We show that the complexity of the recently introduced medoid-shift algorithm in clustering N points is O(N 2), with a small constant, if the underlying distance is Euclidean. This makes medoid shift considerably faster than mean shift, contrarily to what previously believed. We then exploit kernel methods to extend both mean shift and the improved medoid shift to a large family of distances, with complexity bounded by the effective rank of the resulting kernel matrix, and with explicit regularization constraints. Finally, we show that, under certain conditions, medoid shift fails to cluster data points belonging to the same mode, resulting in over-fragmentation. We propose remedies for this problem, by introducing a novel, simple and extremely efficient clustering algorithm, called quick shift, that explicitly trades off under- and over-fragmentation. Like medoid shift, quick shift operates in non-Euclidean spaces in a straightforward manner. We also show that the accelerated medoid shift can be used to initialize mean shift for increased efficiency. We illustrate our algorithms to clustering data on manifolds, image segmentation, and the automatic discovery of visual categories.

/pdf/quick-shift-and-kernel-methods-for-mode-seeking-1hz87wa3cn.pdf

Quick Shift and Kernel Methods for Mode Seeking

https://sci2s.ugr.es/sites/default/files/files/ScientificImpact/2012-Martinez-INS.pdf

An overview on the 2-tuple linguistic model for computing with words in decision making: Extensions, applications and challenges

Meta-synthesis approach to complex system modeling

Aiming at the diversity of user features, the uncertainty and the variation characteristics of quality of service (QoS), by exploiting the continuous monitoring data of cloud services, this paper proposes a multi-valued collaborative approach to predict the unknown QoS values via time series analysis for potential users. In this approach, the multi-valued QoS evaluations consisting of single-value data and time series data from consumers are transformed into cloud models, and the differences between potential users and other consumers in every period are measured based on these cloud models. Against the deficiency of existing methods of similarity measurement between cloud models, this paper presents a new vector comparison method combining the orientation similarity and dimension similarity to improve the precision of similarity calculation. The fuzzy analytic hierarchy process method is used to help potential users determine the objective weight of every period, and the neighboring users are selected for the potential user according to their comprehensive similarities of QoS evaluations in multiple periods. By incorporating the multi-valued QoS evaluations with the objective weights among multiple periods, the predicted results can remain consistent with the periodic variations of QoS. Finally, the experiments based on a real-world dataset demonstrate that this approach can provide high accuracy of collaborative QoS prediction for multi-valued evaluations in the cloud computing paradigm.

Multi-Valued Collaborative Qos Prediction for Cloud Service Via Time Series Analysis

Multi-valued collaborative QoS prediction for cloud service via time series analysis

This paper proposes a technique of piecewise aggregate approximation based on cloud model to resolve the high dimensionality of time series.The entropy of cloud model is used to evaluate the stability of data points in a subsequence and choose the subsequence with lower stability to further divide so that a series of cloud models can be obtained to approximate time series.The similarity between two cloud model series is calculated.The proposed method can reduce the dimensionality,and also can adaptively recognize and represent the essential features of time series.The results of experiments indicate that the proposed method can guarantee the accuracy of similarity and improve the efficiency of time series data mining under larger compress ratio.

Piecewise aggregate approximation method based on cloud model for time series

This paper respectively analyzed the function and meaning of feature representations and similarity measurements for time seriesIt also summarized the existed methods and analyzed the merits and demeritsMeanwhile,by discussing the noteworthy problems,it provided the further research direction of feature representations and similarity measurements for time series

Survey of feature representations and similarity measurements in time series data mining

We investigate the relationship between the structure and the synchronizability of scale-free networks in geographical space. With an optimization approach, the numerical results indicate that when the network synchronizability is improved, the geographical distance becomes larger while the maximal load decreases. Thus the maximal betweenness can be a candidate factor that affects the network synchronizability both in topological space and in geographical space.

Optimizing Synchronizability of Scale-Free Networks in Geographical Space

To deal with multiple attributes group decision making problems with linguistic assessment information,a two-tuple linguistic multiple attributes group decision making method based on VIKOR method is proposed.This method aggregates single users' decision information to get group's decision information,and obtain the best compromise solution by maximizing group utility for the majority and minimizing individual regret for the opponent.This method is easy to implement and interpret,and can avoid the loss and distortion of assessment information effectively.Moreover,the proposed method can overcome the shortcomings of the ideal solution method,which cannot reflect the relative importance of distances from the alternative to the positive ideal solution and negative ideal solution.Finally,the result of the numerical example shows the effectiveness of the proposed method.

Multiple attributes group decision making method based on two-tuple linguistic information processing

For multiple attributes group decision-making problems with multi-granularity uncertain linguistic information and incomplete attribute weighted information of the decision-makers,a decision analysis method is proposed.The method,firstly,uniforms the multi-granularity linguistic information using a two-tuple linguistic transformation function.Then,an optimization model,which aims to minimize the relative entropy of the alternatives to the positive ideal solution and maximize the relative entropy of the alternatives to the negative ideal solution,is established to determine the attribute weights of the decision-makers.Finally,the uncertain two-tuple ordered weighted averaging(OWA)operator is utilized to obtain the decision group′s evaluation on the alternatives.By calculating the possibility degree to which the alternative is superior to others,the alternatives can be ranked.The numerical example illustrates the feasibility and effectiveness of the proposed method.

Guo Chong-hui

Papers

Piecewise aggregate approximation method based on cloud model for time series

Survey of feature representations and similarity measurements in time series data mining

Optimizing Synchronizability of Scale-Free Networks in Geographical Space

Multiple attributes group decision making method based on two-tuple linguistic information processing

A multi-granularity uncertain linguistic group decision-making method based on relative entropy