areas, this paper studies the construction of minimum-degree spanning trees. We consider the classical node-register state model, with a weakly fair scheduler, and we present a space-optimal \emph{silent} self-stabilizing construction of minimum-degree spanning trees in this model. Computing a spanning tree with minimum degree is NP-hard. Therefore, we actually focus on constructing a spanning tree whose degree is within one from the optimal. Our algorithm uses registers on $O(\log n)$ bits, converges in a polynomial number of rounds, and performs polynomial-time computation at each node. Specifically, the algorithm constructs and stabilizes on a special class of spanning trees, with degree at most $OPT+1$. Indeed, we prove that, unless NP $=$ coNP, there are no proof-labeling schemes involving polynomial-time computation at each node for the whole family of spanning trees with degree at most $OPT+1$. Up to our knowledge, this is the first example of the design of a compact silent self-stabilizing algorithm constructing, and stabilizing on a subset of optimal solutions to a natural problem for which there are no time-efficient proof-labeling schemes. On our way to design our algorithm, we establish a set of independent results that may have interest on their own. In particular, we describe a new space-optimal silent self-stabilizing spanning tree construction, stabilizing on \emph{any} spanning tree, in $O(n)$ rounds, and using just \emph{one} additional bit compared to the size of the labels used to certify trees. We also design a silent loop-free self-stabilizing algorithm for transforming a tree into another tree. Last but not least, we provide a silent self-stabilizing algorithm for computing and certifying the labels of a NCA-labeling scheme

Efficient Version-Space Reduction for Visual Tracking

Discrminative trackers, employ a classification approach to separate the target from its background. To cope with variations of the target shape and appearance, the classifier is updated online with different samples of the target and the background. Sample selection, labeling and updating the classifier is prone to various sources of errors that drift the tracker. We introduce the use of an efficient version space shrinking strategy to reduce the labeling errors and enhance its sampling strategy by measuring the uncertainty of the tracker about the samples. The proposed tracker, utilize an ensemble of classifiers that represents different hypotheses about the target, diversify them using boosting to provide a larger and more consistent coverage of the version-space and tune the classifiers' weights in voting. The proposed system adjusts the model update rate by promoting the co-training of the short-memory ensemble with a long-memory oracle. The proposed tracker outperformed state-of-the-art trackers on different sequences bearing various tracking challenges.Comment: CRV'17 Conferenc

A note on models for graph representations

AbstractThis paper is intended more to ask questions than give answers. Specifically, we consider models for labeling schemes, and discuss issues regarding the number of labels consulted vs. the sizes of the labels.Recently, quite a few papers studied methods for representing network properties by assigning informative labels to the vertices of a network. Consider a graph function f on pairs of vertices (for example, f can be the distance function). In an f-labeling scheme, the labels are constructed in such a way so that given the labels of any two vertices u and v, one can compute the function f(u,v) (e.g. the graph distance between u and v) just by looking at these two labels. Some very involved lower bounds for the sizes of the labels were proven. Also, some highly sophisticated labeling schemes were developed to ensure short labels.In this paper, we demonstrate that such lower bounds are very sensitive to the number of vertices consulted. That is, we show several constructions of such labeling schemes that beat the lower bounds by large margins. Moreover, as opposed to the strong technical skills that were needed to develop the traditional labeling schemes, most of our schemes are almost trivial. The catch is that in our model, one needs to consult the labels of three vertices instead of two. That is, a query about vertices u and v can access also the label of some third vertex w (w is determined by the labels of u and v). More generally, we address the model in which a query about vertices u and v can access also the labels of c other vertices. We term our generalized model labeling schemes with queries.The main importance of this model is theoretical. Specifically, this paper may serve as a first step towards investigating different tradeoffs between the amount of labels consulted and the amount of information stored at each vertex. As we show, if all vertices can be consulted then the problem almost reduces to the corresponding sequential problem. On the other hand, consulting just the labels of u and v (or even just the label of u) reduces the problem to a purely distributed one. Therefore, in a sense, our model spans a range of intermediate notions between the sequential and the distributed settings.In addition to the theoretical interest, we also show cases that schemes constructed for our model can be translated to the traditional model or to the sequential model, thus, simplifying the construction for those models as well. For implementing query labeling schemes in a distributed environment directly, we point at a potential usage for some new paradigms that became common recently, such as P2P and overlay networks

Medical image retrieval and automatic annotation: VPA-SABANCI at ImageCLEF 2009

Advances in the medical imaging technology has lead to an exponential growth in the number of digital images that needs to be acquired, analyzed, classified, stored and retrieved in medical centers. As a result, medical image classification and retrieval has recently gained high interest in the scientific community. Despite several attempts, such as the yearly-held ImageCLEF Medical Image Annotation Competition, the proposed solutions are still far from being su±ciently accurate for real-life implementations. In this paper we summarize the technical details of our experiments for the ImageCLEF 2009 medical image annotation task. We use a direct and two hierarchical classification schemes that employ support vector machines and local binary patterns, which are recently developed low-cost texture descriptors. The direct scheme employs a single SVM to automatically annotate X-ray images. The two proposed hierarchi-cal schemes divide the classification task into sub-problems. The first hierarchical scheme exploits ensemble SVMs trained on IRMA sub-codes. The second learns from subgroups of data defined by frequency of classes. Our experiments show that hier-archical annotation of images by training individual SVMs over each IRMA sub-code dominates its rivals in annotation accuracy with increased process time relative to the direct scheme

One Class One Click: Quasi Scene-level Weakly Supervised Point Cloud Semantic Segmentation with Active Learning

Reliance on vast annotations to achieve leading performance severely restricts the practicality of large-scale point cloud semantic segmentation. For the purpose of reducing data annotation costs, effective labeling schemes are developed and contribute to attaining competitive results under weak supervision strategy. Revisiting current weak label forms, we introduce One Class One Click (OCOC), a low cost yet informative quasi scene-level label, which encapsulates point-level and scene-level annotations. An active weakly supervised framework is proposed to leverage scarce labels by involving weak supervision from global and local perspectives. Contextual constraints are imposed by an auxiliary scene classification task, respectively based on global feature embedding and point-wise prediction aggregation, which restricts the model prediction merely to OCOC labels. Furthermore, we design a context-aware pseudo labeling strategy, which effectively supplement point-level supervisory signals. Finally, an active learning scheme with a uncertainty measure - temporal output discrepancy is integrated to examine informative samples and provides guidance on sub-clouds query, which is conducive to quickly attaining desirable OCOC annotations and reduces the labeling cost to an extremely low extent. Extensive experimental analysis using three LiDAR benchmarks collected from airborne, mobile and ground platforms demonstrates that our proposed method achieves very promising results though subject to scarce labels. It considerably outperforms genuine scene-level weakly supervised methods by up to 25\% in terms of average F1 score and achieves competitive results against full supervision schemes. On terrestrial LiDAR dataset - Semantics3D, using approximately 2\textpertenthousand{} of labels, our method achieves an average F1 score of 85.2\%, which increases by 11.58\% compared to the baseline model