23 research outputs found
Efficient Regularized Least-Squares Algorithms for Conditional Ranking on Relational Data
In domains like bioinformatics, information retrieval and social network
analysis, one can find learning tasks where the goal consists of inferring a
ranking of objects, conditioned on a particular target object. We present a
general kernel framework for learning conditional rankings from various types
of relational data, where rankings can be conditioned on unseen data objects.
We propose efficient algorithms for conditional ranking by optimizing squared
regression and ranking loss functions. We show theoretically, that learning
with the ranking loss is likely to generalize better than with the regression
loss. Further, we prove that symmetry or reciprocity properties of relations
can be efficiently enforced in the learned models. Experiments on synthetic and
real-world data illustrate that the proposed methods deliver state-of-the-art
performance in terms of predictive power and computational efficiency.
Moreover, we also show empirically that incorporating symmetry or reciprocity
properties can improve the generalization performance
Transductive Ranking on Graphs
In ranking, one is given examples of order relationships among objects, and the goal is to learn from these examples a real-valued ranking function that induces a ranking or ordering over the object space. We consider the problem of learning such a ranking function in a transductive, graph-based setting, where the object space is finite and is represented as a graph in which vertices correspond to objects and edges encode similarities between objects. Building on recent developments in regularization theory for graphs and corresponding Laplacian-based learning methods, we develop an algorithmic framework for learning ranking functions on graphs. We derive generalization bounds for our algorithms in transductive models similar to those used to study other transductive learning problems, and give experimental evidence of the potential benefits of our framework
ΠΡΠΈΠΊΠ»Π°Π΄Π½ΡΠ΅ Π°ΡΠΏΠ΅ΠΊΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π΄Π»Ρ ΠΎΡΠΈΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½Π½ΡΡ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΡΡ Π³ΡΠ°ΡΠΎΠ²(Π½Π° ΠΏΡΠΈΠΌΠ΅ΡΠ΅ Π³ΡΠ°ΡΠΎΠ² ΡΠΎΡΠΈΠ°Π»ΡΠ½ΡΡ ΡΠ΅ΡΠ΅ΠΉ)
