Convexity and logical analysis of data
نویسندگان
چکیده
A Boolean function is called k-convex if for any pair x; y of its true points at Hamming distance at most k, every point \between" x and y is also true. Given a set of true points and a set of false points, the central question of Logical Analysis of Data is the study of the Boolean functions whose values agree with those of the given points. In this paper we examine such data sets which admit k-convex Boolean extensions. We provide polynomial algorithms for nding a k-convex extension, if any, and for nding the maximum k for which a k-convex extension exists. We study the problem of uniqueness, and provide a polynomial algorithm for checking whether all k-convex extensions agree in a point outside the given data set. We estimate the number of k-convex Boolean functions, and show that for small k this number is double-exponential. On the other hand, we also show that for very large k the class of k-convex Boolean functions is PAC-learnable.
منابع مشابه
Calculating Cost Efficiency with Integer Data in the Absence of Convexity
One of the new topics in DEA is the data with integer values. In DEA classic models, it is assumed that input and output variables have real values. However, in many cases, some inputs or outputs can have integer values. Measuring cost efficiency is another method to evaluate the performance and assess the capabilities of a single decision-making unit for manufacturing current products at a min...
متن کاملData Envelopment Analysis Models In The Presence Of Ratio Data and Non-Discretionary Factors
متن کامل
The convexity of the integral operator on the class of the integral operator on the class B(mu,alpha)
In this paper, we study the convexity of the integral operator
متن کاملCloud field segmentation via multiscale convexity analysis
[1] Cloud fields retrieved from remotely sensed satellite data resemble functions depicting spectral values at each spatial position (x,y). Segmenting such cloud fields through a simple thresholding technique may not provide any structurally significant information about each segmented category. An approach based on the use of multiscale convexity analysis to derive structurally significant reg...
متن کاملLogical selection of potential hub nodes in location of strategic facilities by a hybrid methodology of Data Envelopment Analysis and Analytic Hierarchical Process: Iran Aviation case study
Hub facility location problem looks to find the most appropriate location for deploying such facilities. An important factor in such a problem is the pool of potential locations from which the optimal locations must be selected. The present research was performed to address two key objectives: identifying the factors contributing to the selection locations for hub establishment, and presenting ...
متن کاملEstimation of Returns to Scale in the Presence of Undesirable (bad) Outputs in DEA when the Firm is Regulated
The calculation of RTS amounts to measuring a relationship between inputs and outputs in a production structure. There are many methods to measure RTS in the primal space or the dual space. One of the main approaches is using the multiplier on the convexity constraint. But returns to scale measurements in DEA models are affected by the presence of regulatory constraints. These additional constr...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Theor. Comput. Sci.
دوره 244 شماره
صفحات -
تاریخ انتشار 2000