A Tighter Analysis of Spectral Clustering, and Beyond

This work studies the classical spectral clustering algorithm which embeds the vertices of some graph $G=(V_G, E_G)$ into $\mathbb{R}^k$ using $k$ eigenvectors of some matrix of $G$, and applies $k$-means to partition $V_G$ into $k$ clusters. Our first result is a tighter analysis on the performance of spectral clustering, and explains why it works under some much weaker condition than the ones studied in the literature. For the second result, we show that, by applying fewer than $k$ eigenvectors to construct the embedding, spectral clustering is able to produce better output for many practical instances; this result is the first of its kind in spectral clustering. Besides its conceptual and theoretical significance, the practical impact of our work is demonstrated by the empirical analysis on both synthetic and real-world datasets, in which spectral clustering produces comparable or better results with fewer than $k$ eigenvectors.Comment: A preliminary version of this work appeared at ICML 202

Networked microgrid energy management based on supervised and unsupervised learning clustering

Networked microgrid (NMG) is a novel conceptual paradigm that can bring multiple advantages to the distributed system. Increasing renewable energy utilization, reliability and efficiency of system operation and flexibility of energy sharing amongst several microgrids (MGs) are some specific privileges of NMG. In this paper, residential MGs, commercial MGs, and industrial MGs are considered as a community of NMG. The loads’ profiles are split into multiple sections to evaluate the maximum load demand (MLD). Based on the optimal operation of each MG, the operating reserve (OR) of the MGs is calculated for each section. Then, the self-organizing map as a supervised and a k-means algorithm as an unsupervised learning clustering method is utilized to cluster the MGs and effective energy-sharing. The clustering is based on the maximum load demand of MGs and the operating reserve of dispatchable energy sources, and the goal is to provide a more efficient system with high reliability. Eventually, the performance of this energy management and its benefits to the whole system is surveyed effectively. The proposed energy management system offers a more reliable system due to the possibility of reserved energy for MGs in case of power outage variation or shortage of power.Peer ReviewedPostprint (published version

Heterogeneous Proxytypes Extended: Integrating Theory-like Representations and Mechanisms with Prototypes and Exemplars

The paper introduces an extension of the proposal according to which conceptual representations in cognitive agents should be intended as heterogeneous proxytypes. The main contribution of this paper is in that it details how to reconcile, under a heterogeneous representational perspective, different theories of typicality about conceptual representation and reasoning. In particular, it provides a novel theoretical hypothesis - as well as a novel categorization algorithm called DELTA - showing how to integrate the representational and reasoning assumptions of the theory-theory of concepts with the those ascribed to the prototype and exemplars-based theories

Thematic Annotation: extracting concepts out of documents

Contrarily to standard approaches to topic annotation, the technique used in this work does not centrally rely on some sort of -- possibly statistical -- keyword extraction. In fact, the proposed annotation algorithm uses a large scale semantic database -- the EDR Electronic Dictionary -- that provides a concept hierarchy based on hyponym and hypernym relations. This concept hierarchy is used to generate a synthetic representation of the document by aggregating the words present in topically homogeneous document segments into a set of concepts best preserving the document's content. This new extraction technique uses an unexplored approach to topic selection. Instead of using semantic similarity measures based on a semantic resource, the later is processed to extract the part of the conceptual hierarchy relevant to the document content. Then this conceptual hierarchy is searched to extract the most relevant set of concepts to represent the topics discussed in the document. Notice that this algorithm is able to extract generic concepts that are not directly present in the document.Comment: Technical report EPFL/LIA. 81 pages, 16 figure

Using cross-lingual information to cope with underspecification in formal ontologies

Description logics and other formal devices are frequently used as means for preventing or detecting mistakes in ontologies. Some of these devices are also capable of inferring the existence of inter-concept relationships that have not been explicitly entered into an ontology. A prerequisite, however, is that this information can be derived from those formal definitions of concepts and relationships which are included within the ontology. In this paper, we present a novel algorithm that is able to suggest relationships among existing concepts in a formal ontology that are not derivable from such formal definitions. The algorithm exploits cross-lingual information that is implicitly present in the collection of terms used in various languages to denote the concepts and relationships at issue. By using a specific experimental design, we are able to quantify the impact of cross-lingual information in coping with underspecification in formal ontologies

Methods of conceptual clustering and their relation to numerical taxonomy

Artificial Intelligence (AI) methods for machine learning can be viewed as forms of exploratory data analysis, even though they differ markedly from the statistical methods generally connoted by the term. The distinction between methods of machine learning and statistical data analysis is primarily due to differences in the way techniques of each type represent data and structure within data. That is, methods of machine learning are strongly biased toward symbolic (as opposed to numeric) data representations. We explore this difference within a limited context, devoting the bulk of our paper to the explication of conceptual clustering, an extension to the statistically based methods of numerical taxonomy. In conceptual clustering the formation of object clusters is dependent on the quality of 'higher-level' characterizations, termed concepts, of the clusters. The form of concepts used by existing conceptual clustering systems (sets of necessary and sufficient conditions) is described in some detail. This is followed by descriptions of several conceptual clustering techniques, along with sample output. We conclude with a discussion of how alternative concept representations might enhance the effectiveness of future conceptual clustering systems

Machine learning : techniques and foundations

The field of machine learning studies computational methods for acquiring new knowledge, new skills, and new ways to organize existing knowledge. In this paper we present some of the basic techniques and principles that underlie AI research on learning, including methods for learning from examples, learning in problem solving, learning by analogy, grammar acquisition, and machine discovery. In each case, we illustrate the techniques with paradigmatic examples