The article deals with the applied aspects of the preliminary vertices ranking for oriented weighted graph. In this paper, the authors observed the widespread use of this technique in developing heuristic discrete optimization algorithms. The ranking problem is directly related to the problem of social networks centrality and large real world data sets but as shown in the article ranking is explicitly or implicitly used in the development of algorithms as the initial stage of obtaining a solution for solving applied problems. Examples of such ranking application are given. The examples demonstrate the increase of efficiency for solving some optimization applied problems, which are widely used in mathematical methods of optimization, decision-making not only from the theoretical development point of view but also their applications. The article describes the structure of the first phase of the computational experiment, which is associated with the procedure of obtaining test data sets. The obtained data are presented by weighted graphs that correspond to several groups of the social network Vkontakte with the number of participants in the range from 9000 to 24 thousand. It is shown that the structural characteristics of the obtained graphs differ significantly in the number of connectivity components. Characteristics of centrality (degree's sequences), as shown, have exponential distribution. The main attention is given to the analysis of three approaches to graph vertices ranking. We propose analysis and comparison of the obtained set of ranks by the nature of their distribution. The definition of convergence for graph vertex ranking algorithms is introduced and the differences of their use in considering the data of large dimension and the need to build a solution in the presence of local changes are discussed.Π Π°ΡΡΠΌΠ°ΡΡΠΈΠ²Π°ΡΡΡΡ ΠΏΡΠΈΠΊΠ»Π°Π΄Π½ΡΠ΅ Π°ΡΠΏΠ΅ΠΊΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄Π²Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²Π΅ΡΡΠΈΠ½ ΠΎΡΠΈΠ΅Π½ΡΠΈΡΠΎΠ²Π°Π½Π½ΠΎΠ³ΠΎ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΠΎΠ³ΠΎ Π³ΡΠ°ΡΠ°. ΠΡΠΎΠ±ΠΎΠ΅ Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅ ΡΠ΄Π΅Π»ΡΠ΅ΡΡΡ ΡΠΈΡΠΎΠΊΠΎΠΌΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΡΠ°ΠΊΠΎΠ³ΠΎ ΠΏΡΠΈΠ΅ΠΌΠ° Π² ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ ΡΠ²ΡΠΈΡΡΠΈΡΠ΅ΡΠΊΠΈΡ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² Π΄ΠΈΡΠΊΡΠ΅ΡΠ½ΠΎΠΉ ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π΄Π°ΡΠ° ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ ΠΈΠΌΠ΅Π΅Ρ Π½Π΅ΠΏΠΎΡΡΠ΅Π΄ΡΡΠ²Π΅Π½Π½ΠΎΠ΅ ΠΎΡΠ½ΠΎΡΠ΅Π½ΠΈΠ΅ ΠΊ ΠΏΡΠΎΠ±Π»Π΅ΠΌΠ΅ ΠΎΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΡΡΠΈ Π² ΡΠΎΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡ
, ΠΎΠ±ΡΠ°Π±ΠΎΡΠΊΠ΅ Π±ΠΎΠ»ΡΡΠΈΡ
ΠΌΠ°ΡΡΠΈΠ²ΠΎΠ² Π΄Π°Π½Π½ΡΡ
ΡΠ΅Π°Π»ΡΠ½ΠΎΠ³ΠΎ ΠΌΠΈΡΠ°, Π½ΠΎ ΠΊΠ°ΠΊ ΠΏΠΎΠΊΠ°Π·Π°Π½ΠΎ Π² ΡΡΠ°ΡΡΠ΅, ΡΠ²Π½ΠΎ ΠΈΠ»ΠΈ ΠΊΠΎΡΠ²Π΅Π½Π½ΠΎ ΠΈΡΠΏΠΎΠ»ΡΠ·ΡΠ΅ΡΡΡ ΠΏΡΠΈ ΡΠ°Π·ΡΠ°Π±ΠΎΡΠΊΠ΅ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠ΅ΡΠ΅Π½ΠΈΡ ΠΏΡΠΈΠΊΠ»Π°Π΄Π½ΡΡ
Π·Π°Π΄Π°Ρ Π² ΠΊΠ°ΡΠ΅ΡΡΠ²Π΅ Π½Π°ΡΠ°Π»ΡΠ½ΠΎΠ³ΠΎ ΡΡΠ°ΠΏΠ° ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ. ΠΡΠΈΠ²ΠΎΠ΄ΡΡΡΡ ΠΏΡΠΈΠΌΠ΅ΡΡ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠ΅Π΄Π²Π°ΡΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ, Π² ΠΊΠΎΡΠΎΡΡΡ
ΠΏΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠΎΠ²Π°Π½ΠΎ ΠΏΠΎΠ²ΡΡΠ΅Π½ΠΈΠ΅ ΡΡΡΠ΅ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π½Π΅ΠΊΠΎΡΠΎΡΡΡ
ΠΏΡΠΈΠΊΠ»Π°Π΄Π½ΡΡ
Π·Π°Π΄Π°Ρ, ΠΈΠΌΠ΅ΡΡΠΈΡ
ΡΠΈΡΠΎΠΊΠΎΠ΅ ΠΏΡΠΈΠΌΠ΅Π½Π΅Π½ΠΈΠ΅ Π² ΠΌΠ°ΡΠ΅ΠΌΠ°ΡΠΈΡΠ΅ΡΠΊΠΈΡ
ΠΌΠ΅ΡΠΎΠ΄Π°Ρ
ΠΎΠΏΡΠΈΠΌΠΈΠ·Π°ΡΠΈΠΈ. ΠΠ°Π½ΠΎ ΠΎΠΏΠΈΡΠ°Π½ΠΈΠ΅ ΡΡΡΡΠΊΡΡΡΡ ΠΏΠ΅ΡΠ²ΠΎΠΉ ΡΠ°Π·Ρ Π²ΡΡΠΈΡΠ»ΠΈΡΠ΅Π»ΡΠ½ΠΎΠ³ΠΎ ΡΠΊΡΠΏΠ΅ΡΠΈΠΌΠ΅Π½ΡΠ°, ΠΊΠΎΡΠΎΡΠ°Ρ ΡΠ²ΡΠ·Π°Π½Π° Ρ ΠΏΠΎΠ»ΡΡΠ΅Π½ΠΈΠ΅ΠΌ ΡΠ΅ΡΡΠΎΠ²ΡΡ
Π½Π°Π±ΠΎΡΠΎΠ² Π΄Π°Π½Π½ΡΡ
. ΠΠΎΠ»ΡΡΠ΅Π½Π½ΡΠ΅ Π΄Π°Π½Π½ΡΠ΅ ΠΏΡΠ΅Π΄ΡΡΠ°Π²Π»Π΅Π½Ρ Π²Π·Π²Π΅ΡΠ΅Π½Π½ΡΠΌΠΈ Π³ΡΠ°ΡΠ°ΠΌΠΈ, ΠΊΠΎΡΠΎΡΡΠ΅ ΡΠΎΠΎΡΠ²Π΅ΡΡΡΠ²ΡΡΡ Π½Π΅ΡΠΊΠΎΠ»ΡΠΊΠΈΠΌ Π³ΡΡΠΏΠΏΠ°ΠΌ ΡΠΎΡΠΈΠ°Π»ΡΠ½ΠΎΠΉ ΡΠ΅ΡΠΈ ΠΠΠΎΠ½ΡΠ°ΠΊΡΠ΅ Ρ ΡΠΈΡΠ»ΠΎΠΌ Π²Π΅ΡΡΠΈΠ½ Π² Π΄ΠΈΠ°ΠΏΠ°Π·ΠΎΠ½Π΅ ΠΎΡ 9000 Π΄ΠΎ 24 ΡΡΡΡΡ ΡΡΠ°ΡΡΠ½ΠΈΠΊΠΎΠ². ΠΠΎΠΊΠ°Π·Π°Π½ΠΎ, ΡΡΠΎ ΡΡΡΡΠΊΡΡΡΠ½ΡΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
Π³ΡΠ°ΡΠΎΠ² ΠΏΠΎ ΡΠΈΡΠ»Ρ ΠΊΠΎΠΌΠΏΠΎΠ½Π΅Π½Ρ ΡΠ²ΡΠ·Π½ΠΎΡΡΠΈ ΡΡΡΠ΅ΡΡΠ²Π΅Π½Π½ΠΎ ΡΠ°Π·Π»ΠΈΡΠ°ΡΡΡΡ. ΠΡΠΎΠ΄Π΅ΠΌΠΎΠ½ΡΡΡΠΈΡΠΎΠ²Π°Π½Ρ Π½Π΅ΠΊΠΎΡΠΎΡΡΠ΅ Ρ
Π°ΡΠ°ΠΊΡΠ΅ΡΠΈΡΡΠΈΠΊΠΈ ΡΠ΅Π½ΡΡΠ°Π»ΡΠ½ΠΎΡΡΠΈ (ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΡ ΡΡΠ΅ΠΏΠ΅Π½Π½ΡΡ
ΠΏΠΎΡΠ»Π΅Π΄ΠΎΠ²Π°ΡΠ΅Π»ΡΠ½ΠΎΡΡΠ΅ΠΉ), ΠΊΠΎΡΠΎΡΡΠ΅ ΠΈΠΌΠ΅ΡΡ ΡΠΊΡΠΏΠΎΠ½Π΅Π½ΡΠΈΠ°Π»ΡΠ½ΡΠΉ Ρ
Π°ΡΠ°ΠΊΡΠ΅Ρ. ΠΡΠ½ΠΎΠ²Π½ΠΎΠ΅ Π²Π½ΠΈΠΌΠ°Π½ΠΈΠ΅ ΡΠ΄Π΅Π»ΡΠ΅ΡΡΡ Π°Π½Π°Π»ΠΈΠ·Ρ ΡΡΠ΅Ρ
Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΠΈΠ΅ΡΠ°ΡΡ
ΠΈΠΈ ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²Π΅ΡΡΠΈΠ½ Π³ΡΠ°ΡΠΎΠ², ΠΏΡΠ΅Π΄Π»Π°Π³Π°ΡΡΡΡ Π½ΠΎΠ²ΡΠ΅ ΠΏΠΎΠ΄Ρ
