A Graph-Based Approach for Modeling and Indexing Video Data

Lee, J.

doi:10.1109/ism.2006.4

Cited by 7 publications

(3 citation statements)

References 69 publications

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“…Otherwise, the solution of this problem minimizes the disagreement of ZAZ T and B in the Frobenius norm sense. Solving inexact graph isomorphism problems is of interest in pattern recognition [CFSV04, RP94], computer vision [SRS01], shape analysis [SKK04,HHW06], image and video indexing [Lee06], and neuroscience [VCP + 11]. In many of the aforementioned fields graphs are used to represent geometric structures, and ZAZ T − B 2 F can be interpreted as the strength of geometric deformation.…”

Section: Inexact Graph Isomorphismmentioning

confidence: 99%

A general system for heuristic minimization of convex functions over non-convex sets

Diamond

Takapoui

Boyd

2017

Optimization Methods and Software

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We describe general heuristics to approximately solve a wide variety of problems with convex objective and decision variables from a nonconvex set. The heuristics, which employ convex relaxations, convex restrictions, local neighbor search methods, and the alternating direction method of multipliers (ADMM), require the solution of a modest number of convex problems, and are meant to apply to general problems, without much tuning. We describe an implementation of these methods in a package called NCVX, as an extension of CVXPY, a Python package for formulating and solving convex optimization problems. We study several examples of well known nonconvex problems, and show that our general purpose heuristics are effective in finding approximate solutions to a wide variety of problems.is often a Cartesian product, C = C 1 × · · · × C k , where C i ⊂ R q i are sets that are simple to describe, e.g., C i = {0, 1}. We denote the optimal value of the problem (1) as p , with the usual conventions that p = +∞ if the problem is infeasible, and p = −∞ if the problem is unbounded below. Special casesMixed-integer convex optimization. When C = {0, 1} q , the problem (1) is a general mixed integer convex program, i.e., a convex optimization problem in which some variables are constrained to be Boolean. (Mixed Boolean convex program would be a more accurate name for such a problem, but 'mixed integer' is commonly used.) It follows that the problem (1) is hard; it includes as a special case, for example, the general Boolean satisfaction problem.Cardinality constrained convex optimization. As another broad special case of (1),is the number of nonzero elements of z, and k and M are given. We call this the general cardinality-constrained convex problem. It arises in many interesting applications, such as regressor selection.Other special cases. As we will see in §6, many (hard) problems can be formulated in the form (1). More examples include regressor selection, 3-SAT, circle packing, the traveling salesman problem, factor analysis modeling, job selection, the maximum coverage problem, inexact graph isomorphism, and many more. Convex relaxationConvex relaxation of a set. A compact set C always has a tractable convex relaxation. By this we mean a (modest-sized) set of convex inequality and linear equality constraints that hold for every z ∈ C:We will assume that these relaxation constraints are included in the convex constraints of (1). Adding these relaxation constraints to the original problem yields an equivalent problem (since the added constraints are redundant), but can improve the convergence of any method, global or heuristic. By tractable, we mean that the number of added constraints is modest, and in particular, polynomial in q. For example, when C = {0, 1} q , we have the inequalities 0 ≤ z i ≤ 1, i = 1, . . . , q. (These inequalities define the convex hull of C, i.e., all other convex inequalities that hold for all z ∈ C are implied by them.) When

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Section: Inexact Graph Isomorphismmentioning

confidence: 99%

A general system for heuristic minimization of convex functions over non-convex sets

Diamond

Takapoui

Boyd

2017

Optimization Methods and Software

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“…We observe that Lee [44] proposed a graph-based approach to model and index video data. For this purpose, a a new graph-based video data structure is proposed, called the Spatio-Temporal Region Graph (STRG), which represents spatio-temporal features and the relationships among the video objects.…”

Section: Graph Modellingmentioning

confidence: 99%

LPaMI: A Graph-Based Lifestyle Pattern Mining Application Using Personal Image Collections in Smartphones

et al. 2017

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Normally, individuals use smartphones for a variety of purposes like photography, schedule planning, playing games, and so on, apart from benefiting from the core tasks of call-making and short messaging. These services are sources of personal data generation. Therefore, any application that utilises personal data of a user from his/her smartphone is truly a great witness of his/her interests and this information can be used for various personalised services. In this paper, we present Lifestyle Pattern MIning (LPaMI), which is a personalised application for mining the lifestyle patterns of a smartphone user. LPaMI uses the personal photograph collections of a user, which reflect the day-to-day photos taken by a smartphone, to recognise scenes (called objects of interest in our work). These are then mined to discover lifestyle patterns. The uniqueness of LPaMI lies in our graph-based approach to mining the patterns of interest. Modelling of data in the form of graphs is effective in preserving the lifestyle behaviour maintained over the passage of time. Graph-modelled lifestyle data enables us to apply variety of graph mining techniques for pattern discovery. To demonstrate the effectiveness of our proposal, we have developed a prototype system for LPaMI to implement its end-to-end pipeline. We have also conducted an extensive evaluation for various phases of LPaMI using different real-world datasets. We understand that the output of LPaMI can be utilised for variety of pattern discovery application areas like trip and food recommendations, shopping, and so on.

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“…As a general data structure, graphs can be used to model many complex relationships between data, and have been widely used in bioinformatics [1], chemoinformatics [2], computer vision [3], video indexing [4], text retrieval [5], efficient database indexing and other fields. The problem of frequent subgraph mining is to find all frequently occurring subgraph structures in a given graph data set.…”

Section: Introductionmentioning

confidence: 99%

SDM: A frequent subgraph mining algorithm for sequential directed graphs

Gao

Wu²

2022

International Conference on Mechanisms and Robotics (ICMAR 2022)

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Current research on frequent subgraph mining mainly focuses on the mining of undirected graphs, but in fact, the research on the mining of directed graphs has more practical significance. A new algorithm for mining frequent subgraphs based on directed graphs, SDM, is proposed. This algorithm uses breadth-first search strategy to mine frequent subgraphs by establishing a hierarchical tree space. And provide an efficient method in the process of frequent subgraph generation and counting. Experimental research shows that compared with other frequent subgraph mining algorithms, SDM has achieved a significant performance improvement.

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A Graph-Based Approach for Modeling and Indexing Video Data

Cited by 7 publications

References 69 publications

A general system for heuristic minimization of convex functions over non-convex sets

A general system for heuristic minimization of convex functions over non-convex sets

LPaMI: A Graph-Based Lifestyle Pattern Mining Application Using Personal Image Collections in Smartphones

SDM: A frequent subgraph mining algorithm for sequential directed graphs

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