scholarly journals Hyperbolic matrix factorization reaffirms the negative curvature of the native biological space

2020 ◽  
Author(s):  
Aleksandar Poleksic
Keyword(s):  
Hyperbolic Space ◽  
Matrix Factorization ◽  
Biological Networks ◽  
Hierarchical Structures ◽  
Past Research ◽  
Computational Procedure ◽  
Mathematical Framework ◽  
Biological Databases ◽  
Latent Dimension ◽  
Hyperbolic Embedding

AbstractPast research in systems biology has taken for granted the Euclidean geometry of biological space. This has not only drawn parallels to other fields but has also been convenient due to the ample statistical and numerical optimization tools available to address the core task and downstream machine learning problems. However, emerging theoretical studies now demonstrate that biological databases exhibit hierarchical topology, characterized by heterogeneous degree distribution and a high degree of clustering, thus contradicting the flat geometry assumption. Namely, since the number of nodes in hierarchical structures grows exponentially with node depth, the biological networks naturally reside in a hyperbolic space where the circle circumference and disk area are the exponential functions of the radius. To test these claims and assess potential benefits of the applications grounded in the above hypothesis, we have developed a mathematical framework and an accompanying computational procedure for matrix factorization and implied biological relationship inference in hyperbolic space. Not only does our study demonstrate a significant increase in the accuracy of hyperbolic embedding compared to Euclidean embedding, but it also shows that the latent dimension of an optimal hyperbolic embedding is by more than an order of magnitude smaller than the latent dimension of an optimal Euclidean embedding. We see this as additional evidence that hyperbolic geometry, rather than Euclidean, underlines the biological system.

scholarly journals Retweet Prediction Based on User Behavior

2021 ◽  
Author(s):  
Syeda Nadia Firdaus
Keyword(s):  
Machine Learning ◽  
Social Networks ◽  
Social Network ◽  
Prediction Model ◽  
Matrix Factorization ◽  
Information Diffusion ◽  
User Behavior ◽  
Past Research ◽  
The Difference ◽  
The Impact

Social network is a hot topic of interest for researchers in the field of computer science in recent years. These social networks such as Facebook, Twitter, Instagram play an important role in information diffusion. Social network data are created by its users. Users’ online activities and behavior have been studied in various past research efforts in order to get a better understanding on how information is diffused on social networks. In this study, we focus on Twitter and we explore the impact of user behavior on their retweet activity. To represent a user’s behavior for predicting their retweet decision, we introduce 10-dimentional emotion and 35-dimensional personality related features. We consider the difference of a user being an author and a retweeter in terms of their behaviors, and propose a machine learning based retweet prediction model considering this difference. We also propose two approaches for matrix factorization retweet prediction model which learns the latent relation between users and tweets to predict the user’s retweet decision. In the experiment, we have tested our proposed models. We find that models based on user behavior related features provide good improvement (3% - 6% in terms of F1- score) over baseline models. By only considering user’s behavior as a retweeter, the data processing time is reduced while the prediction accuracy is comparable to the case when both retweeting and posting behaviors are considered. In the proposed matrix factorization models, we include tweet features into the basic factorization model through newly defined regularization terms and improve the performance by 3% - 4% in terms of F1-score. Finally, we compare the performance of machine learning and matrix factorization models for retweet prediction and find that none of the models is superior to the other in all occasions. Therefore, different models should be used depending on how prediction results will be used. Machine learning model is preferable when a model’s performance quality is important such as for tweet re-ranking and tweet recommendation. Matrix factorization is a preferred option when model’s positive retweet prediction capability is more important such as for marketing campaign and finding potential retweeters.

scholarly journals Retweet Prediction Based on User Behavior

2021 ◽  
Author(s):  
Syeda Nadia Firdaus
Keyword(s):  
Machine Learning ◽  
Social Networks ◽  
Social Network ◽  
Prediction Model ◽  
Matrix Factorization ◽  
Information Diffusion ◽  
User Behavior ◽  
Past Research ◽  
The Difference ◽  
The Impact

