We consider the problem of separating two sets of points in an Euclidean space with a hyperplane that minimizes the sum of p-norm distances to the plane of points lying on the “wrong” side of the plane. A Variable Neighborhood Search metaheuristic framework is used to determine the plane coefficients. For a set of examples with L1-norm, L2-norm and L∞-norm, for which the exact solution can be c...

Taxicabs are a critical aspect of the public transit system in New York City. The yellow cabs that are ubiquitous in Manhattan are as iconic as the city’s subway system, and in recent years green taxicabs were introduced by the city to improve taxi service in areas outside of the central business districts and airports. Approximately 500,000 taxi trips are taken daily, carrying about 800,000 pa...

For n ∈ N consider the n-dimensional hypercube as equal to the vector space F2 , where F2 is the field of size two. Endow F2 with the Hamming metric, i.e., with the metric induced by the `1 norm when one identifies F2 with {0, 1} ⊆ R. Denote by `2 (F2 ) the n-fold Pythagorean product of F2 , i.e., the space of all x = (x1, . . . , xn) ∈ ∏n j=1 F n 2 , equipped with the metric ∀x, y ∈ n ∏ j=1 F2...

Fuzzy clustering techniques handle the fuzzy relationships among the data points and with the cluster centers (may be termed as cluster fuzziness). On the other hand, distance measures are important to compute the load of such fuzziness. These are the two important parameters governing the quality of the clusters and the run time. Visualization of multidimensional data clusters into lower dimen...

Kaufman & Rousseeuw (1990) proposed a clustering algorithm Partitioning Around Medoids (PAM) which maps a distance matrix into a specified number of clusters. A particularly nice property is that PAM allows clustering with respect to any specified distance metric. In addition, the medoids are robust representations of the cluster centers, which is particularly important in the common context th...

Using the 2017 National Household Travel Survey (NHTS), this study analyzes America's urban travel trends compared with earlier nationwide surveys, and examines variations in behaviors among a range of socioeconomic groups. The most noticeable trend for NHTS is that although private automobiles continue to be dominant mode American cities, share car trips has slightly steadily decreased since i...

We develop a simple model that links the adoption of a productivity-enhancing technology to increased vertical integration and a less skilled workforce. We test the model’s key prediction using novel microdata on vehicle ownership patterns from the Economic Census during a period when computerized dispatching systems were first adopted by taxicab firms. Controlling for time-invariant firm-speci...

It is well known that RN has subspaces of dimension proportional to N on which the l1 norm is equivalent to the l2 norm; however, no explicit constructions are known. Extending earlier work by Artstein– Avidan and Milman, we prove that such a subspace can be generated using O(N) random bits.