ΠΎΠ΄Ρ ΠΊ Π²ΡΡΠΈΡΠ»Π΅Π½ΠΈΡ ΡΠ°Π½Π³ΠΎΠ² Π²Π΅ΡΡΠΈΠ½ Ρ ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΠ΅ΠΌ ΠΈΠ½ΡΠΎΡΠΌΠ°ΡΠΈΠΈ ΠΎΠ± Π°ΠΊΡΠΈΠ²Π½ΠΎΡΡΠΈ ΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°ΡΠ΅Π»Π΅ΠΉ Π² ΡΠΎΡΠΈΠ°Π»ΡΠ½ΡΡ
ΡΠ΅ΡΡΡ
. ΠΡΠΎΠ²ΠΎΠ΄ΠΈΡΡΡ ΡΡΠ°Π²Π½Π΅Π½ΠΈΠ΅ ΡΠ°ΡΠΏΡΠ΅Π΄Π΅Π»Π΅Π½ΠΈΠΉ ΠΏΠΎΠ»ΡΡΠ΅Π½Π½ΡΡ
ΡΠΎΠ²ΠΎΠΊΡΠΏΠ½ΠΎΡΡΠ΅ΠΉ ΡΠ°Π½Π³ΠΎΠ². ΠΠ²ΠΎΠ΄ΠΈΡΡΡ ΠΏΠΎΠ½ΡΡΠΈΠ΅ ΡΡ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ Π°Π»Π³ΠΎΡΠΈΡΠΌΠΎΠ² ΡΠ°Π½ΠΆΠΈΡΠΎΠ²Π°Π½ΠΈΡ Π²Π΅ΡΡΠΈΠ½ Π³ΡΠ°ΡΠΎΠ², Π° ΡΠ°ΠΊΠΆΠ΅ ΠΎΠ±ΡΡΠΆΠ΄Π°ΡΡΡΡ ΡΠ°Π·Π»ΠΈΡΠΈΡ ΠΈΡ
ΠΈΡΠΏΠΎΠ»ΡΠ·ΠΎΠ²Π°Π½ΠΈΡ ΠΏΡΠΈ ΡΠ°ΡΡΠΌΠΎΡΡΠ΅Π½ΠΈΠΈ Π΄Π°Π½Π½ΡΡ
Π±ΠΎΠ»ΡΡΠΎΠΉ ΡΠ°Π·ΠΌΠ΅ΡΠ½ΠΎΡΡΠΈ ΠΈ Π½Π΅ΠΎΠ±Ρ
ΠΎΠ΄ΠΈΠΌΠΎΡΡΠΈ ΠΏΠΎΡΡΡΠΎΠ΅Π½ΠΈΡ ΡΠ΅ΡΠ΅Π½ΠΈΡ Π² ΡΠ»ΡΡΠ°Π΅ ΡΡΠ΅ΡΠ° ΡΠΎΠ»ΡΠΊΠΎ Π»ΠΎΠΊΠ°Π»ΡΠ½ΡΡ
ΠΈΠ·ΠΌΠ΅Π½Π΅Π½ΠΈΠΉ
Multiobjective e-commerce recommendations based on hypergraph ranking
Β© 2018 Recommender systems are emerging in e-commerce as important promotion tools to assist customers to discover potentially interesting items. Currently, most of these are single-objective and search for items that fit the overall preference of a particular user. In real applications, such as restaurant recommendations, however, users often have multiple objectives such as group preferences and restaurant ambiance. This paper highlights the need for multi-objective recommendations and provides a solution using hypergraph ranking. A general UserβItemβAttributeβContext data model is proposed to summarize different information resources and high-order relationships for the construction of a multipartite hypergraph. This study develops an improved balanced hypergraph ranking method to rank different types of objects in hypergraph data. An overall framework is then proposed as a guideline for the implementation of multi-objective recommender systems. Empirical experiments are conducted with the dataset from a review site Yelp.com, and the outcomes demonstrate that the proposed model performs very well for multi-objective recommendations. The experiments also demonstrate that this framework is still compatible for traditional single-objective recommendations and can improve accuracy significantly. In conclusion, the proposed multi-objective recommendation framework is able to handle complex and changing demands for e-commerce customers