Social network is a hot topic of interest for researchers in the field of computer science in recent years. These social networks such as Facebook, Twitter, Instagram play an important role in information diffusion. Social network data are created by its users. Users’ online activities and behavior have been studied in various past research efforts in order to get a better understanding on how information is diffused on social networks. In this study, we focus on Twitter and we explore the impact of user behavior on their retweet activity. To represent a user’s behavior for predicting their retweet decision, we introduce 10-dimentional emotion and 35-dimensional personality related features. We consider the difference of a user being an author and a retweeter in terms of their behaviors, and propose a machine learning based retweet prediction model considering this difference. We also propose two approaches for matrix factorization retweet prediction model which learns the latent relation between users and tweets to predict the user’s retweet decision. In the experiment, we have tested our proposed models. We find that models based on user behavior related features provide good improvement (3% - 6% in terms of F1- score) over baseline models. By only considering user’s behavior as a retweeter, the data processing time is reduced while the prediction accuracy is comparable to the case when both retweeting and posting behaviors are considered. In the proposed matrix factorization models, we include tweet features into the basic factorization model through newly defined regularization terms and improve the performance by 3% - 4% in terms of F1-score. Finally, we compare the performance of machine learning and matrix factorization models for retweet prediction and find that none of the models is superior to the other in all occasions. Therefore, different models should be used depending on how prediction results will be used. Machine learning model is preferable when a model’s performance quality is important such as for tweet re-ranking and tweet recommendation. Matrix factorization is a preferred option when model’s positive retweet prediction capability is more important such as for marketing campaign and finding potential retweeters.

scholarly journals HOMOTOPY OF POSETS, NET-COHOMOLOGY AND SUPERSELECTION SECTORS IN GLOBALLY HYPERBOLIC SPACE-TIMES

2005 ◽  
Vol 17 (09) ◽  
pp. 1021-1070 ◽  
Author(s):  
GIUSEPPE RUZZI
Keyword(s):  
Hyperbolic Space ◽  
Space Time ◽  
Fundamental Groups ◽  
Mathematical Framework ◽  
Permutation Symmetry ◽  
Index Set ◽  
Globally Hyperbolic ◽  
Underlying Space ◽  
Local Observables ◽  
Suitable Change

We study sharply localized sectors, known as sectors of DHR-type, of a net of local observables, in arbitrary globally hyperbolic space-times with dimension ≥ 3. We show that these sectors define, as it happens in Minkowski space, a C*-category in which the charge structure manifests itself by the existence of a tensor product, a permutation symmetry and a conjugation. The mathematical framework is that of the net-cohomology of posets according to J. E. Roberts. The net of local observables is indexed by a poset formed by a basis for the topology of the space-time ordered under inclusion. The category of sectors, is equivalent to the category of 1-cocycles of the poset with values in the net. We succeed in analyzing the structure of this category because we show how topological properties of the space-time are encoded in the poset used as index set: the first homotopy group of a poset is introduced and it is shown that the fundamental group of the poset and one of the underlying space-time are isomorphic; any 1-cocycle defines a unitary representation of these fundamental groups. Another important result is the invariance of the net-cohomology under a suitable change of index set of the net.

scholarly journals Interactive exploration of heterogeneous biological networks with Biomine Explorer

2019 ◽  
Vol 35 (24) ◽  
pp. 5385-5388
Author(s):  
Vid Podpečan ◽  
Živa Ramšak ◽  
Kristina Gruden ◽  
Hannu Toivonen ◽  
Nada Lavrač
Keyword(s):  
Biological Networks ◽  
Web Application ◽  
Biological Knowledge ◽  
Biological Databases ◽  
Scientific Publications ◽  
Public And Private ◽  
Interactive Exploration ◽  
Probabilistic Network ◽  
Private Network ◽  
User Friendly

Abstract Summary Biomine Explorer is a web application that enables interactive exploration of large heterogeneous biological networks constructed from selected publicly available biological knowledge sources. It is built on top of Biomine, a system which integrates cross-references from several biological databases into a large heterogeneous probabilistic network. Biomine Explorer offers user-friendly interfaces for search, visualization, exploration and manipulation as well as public and private storage of discovered subnetworks with permanent links suitable for inclusion into scientific publications. A JSON-based web API for network search queries is also available for advanced users. Availability and implementation Biomine Explorer is implemented as a web application, which is publicly available at https://biomine.ijs.si. Registration is not required but registered users can benefit from additional features such as private network repositories.

