Different Notions Of Similarity Research Articles

Predicting Psychotic Relapse in Schizophrenia With Mobile Sensor Data: Routine Cluster Analysis.

BackgroundBehavioral representations obtained from mobile sensing data can be helpful for the prediction of an oncoming psychotic relapse in patients with schizophrenia and the delivery of timely interventions to mitigate such relapse.ObjectiveIn this study, we aim to develop clustering models to obtain behavioral representations from continuous multimodal mobile sensing data for relapse prediction tasks. The identified clusters can represent different routine behavioral trends related to daily living of patients and atypical behavioral trends associated with impending relapse.MethodsWe used the mobile sensing data obtained from the CrossCheck project for our analysis. Continuous data from six different mobile sensing-based modalities (ambient light, sound, conversation, acceleration, etc) obtained from 63 patients with schizophrenia, each monitored for up to a year, were used for the clustering models and relapse prediction evaluation. Two clustering models, Gaussian mixture model (GMM) and partition around medoids (PAM), were used to obtain behavioral representations from the mobile sensing data. These models have different notions of similarity between behaviors as represented by the mobile sensing data, and thus, provide different behavioral characterizations. The features obtained from the clustering models were used to train and evaluate a personalized relapse prediction model using balanced random forest. The personalization was performed by identifying optimal features for a given patient based on a personalization subset consisting of other patients of similar age.ResultsThe clusters identified using the GMM and PAM models were found to represent different behavioral patterns (such as clusters representing sedentary days, active days but with low communication, etc). Although GMM-based models better characterized routine behaviors by discovering dense clusters with low cluster spread, some other identified clusters had a larger cluster spread, likely indicating heterogeneous behavioral characterizations. On the other hand, PAM model-based clusters had lower variability of cluster spread, indicating more homogeneous behavioral characterization in the obtained clusters. Significant changes near the relapse periods were observed in the obtained behavioral representation features from the clustering models. The clustering model-based features, together with other features characterizing the mobile sensing data, resulted in an F2 score of 0.23 for the relapse prediction task in a leave-one-patient-out evaluation setting. The obtained F2 score was significantly higher than that of a random classification baseline with an average F2 score of 0.042.ConclusionsMobile sensing can capture behavioral trends using different sensing modalities. Clustering of the daily mobile sensing data may help discover routine and atypical behavioral trends. In this study, we used GMM-based and PAM-based cluster models to obtain behavioral trends in patients with schizophrenia. The features derived from the cluster models were found to be predictive for detecting an oncoming psychotic relapse. Such relapse prediction models can be helpful in enabling timely interventions.

Vertex-removal, vertex-addition and different notions of similarity for vertices of a graph

This work examines different notions of similarity for a pair u, v of vertices of a graph G. The considered similarity notions are either of removal type or attachment type. In the removal case, checking similarity between u and v is a matter of comparing the vertex-deleted subgraphs G−u and G−v according to a certain criterion (isomorphism, degree sequence, index, characteristic polynomial, complementarity spectrum, etc.). In the attachment case, we compare the expanded graphs and obtained by attaching a pendant vertex to u and v, respectively. The duality between vertex-removal and vertex-attachment serves as central axis for the exposition.

Improving Deep Metric Learning by Divide and Conquer.

Deep metric learning (DML) is a cornerstone of many computer vision applications. It aims at learning a mapping from the input domain to an embedding space, where semantically similar objects are located nearby and dissimilar objects far from another. The target similarity on the training data is defined by user in form of ground-truth class labels. However, while the embedding space learns to mimic the user-provided similarity on the training data, it should also generalize to novel categories not seen during training. Besides user-provided groundtruth training labels, a lot of additional visual factors (such as viewpoint changes or shape peculiarities) exist and imply different notions of similarity between objects, affecting the generalization on the images unseen during training. However, existing approaches usually directly learn a single embedding space on all available training data, struggling to encode all different types of relationships, and do not generalize well. We propose to build a more expressive representation by jointly splitting the embedding space and the data hierarchically into smaller sub-parts. We successively focus on smaller subsets of the training data, reducing its variance and learning a different embedding subspace for each data subset. Moreover, the subspaces are learned jointly to cover not only the intricacies, but the breadth of the data as well. Only after that, we build the final embedding from the subspaces in the conquering stage. The proposed algorithm acts as a transparent wrapper that can be placed around arbitrary existing DML methods. Our approach significantly improves upon the state-of-the-art on image retrieval, clustering, and re-identification tasks evaluated using CUB200-2011, CARS196, Stanford Online Products, In-shop Clothes, and PKU VehicleID datasets.

