Makiko Konoshima

Yuki Furue, Makiko Konoshima, Hirotaka Tamura et al.

Annealing machines specialized for combinatorial optimization problems have been developed, and some companies offer services to use those machines. Such specialized machines can only handle binary variables, and their input format is the quadratic unconstrained binary optimization (QUBO) formulation. Therefore, discretization is necessary to solve problems with continuous variables. However, there is a severe constraint on the number of binary variables with such machines. Although the simple binary expansion in the previous research requires many binary variables, we need to reduce the number of such variables in the QUBO formulation due to the constraint. We propose a discretization method that involves using correlations of continuous variables. We numerically show that the proposed method reduces the number of necessary binary variables in the QUBO formulation without a significant loss in prediction accuracy.

Makiko Konoshima, Hirotaka Tamura, Yoshiyuki Kabashima

The 0/1 matrix factorization defines matrix products using logical AND and OR as product-sum operators, revealing the factors influencing various decision processes. Instances and their characteristics are arranged in rows and columns. Formulating matrix factorization as an energy minimization problem and exploring it with Simulated Annealing (SA) theoretically enables finding a minimum solution in sufficient time. However, searching for the optimal solution in practical time becomes problematic when the energy landscape has many plateaus with flat slopes. In this work, we propose a method to facilitate the solution process by applying a gradient to the energy landscape, using a rectified linear type cost function readily available in modern annealing machines. We also propose a method to quickly obtain a solution by updating the cost function's gradient during the search process. Numerical experiments were conducted, confirming the method's effectiveness with both noise-free artificial and real data.

Yoshiki Sato, Makiko Konoshima, Hirotaka Tamura et al.

Ising formulations are widely utilized to solve combinatorial optimization problems, and a variety of quantum or semiconductor-based hardware has recently been made available. In combinatorial optimization problems, the existence of local minima in energy landscapes is problematic to use to seek the global minimum. We note that the aim of the optimization is not to obtain exact samplings from the Boltzmann distribution, and there is thus no need to satisfy detailed balance conditions. In light of this fact, we develop an algorithm to get out of the local minima efficiently while it does not yield the exact samplings. For this purpose, we utilize a feature that characterizes locality in the current state, which is easy to obtain with a type of specialized hardware. Furthermore, as the proposed algorithm is based on a rejection-free algorithm, the computational cost is low. In this work, after presenting the details of the proposed algorithm, we report the results of numerical experiments that demonstrate the effectiveness of the proposed feature and algorithm.

Tomohiro Yokota, Makiko Konoshima, Hirotaka Tamura et al.

We propose a quadratic unconstrained binary optimization (QUBO) formulation of the l1-norm, which enables us to perform sparse estimation of Ising-type annealing methods such as quantum annealing. The QUBO formulation is derived using the Legendre transformation and the Wolfe theorem, which have recently been employed to derive the QUBO formulations of ReLU-type functions. It is shown that a simple application of the derivation method to the l1-norm case results in a redundant variable. Finally a simplified QUBO formulation is obtained by removing the redundant variable.

Yui Noma, Makiko Konoshima

The similarity searches that use high-dimensional feature vectors consisting of a vast amount of data have a wide range of application. One way of conducting a fast similarity search is to transform the feature vectors into binary vectors and perform the similarity search by using the Hamming distance. Such a transformation is a hashing method, and the choice of hashing function is important. Hashing methods using hyperplanes or hyperspheres are proposed. One study reported here is inspired by Spherical LSH, and we use hypersperes to hash the feature vectors. Our method, called Eclipse-hashing, performs a compactification of R^n by using the inverse stereographic projection, which is a kind of Alexandrov compactification. By using Eclipse-hashing, one can obtain the hypersphere-hash function without explicitly using hyperspheres. Hence, the number of nonlinear operations is reduced and the processing time of hashing becomes shorter. Furthermore, we also show that as a result of improving the approximation accuracy, Eclipse-hashing is more accurate than hyperplane-hashing.

Yui Noma, Makiko Konoshima

Since Hamming distances can be calculated by bitwise computations, they can be calculated with less computational load than L2 distances. Similarity searches can therefore be performed faster in Hamming distance space. The elements of Hamming distance space are bit strings. On the other hand, the arrangement of hyperplanes induce the transformation from the feature vectors into feature bit strings. This transformation method is a type of locality-sensitive hashing that has been attracting attention as a way of performing approximate similarity searches at high speed. Supervised learning of hyperplane arrangements allows us to obtain a method that transforms them into feature bit strings reflecting the information of labels applied to higher-dimensional feature vectors. In this p aper, we propose a supervised learning method for hyperplane arrangements in feature space that uses a Markov chain Monte Carlo (MCMC) method. We consider the probability density functions used during learning, and evaluate their performance. We also consider the sampling method for learning data pairs needed in learning, and we evaluate its performance. We confirm that the accuracy of this learning method when using a suitable probability density function and sampling method is greater than the accuracy of existing learning methods.

Makiko Konoshima, Yui Noma

We propose a learning method with feature selection for Locality-Sensitive Hashing. Locality-Sensitive Hashing converts feature vectors into bit arrays. These bit arrays can be used to perform similarity searches and personal authentication. The proposed method uses bit arrays longer than those used in the end for similarity and other searches and by learning selects the bits that will be used. We demonstrated this method can effectively perform optimization for cases such as fingerprint images with a large number of labels and extremely few data that share the same labels, as well as verifying that it is also effective for natural images, handwritten digits, and speech features.