Recommendation System for Purchasing Goods Based on the Decision Tree Algorithm

Over the past few years, interest in applications related to recommendation systems has increased significantly. Many modern services create recommendation systems that, based on user profile information and his behavior. This services determine which objects or products may be interesting to users. Recommendation systems are a modern tool for understanding customer needs. The main methods of constructing recommendation systems are the content-based filtering method and the collaborative filtering method. This article presents the implementation of these methods based on decision trees. The content-based filtering method is based on the description of the object and the customer’s preference profile. An object description is a finite set of its descriptors, such as keywords, binary descriptors, etc., and a preference profile is a weighted vector of object descriptors in which scales reflect the importance of each descriptor to the client and its contribution to the final decision. This model selects items that are similar to the customer’s favorite items before. The second model, which implements the method of collaborative filtering, is based on information about the history of behavior of all customers on the resource: data on their purchases, assessments of product quality, reviews, marked product. The model finds clients that are similar in behavior and the recommendation is based on their assessments of this element. Voting was used to combine the results issued by individual models — the best result is chosen from the results of two models of the ensemble. This approach minimizes the impact of randomness and averages the errors of each model. The aim: The purpose of work is to create real competitive recommendation system for short period of time and minimum costs.

Exploiting MUSIC model to solve cold-start user problem in content-based music recommender systems

The new user cold-start problem is a grand challenge in content-based music recommender systems. This happens when the systems do not have sufficient information regarding the user’s preferences. Towards solving this problem, in this study, a rating prediction framework is proposed. The proposed framework allows the systems to predict the user’s rating scores for unrated musical pieces, by which good recommendations can be generated. The core idea here is to leverage the so-called MUSIC model, i.e., a five-factor musical preference model, which is characterized by Mellow, Unpretentious, Sophisticated, Intense, and Contemporary as the user’s musical preference profiles. When a user newly joins the systems, the first five-factor musical preference profile is established based on the user’s age and brain type information which is extracted from questionnaires. When the user experiences the systems for a certain period, his/her rating scores for experienced musical pieces are utilized for generating the second five-factor musical preference profile. The recommendations are then provided based on the rating scores predicted from a non-linear combination of these two five-factor musical preference profiles. The results demonstrated the effectiveness of the five-factor musical preference in alleviating the new user cold-start problem. In addition, the proposed method can potentially provide high-quality recommendations.

Representative Committees of Peers

A population of voters must elect representatives among themselves to decide on a sequence of possibly unforeseen binary issues. Voters care only about the final decision, not the elected representatives. The disutility of a voter is proportional to the fraction of issues, where his preferences disagree with the decision. While an issue-by-issue vote by all voters would maximize social welfare, we are interested in how well the preferences of the population can be approximated by a small committee. We show that a k-sortition (a random committee of k voters with the majority vote within the committee) leads to an outcome within the factor 1+O(1/√ k) of the optimal social cost for any number of voters n, any number of issues m, and any preference profile. For a small number of issues m, the social cost can be made even closer to optimal by delegation procedures that weigh committee members according to their number of followers. However, for large m, we demonstrate that the k-sortition is the worst-case optimal rule within a broad family of committee-based rules that take into account metric information about the preference profile of the whole population.

Unanimous and Strategy-Proof Probabilistic Rules for Single-Peaked Preference Profiles on Graphs

Finitely many agents have preferences on a finite set of alternatives, single-peaked with respect to a connected graph with these alternatives as vertices. A probabilistic rule assigns to each preference profile a probability distribution over the alternatives. First, all unanimous and strategy-proof probabilistic rules are characterized when the graph is a tree. These rules are uniquely determined by their outcomes at those preference profiles at which all peaks are on leaves of the tree and, thus, extend the known case of a line graph. Second, it is shown that every unanimous and strategy-proof probabilistic rule is random dictatorial if and only if the graph has no leaves. Finally, the two results are combined to obtain a general characterization for every connected graph by using its block tree representation.

Small one-dimensional Euclidean preference profiles

We characterize one-dimensional Euclidean preference profiles with a small number of alternatives and voters. We show that every single-peaked preference profile with two voters is one-dimensional Euclidean, and that every preference profile with up to five alternatives is one-dimensional Euclidean if and only if it is both single-peaked and single-crossing. By the work of Chen et al. (Social Choice and Welfare 48(2):409–432, 2017), we thus obtain that the smallest single-peaked and single-crossing preference profiles that are not one-dimensional Euclidean consist of three voters and six alternatives.

Incomplete Preferences in Single-Peaked Electorates

Incomplete preferences are likely to arise in real-world preference aggregation scenarios. This paper deals with determining whether an incomplete preference profile is single-peaked. This is valuable information since many intractable voting problems become tractable given singlepeaked preferences. We prove that the problem of recognizing single-peakedness is NP-complete for incomplete profiles consisting of partial orders. Despite this intractability result, we find several polynomial-time algorithms for reasonably restricted settings. In particular, we give polynomial-time recognition algorithms for weak orders, which can be viewed as preferences with indifference.