Counts-of-counts similarity for prediction and search in relational data

Defining appropriate distance functions is a crucial aspect of effective and efficient similarity-based prediction and retrieval. Relational data are especially challenging in this regard. By viewing relational data as multi-relational graphs, one can easily see that a distance between a pair of nodes can be defined in terms of a virtually unlimited class of features, including node attributes, attributes of node neighbors, structural aspects of the node neighborhood and arbitrary combinations of these properties. In this paper we propose a rich and flexible class of metrics on graph entities based on earth mover’s distance applied to a hierarchy of complex counts-of-counts statistics. We further propose an approximate version of the distance using sums of marginal earth mover’s distances. We show that the approximation is correct for many cases of practical interest and allows efficient nearest-neighbor retrieval when combined with a simple metric tree data structure. An experimental evaluation on two real-world scenarios highlights the flexibility of our framework for designing metrics representing different notions of similarity. Substantial improvements in similarity-based prediction are reported when compared to solutions based on state-of-the-art graph kernels.

A combined Weisfeiler–Lehman graph kernel for structured data

Different graph kernels may correspond to using different notions of similarity or may be using information coming from multiple sources. In this paper, we develop a common method to construct combined graph kernel (CGK) which is based on a family of graph kernels. We define three kinds of CGK. The first one is called the weighted combined graph kernel and is a parametric CGK. The second one is called the accuracy ratio weighted combined graph kernel and is a non-parametric CGK. The third one is called the product combined graph kernel and also belongs to non-parametric CGK. The three kinds of definition of CGK can be applied for constructing CGK based on a family of graph kernels. This family of kernels is demonstrated based on the Weisfeiler–Lehman (WL) sequence of graphs in this paper, including a highly efficient subtree kernel, edge kernel, and shortest path kernel. Experiments demonstrate that our CGK based on WL graph kernels outperforms the corresponding single WL graph kernel on several classification benchmark data sets.

Multiclass multiple kernel learning using hypersphere for pattern recognition

Confronting with plenty of information from multiple targets and multiple sources, it is core and important to learn and decide for the bionic brain or robot within limited capacity in the bionic-technology field. Several multiclass multiple kernel learning algorithms are proposed instead of a single one, which can not only combine multiple kernels corresponding to different notions of similarity or information from multiple feature subsets, but also avoid kernel parameters selecting and fuse distinctions of multiple kernels. The core of these algorithms is the small sphere and large margin approach with hypersphere boundary, which takes the advantages of support vector machine (SVM) and support vector data description (SVDD), making the volume of sphere as small as well and the margin as large as possible, in other words, minimizing the within-class divergence like SVDD and maximizing the between-class margin like SVM. Meanwhile, The one-class essence of SSLM can relieve problem of the data imbalance. Besides, the one-against-all strategy is adopted for multiclass recognition. Hence, there will be a remarkable improvement of recognition accuracy. Numerical experiments based on three publicly UCI datasets demonstrate that using multiple kernels instead of a single one is useful and promising. These MMKL algorithms are ideal for classification and recognition of multiple targets and sources in artificial intelligence field.

Convergent sequences of sparse graphs: A large deviations approach

Models based on sparse graphs are of interest to many communities: they appear as basic models in combinatorics, probability theory, optimization, statistical physics, information theory, and more applied fields of social sciences and economics. Different notions of similarity (and hence convergence) of sparse graphs are of interest in different communities. In probability theory and combinatorics, the notion of Benjamini-Schramm convergence, also known as left-convergence, is used quite frequently. Statistical physicists are interested in the the existence of the thermodynamic limit of free energies, which leads naturally to the notion of right-convergence. Combinatorial optimization problems naturally lead to so-called partition convergence, which relates to the convergence of optimal values of a variety of constraint satisfaction problems. The relationship between these different notions of similarity and convergence is, however, poorly understood. In this paper we introduce a new notion of convergence of sparse graphs, which we call Large Deviations or LD-convergence, and which is based on the theory of large deviations. The notion is introduced by “decorating” the nodes of the graph with random uniform i.i.d. weights and constructing corresponding random measures on [0,1] and [0,1]2. A graph sequence is defined to be converging if the corresponding sequence of random measures satisfies the Large Deviations Principle with respect to the topology of weak convergence on bounded measures on [0,1]d,d=1,2. The corresponding large deviations rate function can be interpreted as the limit object of the sparse graph sequence. In particular, we can express the limiting free energies in terms of this limit object. We then establish that LD-convergence implies the other three notions of convergence discussed above, and at the same time establish several previously unknown relationships between the other notions of convergence. In particular, we show that partition-convergence does not imply left- or right-convergence, and that right-convergence does not imply partition-convergence. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 2016

Semi-supervised classification with Laplacian multiple kernel learning

Laplacian Support Vector Machine (lapSVM) is a SVM with an additional graph-based regularization for semi-supervised learning (SSL). As its base classifier is a single kernel SVM, it may be inefficient to deal with multi-source or multi-attribute complex datasets. Instead of one single kernel, we know that multiple kernels could correspond to different notions of similarity or information from multiple sources and represent differences between features. Therefore, we extend lapSVM to multiple kernel occasion, namely Laplacian Multiple Kernel Learning (lapMKL), improving the ability of processing more complex data in semi-supervised classification task. The proposed lapMKL is solved by Level Method, which was used in multiple kernel learning (MKL) and showed relatively high efficiency. Experiments on several data sets and comparisons with state of the art methods show that the proposed lapMKL is competitive and even better.

