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.

Input: Consider Input: A two–step Christoffel function based solution is proposed to distribution regression problem. On the first step, to model distribution of observations inside a bag, build Christoffel function for each bag of observations. Then, on the second step, build outcome variable Christoffel function, but use the bag’s Christoffel function value at given point as the weight for the bag’s outcome. The approach allows the result to be obtained in closed form and then to be evaluated numerically. While most of existing approaches minimize some kind an error between outcome and prediction, the proposed approach is conceptually different, because it uses Christoffel function for knowledge representation, what is conceptually equivalent working with probabilities only. To receive possible outcomes and their probabilities Gauss quadrature for second–step measure can be built, then the nodes give possible outcomes and normalized weights – outcome probabilities. A library providing numerically stable polynomial basis for these calculations is available, what make the proposed approach practical.

Output: Multiple–Instance Learning: Christoffel Function Approach to Distribution Regression Problem


Input: Consider Input: Abstract—Spectral clustering is a powerful tool for unsupervised data analysis. In this paper, we propose a contextaware hypergraph similarity measure (CAHSM), which leads to robust spectral clustering in the case of noisy data. We construct three types of hypergraph—the pairwise hypergraph, the k-nearest-neighbor (kNN) hypergraph, and the high-order over-clustering hypergraph. The pairwise hypergraph captures the pairwise similarity of data points; the kNN hypergraph captures the neighborhood of each point; and the clustering hypergraph encodes high-order contexts within the dataset. By combining the affinity information from these three hypergraphs, the CAHSM algorithm is able to explore the intrinsic topological information of the dataset. Therefore, data clustering using CAHSM tends to be more robust. Considering the intracluster compactness and the inter-cluster separability of vertices, we further design a discriminative hypergraph partitioning criterion (DHPC). Using both CAHSM and DHPC, a robust spectral clustering algorithm is developed. Theoretical analysis and experimental evaluation demonstrate the effectiveness and robustness of the proposed algorithm.

Output: Context-Aware Hypergraph Construction for Robust Spectral Clustering


Input: Consider Input: Classification involves the learning of the mapping function that associates input samples to corresponding target label. There are two major categories of classification problems: Single-label classification and Multi-label classification. Traditional binary and multi-class classifications are subcategories of single-label classification. Several classifiers are developed for binary, multi-class and multi-label classification problems, but there are no classifiers available in the literature capable of performing all three types of classification. In this paper, a novel online universal classifier capable of performing all the three types of classification is proposed. Being a high speed online classifier, the proposed technique can be applied to streaming data applications. The performance of the developed classifier is evaluated using datasets from binary, multi-class and multi-label problems. The results obtained are compared with state-of-the-art techniques from each of the classification types. Keywords—Universal, Classification, Binary, Multi-class, Multi-label, Online, Extreme learning machines, Data stream.


Output: An Online Universal Classifier for Binary, Multi- class and Multi-label Classification