scholarly journals Evolving Hierarchical and Tag Information via the Deeply Enhanced Weighted Non-Negative Matrix Factorization of Rating Predictions

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1930
Author(s):  
Alpamis Kutlimuratov ◽  
Akmalbek Abdusalomov ◽  
Taeg Keun Whangbo
Keyword(s):  
Matrix Factorization ◽  
Recommendation System ◽  
Hierarchical Structures ◽  
The Matrix ◽  
Item Characteristics ◽  
Deep Relationship ◽  
Hierarchical Features ◽  
Novel Model ◽  
Prediction Efficiency ◽  
Non Negative Matrix Factorization

Identifying the hidden features of items and users of a modern recommendation system, wherein features are represented as hierarchical structures, allows us to understand the association between the two entities. Moreover, when tag information that is added to items by users themselves is coupled with hierarchically structured features, the rating prediction efficiency and system personalization are improved. To this effect, we developed a novel model that acquires hidden-level hierarchical features of users and items and combines them with the tag information of items that regularizes the matrix factorization process of a basic weighted non-negative matrix factorization (WNMF) model to complete our prediction model. The idea behind the proposed approach was to deeply factorize a basic WNMF model to obtain hidden hierarchical features of user’s preferences and item characteristics that reveal a deep relationship between them by regularizing the process with tag information as an auxiliary parameter. Experiments were conducted on the MovieLens 100K dataset, and the empirical results confirmed the potential of the proposed approach and its superiority over models that use the primary features of users and items or tag information separately in the prediction process.

scholarly journals Hyperbolic Wheel: A Novel Hyperbolic Space Graph Viewer for Hierarchical Information Content

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Ho-Ching Lam ◽  
Ivo D. Dinov
Keyword(s):  
Euclidean Space ◽  
Hyperbolic Space ◽  
Hierarchical Structures ◽  
Graph Visualization ◽  
Nested Partitions ◽  
Tree Graphs ◽  
Graph Viewer ◽  
Hyperbolic Graph ◽  
Data Objects ◽  
Interactive Manipulation

Tree and graph structures have been widely used to present hierarchical and linked data. Hyperbolic trees are special types of graphs composed of nodes (points or vertices) and edges (connecting lines), which are visualized on a non-Euclidean space. In traditional Euclidean space graph visualization, distances between nodes are measured by straight lines. Displays of large graphs in Euclidean spaces may not utilize efficiently the available space and may impose limitations on the number of graph nodes. The special hyperbolic space rendering of tree-graphs enables adaptive and efficient use of the available space and facilitates the display of large hierarchical structures. In this paper we report on a newly developed advanced hyperbolic graph viewer, Hyperbolic Wheel, which enables the navigation, traversal, discovery and interactive manipulation of information stored in large hierarchical structures. Examples of such structures include personnel records, disc directory structures, ontological constructs, web-pages and other nested partitions. The Hyperbolic Wheel framework provides an intuitive and dynamic graphical interface to explore and retrieve information about individual nodes (data objects) and their relationships (data associations). The Hyperbolic Wheel is freely available online for educational and research purposes.

scholarly journals Overcoming sparseness of biomedical networks to identify drug repositioning candidates

2020 ◽  
Author(s):  
Aleksandar Poleksic
Keyword(s):  
Biological Networks ◽  
Drug Targets ◽  
Drug Repositioning ◽  
Drug Repurposing ◽  
Drug Efficacy ◽  
Computational Procedure ◽  
Computational Method ◽  
Biomedical Data ◽  
Disease Associations ◽  
Disease Associated Genes

AbstractModeling complex biological systems is necessary to understand biochemical interactions behind pharmacological effects of drugs. Successful in silico drug repurposing requires a thorough exploration of diverse biochemical concepts and their relationships, including drug’s adverse reactions, drug targets, disease symptoms, as well as disease associated genes and their pathways, to name a few. We present a computational method for inferring drug-disease associations from complex but incomplete and biased biological networks. Our method employs the compressed sensing technique to overcome the sparseness of biomedical data and, in turn, to enrich the set of verified relationships between different biomedical entities. We present a strategy for identifying network paths supportive of drug efficacy as well as a computational procedure capable of combining different network patterns to better distinguish treatments from non-treatments. The data and programs are freely available at http://bioinfo.cs.uni.edu/AEONET.html.

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