Multiple Kernel Learning Algorithms

In recent years, several methods have been proposed to combine multiple kernels instead of using a single one. These different kernels may correspond to using different notions of similarity or may...

Regularizing multiple kernel learning using response surface methodology

In recent years, several methods have been proposed to combine multiple kernels using a weighted linear sum of kernels. These different kernels may be using information coming from multiple sources or may correspond to using different notions of similarity on the same source. We note that such methods, in addition to the usual ones of the canonical support vector machine formulation, introduce new regularization parameters that affect the solution quality and, in this work, we propose to optimize them using response surface methodology on cross-validation data. On several bioinformatics and digit recognition benchmark data sets, we compare multiple kernel learning and our proposed regularized variant in terms of accuracy, support vector count, and the number of kernels selected. We see that our proposed variant achieves statistically similar or higher accuracy results by using fewer kernel functions and/or support vectors through suitable regularization; it also allows better knowledge extraction because unnecessary kernels are pruned and the favored kernels reflect the properties of the problem at hand.

Fragment-based approximate retrieval in highly heterogeneous XML collections

Due to the heterogeneous nature of XML data for internet applications exact matching of queries is often inadequate. The need arises to quickly identify subtrees of XML documents in a collection that are similar to a given pattern. Similarity involves both tags, that are not required to coincide, and structure, in which not all the relationships among nodes in the tree structure are strictly preserved. In this paper we present an efficient approach to the identification of similar subtrees, relying on ad-hoc indexing structures. The approach allows to quickly detect, in a heterogeneous document collection, the minimal portions that exhibit some similarity with the pattern. These candidate portions are then ranked according to their actual similarity. The approach supports different notions of similarity, thus it can be customized to different application domains. In the paper, three different similarity measures are proposed and compared. The approach is experimentally validated and the experimental results are extensively discussed.

Product modeling to support case-based construction planning and scheduling

Many human schedulers create schedules by reusing past similar schedules. The retrieval and reuse of similar schedules are subjective and experience-based. This paper explores different notions of similarity required when performing different scheduling tasks. It describes the CasePlan system that helps schedulers retrieve and reuse parts of existing schedules based on a generic product model, and apply case-based reasoning to generate new schedules. The validation experiment demonstrated CasePlan's accuracy in determining individual subnetworks and activity durations, but weak performance in determining interlinks between subnetworks, which highly depends upon the availability of pertinent cases and the level of detail of project information.

Similarity-based unification: a multi-adjoint approach

The aim of this paper is to build a formal model for similarity-based fuzzy unification in multi-adjoint logic programs. Specifically, a general framework of logic programming which allows the simultaneous use of different implications in the rules and rather general connectives in the bodies is introduced, then a procedural semantics for this framework is presented, and an approximative-completeness theorem proved. On this computational model, a similarity-based unification approach is constructed by simply adding axioms of fuzzy similarities and using classical crisp unification which provides a semantic framework for logic programming with different notions of similarity.

A Multi-Adjoint Approach to Similarity-Based Unification

A formal model for similarity-based fuzzy unification in multi-adjoint logic programs is presented. On this computational model, a similarity-based unification approach is constructed by simply adding axioms of fuzzy similarities and using classical crisp unification which provides a semantic framework for logic programming with different notions of similarity.

