Related papers: A Representation of Binary Matrices
The null linear discriminant analysis method is a competitive approach for dimensionality reduction. The implementation of this method, however, is computationally expensive. Recently, a fast implementation of null linear discriminant…
Applications of Binary Neural Networks (BNNs) are promising for embedded systems with hard constraints on computing power. Contrary to conventional neural networks with the floating-point datatype, BNNs use binarized weights and activations…
This paper introduces a series of methods for traversing binary decision trees using arithmetic operations. We present a suite of binary tree traversal algorithms that leverage novel representation matrices to flatten the full binary tree…
Sorting is needed in many application domains. The data is read from memory and sent to a general purpose processor or application specific hardware for sorting. The sorted data is then written back to the memory. Reading/writing data…
Random unitary matrices find a number of applications in quantum information science, and are central to the recently defined boson sampling algorithm for photons in linear optics. We describe an operationally simple method to directly…
The binary string matching problem consists in finding all the occurrences of a pattern in a text where both strings are built on a binary alphabet. This is an interesting problem in computer science, since binary data are omnipresent in…
Given some binary matrix $M$, suppose we are presented with the collection of its rows and columns in independent arbitrary orderings. From this information, are we able to recover the unique original orderings and matrix? We present an…
Quantum computing provides a powerful framework for tackling computational problems that are classically intractable. The goal of this paper is to explore the use of quantum computers for solving relevant problems in systems and control…
Two matrices are said non-overlapping if one of them can not be put on the other one in a way such that the corresponding entries coincide. We provide a set of non-overlapping binary matrices and a formula to enumerate it which involves the…
Boolean matrix factorization is a natural and a popular technique for summarizing binary matrices. In this paper, we study a problem of Boolean matrix factorization where we additionally require that the factor matrices have consecutive…
We define a special matrix multiplication among a special subset of $2N\x 2N$ matrices, and study the resulting (non-associative) algebras and their subalgebras. We derive the conditions under which these algebras become alternative…
Binary neural networks have attracted tremendous attention due to the efficiency for deploying them on mobile devices. Since the weak expression ability of binary weights and features, their accuracy is usually much lower than that of…
Recent work in time series forecasting has explored reformulating regression as a classification task. By discretizing the continuous target space into bins and predicting over a fixed set of classes, these approaches benefit from more…
The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…
Converting binary integers to variable-length decimal strings is a fundamental operation in computing. Conventional fast approaches rely on recursive division and small lookup tables. We propose a SIMD-based algorithm that leverages integer…
Sorting is a common and ubiquitous activity for computers. It is not surprising that there exist a plethora of sorting algorithms. For all the sorting algorithms, it is an accepted performance limit that sorting algorithms are linearithmic…
We present a method for randomizing formulas for bilinear computation of matrix products. We consider the implications of such randomization when there are two sources of error: One due to the formula itself only being approximately…
The power of real-time Turing machines using sublinear space is investigated. In contrast to a claim appearing in the literature, such machines can accept non-regular languages, even if working in deterministic mode. While maintaining a…
In this work, we propose an ensemble of classification trees (CT) and artificial neural networks (ANN). Several statistical properties including universal consistency and upper bound of an important parameter of the proposed classifier are…
We present an efficient algorithm for the application of sequences of planar rotations to a matrix. Applying such sequences efficiently is important in many numerical linear algebra algorithms for eigenvalues. Our algorithm is novel in…