There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

In recent years, spectral clustering has become one of the most popular modern clustering algorithms. It is simple to implement, can be solved efficiently by standard linear algebra software, and very often outperforms traditional clustering algorithms such as the k-means algorithm. On the first glance spectral clustering appears slightly mysterious, and it is not obvious to see why it works at all and what it really does. The goal of this tutorial is to give some intuition on those questions. We describe different graph Laplacians and their basic properties, present the most common spectral clustering algorithms, and derive those algorithms from scratch by several different approaches. Advantages and disadvantages of the different spectral clustering algorithms are discussed.

/pdf/a-tutorial-on-spectral-clustering-536pmg9onu.pdf

A tutorial on spectral clustering

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices of the same cluster and comparatively few edges joining vertices of different clusters. Such clusters, or communities, can be considered as fairly independent compartments of a graph, playing a similar role like, e. g., the tissues or the organs in the human body. Detecting communities is of great importance in sociology, biology and computer science, disciplines where systems are often represented as graphs. This problem is very hard and not yet satisfactorily solved, despite the huge effort of a large interdisciplinary community of scientists working on it over the past few years. We will attempt a thorough exposition of the topic, from the definition of the main elements of the problem, to the presentation of most methods developed, with a special focus on techniques designed by statistical physicists, from the discussion of crucial issues like the significance of clustering and how methods should be tested and compared against each other, to the description of applications to real networks.

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Community detection in graphs

Despite many empirical successes of spectral clustering methods— algorithms that cluster points using eigenvectors of matrices derived from the data—there are several unresolved issues. First. there are a wide variety of algorithms that use the eigenvectors in slightly different ways. Second, many of these algorithms have no proof that they will actually compute a reasonable clustering. In this paper, we present a simple spectral clustering algorithm that can be implemented using a few lines of Matlab. Using tools from matrix perturbation theory, we analyze the algorithm, and give conditions under which it can be expected to do well. We also show surprisingly good experimental results on a number of challenging clustering problems.

/pdf/on-spectral-clustering-analysis-and-an-algorithm-w9vnbkmp9q.pdf

On Spectral Clustering: Analysis and an algorithm

Partitioning of circuit netlists in VLSI design is considered. It is shown that the second smallest eigenvalue of a matrix derived from the netlist gives a provably good approximation of the optimal ratio cut partition cost. It is also demonstrated that fast Lanczos-type methods for the sparse symmetric eigenvalue problem are a robust basis for computing heuristic ratio cuts based on the eigenvector of this second eigenvalue. Effective clustering methods are an immediate by-product of the second eigenvector computation and are very successful on the difficult input classes proposed in the CAD literature. The intersection graph representation of the circuit netlist is considered, as a basis for partitioning, a heuristic based on spectral ratio cut partitioning of the netlist intersection graph is proposed. The partitioning heuristics were tested on industry benchmark suites, and the results were good in terms of both solution quality and runtime. Several types of algorithmic speedups and directions for future work are discussed. >

/pdf/fast-spectral-methods-for-ratio-cut-partitioning-and-5apwqoc7bz.pdf

Fast spectral methods for ratio cut partitioning and clustering

As industry moves towards many-core chips, networks-on-chip (NoCs) are emerging as the scalable fabric for interconnecting the cores. With power now the first-order design constraint, early-stage estimation of NoC power has become crucially important. ORION [29] was amongst the first NoC power models released, and has since been fairly widely used for early-stage power estimation of NoCs. However, when validated against recent NoC prototypes -- the Intel 80-core Teraflops chip and the Intel Scalable Communications Core (SCC) chip -- we saw significant deviation that can lead to erroneous NoC design choices. This prompted our development of ORION 2.0, an extensive enhancement of the original ORION models which includes completely new subcomponent power models, area models, as well as improved and updated technology models. Validation against the two Intel chips confirms a substantial improvement in accuracy over the original ORION. A case study with these power models plugged within the COSI-OCC NoC design space exploration tool [23] confirms the need for, and value of, accurate early-stage NoC power estimation. To ensure the longevity of ORION 2.0, we will be releasing it wrapped within a semi-automated flow that automatically updates its models as new technology files become available.

/pdf/orion-2-0-a-fast-and-accurate-noc-power-and-area-model-for-3pivncxvm6.pdf

ORION 2.0: a fast and accurate NoC power and area model for early-stage design space exploration

There has been increased research interest in systems composed of multiple autonomous mobile robots exhibiting collective behavior. Groups of mobile robots are constructed, with an aim to studying such issues as group architecture, resource conflict, origin of cooperation, learning, and geometric problems. As yet, few applications of collective robotics have been reported, and supporting theory is still in its formative stages. In this paper, the authors give a critical survey of existing works and discuss open problems in this field, emphasizing the various theoretical issues that arise in the study of cooperative robotics. The authors describe the intellectual heritages that have guided early research, as well as possible additions to the set of existing motivations.

/pdf/cooperative-mobile-robotics-antecedents-and-directions-18nltan2ev.pdf

Cooperative mobile robotics: antecedents and directions

Recent directions in netlist partitioning: a survey

Approximation can increase performance or reduce power consumption with a simplified or inaccurate circuit in application contexts where strict requirements are relaxed. For applications related to human senses, approximate arithmetic can be used to generate sufficient results rather than absolutely accurate results. Approximate design exploits a tradeoff of accuracy in computation versus performance and power. However, required accuracy varies according to applications, and 100% accurate results are still required in some situations. In this paper, we propose an accuracy-configurable approximate (ACA) adder for which the accuracy of results is configurable during runtime. Because of its configurability, the ACA adder can adaptively operate in both approximate (inaccurate) mode and accurate mode. The proposed adder can achieve significant throughput improvement and total power reduction over conventional adder designs. It can be used in accuracy-configurable applications, and improves the achievable tradeoff between performance/power and quality. The ACA adder achieves approximately 30% power reduction versus the conventional pipelined adder at the relaxed accuracy requirement.

/pdf/accuracy-configurable-adder-for-approximate-arithmetic-3w6719mdmp.pdf

Andrew B. Kahng

Papers

Fast spectral methods for ratio cut partitioning and clustering

ORION 2.0: a fast and accurate NoC power and area model for early-stage design space exploration

Cooperative mobile robotics: antecedents and directions

Recent directions in netlist partitioning: a survey

Accuracy-configurable adder for approximate arithmetic designs