TASK DEFINITION: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
PROBLEM: In many combinatorial problems one may need to model the diversity or similarity of sets of assignments. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however bounds consistency can be achieved in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor of 12 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.

SOLUTION: Soft Constraints of Difference and Equality

PROBLEM: Class imbalance is one of the challenging problems for machine learning in many real-world applications, such as coal and gas burst accident monitoring: the burst premonition data is extreme smaller than the normal data, however, which is the highlight we truly focus on. Cost-sensitive adjustment approach is a typical algorithm-level method resisting the data set imbalance. For SVMs classifier, which is modified to incorporate varying penalty parameter(C) for each of considered groups of examples. However, the C value is determined empirically, or is calculated according to the evaluation metric, which need to be computed iteratively and time consuming. This paper presents a novel cost-sensitive SVM method whose penalty parameter C optimized on the basis of cluster probability density function(PDF) and the cluster PDF is estimated only according to similarity matrix and some predefined hyper-parameters. Experimental results on various standard benchmark data sets and real-world data with different ratios of imbalance show that the proposed method is effective in comparison with commonly used cost-sensitive techniques.

SOLUTION: Optimizing Cost-Sensitive SVM for Imbalanced Data :Connecting Cluster to Classification

PROBLEM: Pointwise matches between two time series are of great importance in time series analysis, and dynamic time warping (DTW) is known to provide generally reasonable matches. There are situations where time series alignment should be invariant to scaling and offset in amplitude or where local regions of the considered time series should be strongly reflected in pointwise matches. Two different variants of DTW, affine DTW (ADTW) and regional DTW (RDTW), are proposed to handle scaling and offset in amplitude and provide regional emphasis respectively. Furthermore, ADTW and RDTW can be combined in two different ways to generate alignments that incorporate advantages from both methods, where the affine model can be applied either globally to the entire time series or locally to each region. The proposed alignment methods outperform DTW on specific simulated datasets, and one-nearest-neighbor classifiers using their associated difference measures are competitive with the difference measures associated with state-of-the-art alignment methods on real datasets.

SOLUTION:
Affine and Regional Dynamic Time Warping