In the bidirected minimum Manhattan network problem, given a set T of n terminals in the plane, we need to construct a network N (T) of minimum total length with the property that the edges of N (T) are axis-parallel and oriented in a such a way that every ordered pair of terminals is connected in N (T) by a directed Manhattan path. In this paper, we present a polynomial factor 2 approximation ...

Now day’s Outlier Detection is used in various fields such as Credit Card Fraud Detection, Cyber-Intrusion Detection, Medical Anomaly Detection, and Data Mining etc. So to detect anomaly objects from various types of dataset Outlier Detection techniques are used, that detects and remove the anomaly objects from the dataset. Outliers are the containments that divert from the other objects. Outli...

A staircase in this paper is the set of points in Z2 below a given rational line in the plane that have Manhattan Distance less than 1 to the line. Staircases are closely related to Beatty and Sturmian sequences of rational numbers. Connecting the geometry and the number theoretic concepts, we obtain three equivalent characterizations of Sturmian sequences of rational numbers, as well as a new ...

In the last lecture we defined metric spaces, normed spaces, and considered the distortion resulting from certain embeddings. In particular, we proved that l1 norms cannot always be embedded isometrically into l2 by considering a specific four-point l1 norm and showing that it requires at least √ 2 distortion. Today’s lecture further explores the 1 norm. We see a couple of interesting examples ...

Cryptography facilitates selective communication through encryption of messages and or data. Block-cipher processing is one the prominent methods for modern cryptographic symmetric schemes. The rise in attacks on block-ciphers led to development more difficult However, attackers decrypt generic given sufficient time computing. Recent research had applied machine learning classification algorith...

This paper proposes an original statistical decision theory to accomplish a multi-speaker recognition task in cocktail party problem. This theory relies on an assumption that the varied frequencies of speakers obey Gaussian distribution and the relationship of their voiceprints can be represented by Euclidean distance vectors. This paper uses Mel-Frequency Cepstral Coefficients to extract the f...

We modify a fast algorithm which we designed in [15] for computing the Earth mover’s distance (EMD), whose cost is a Manhattan metric. From the theory of optimal transport, the EMD problem can be reformulated as a familiar L1 minimization. We use a regularization which gives us a unique solution for this non strictly convex L1 problem. We adopt a primal-dual algorithm for the regularized proble...