Preface: Volume 66, Issue 5

This part of the volume contains the papers accepted for presentation at the workshop on Unification in Non-Classical Logics (UNCL), co-located with ICALP 2002, which took place on July 12, 2002 in M\\'alaga, Spain.The workshop was concerned with one of the most promising areas of research on non-classical logics and its applications. Unification in non-classical logics, with various approaches to handling generalised terms, has drawn more and more attention in recent years. So far, most popular lines of research include fuzzy unification of (conventional) databases and the use of fuzzy concepts in information retrieval.This workshop was conceived as a forum for the exchange of ideas relevant for the concept of unification in non-classical logics, including, but not limited to, the topics of: •Unification in multiple-valued and fuzzy logic programming.•Unification based on similarities and fuzzy equivalence relations.•Categorical unification.•Practical use of non-classical unification, e.g. in expert systems and information retrieval.The program committee selected six papers after a reviewing process in which each submitted paper received at least two reviews. Considerable effort was devoted for the evaluation of the submissions and to providing the authors with helpful feedback. The criteria for selection were originality, quality, and relevance to the topic of the workshop.Alsinet et al reviewed and compared two models which extend first order possibilistic logic in order to enable fuzzy unification. The extension considers mainly fuzzy constants, and in form of restrictions on existential quantifiers.Banerjee and Bujosa presented a non-classical interpretion of classical unification in terms of geometrical constructions over a suitable R-module M. The main result is that unification of two terms can be seen as the intersection of their corresponding affine varieties on M. This paves the way of using methods from computer algebra in the field of unification.In Eklund et al, substitutions and unifiers appear as constructs in Kleisli categories related to particular composed powerset term monads. It is shown that an often used similarity-based approach to fuzzy unification is compatible with the categorical approach, and can be adequately extended.Kutsia presented a unification procedure for a theory with individual and sequence variables, free fixed and flexible arity function symbols and patterns. These theories have been used in different contexts such as databases, rewriting, programming languages, or theorem proving.Medina et al introduced a formal model for similarity-based fuzzy unification in multi-adjoint logic programs. On this computational model, a similarity-based unification approach which provides a semantic framework for logic programming with different notions of similarity was constructed.Virtanen introduced unification in similarity-based logic programming. One of the crucial points is the definition of similarity degrees between sets, giving rise to [lambda]-interpretations. The selection of so called most significant terms again is one of the cornerstones of the paper.We would like to thank all those who submitted papers for consideration, the authors of accepted papers for their interesting discussions during the workshop, the additional referees for their careful work, and Inma Fortes from the local organising committee for her assistance.

Time series similarity measures and time series indexing (abstract only)

Time series is the simplest form of temporal data. A time series is a sequence of real numbers collected regularly in time, where each number represents a value. Time series data come up in a variety of domains, including stock market analysis, environmental data, telecommunications data, medical data and financial data. Web data that count the number of clicks on given cites, or model the usage of different pages are also modeled as time series. Therefore time series account for a large fraction of the data stored in commercial databases. There is recently increasing recognition of this fact, and support for time series as a different data type in commercial data bases management systems is increasing. IBM DB2 for example implements support for time series using data-blades. The pervasiveness and importance of time series data has sparked a lot of research work on the topic. While the statistics literature on time series is vast, it has not studied methods that would be appropriate for the time series similarity and indexing problems we discuss here; much of the relevant work on these problems has been done by the computer science community. One interesting problem with time series data is finding whether different time series display similar behavior. More formally, the problem can be stated as: Given two time series X and Y , determine whether they are similar or not (in other words, define and compute a distance function dist ( X , Y )). Typically each time series describes the evolution of an object, for example the price of a stock, or the levels of pollution as a function of time at a given data collection station. The objective can be to cluster the different objects to similar groups, or to classify an object based on a set of known object examples. The problem is hard because the similarity model should allow for imprecise matches. One interesting variation is the subsequence similarity problem, where given two time series X and Y , we have to determine those subsequences of X that are similar to pattern Y . To answer these problems, different notions of similarity between time series have been proposed in data mining research. In the tutorial we examine the different time series similarity models that have been proposed, in terms of efficiency and accuracy. The solutions encompass techniques from a wide variety of disciplines, such as databases, signal processing, speech recognition, pattern matching, combinatorics and statistics. We survey proposed similarity techniques, including the L p norms, time warping, longest common subsequence measures, baselines, moving averaging, or deformable Markov model templates. Another problem that comes up in applications is the indexing problem: given a time series X , and a set of time series S = { Y 1 ,…, Y N }, find the time series in S that are most similar to the query X . A variation is the subsequence indexing problem, where given a set of sequences S , and a query sequence (pattern) X , find the sequences in S that contain subsequences that are similar to X . To solve these problems efficiently, appropriate indexing techniques have to be used. Typically, the similarity problem is related to the indexing problem: simple (and possibly inaccurate) similarity measures are usually easy to build indexes for, while more sophisticated similarity measures make the indexing problem hard and interesting. We examine the indexing techniques that can be used for different models, and the dimensionality reduction techniques that have been proposed to improve indexing performance. A time series of length n can be considered as a tuple in an n -dimensional space. Indexing this space directly is inefficient because of the very high dimensionality. The main idea to improve on it is to use a dimensionality reduction technique that takes the n item long time series, and maps it to a lower dimensional space with k dimensions (hopefully, k << n ). We give a detailed description of the most important techniques used for dimensionality reduction. These include: the SVD decomposition, the Fourier transform (and the similar Discrete Cosine transform), the Wavelet decomposition, Multidimensional Scaling, random projection techniques, FastMap (and variants), and Linear partitioning. These techniques have specific strengths and weaknesses, making some of them better suited for specific applications and settings. Finally we consider extensions to the problem of indexing subsequences, as well as to the problem of finding similar high-dimensional sequences, such as trajectories or video frame sequences.