Hema Kumari Achanta

Coprime conditions for Fourier sampling for sparse recovery

This paper considers the spark of L × N submatrices of the N × N Discrete Fourier Transform (DFT) matrix. Here a matrix has spark m if every collection of its m - 1 columns are linearly independent. The motivation comes from such applications of compressed sensing as MRI and synthetic aperture radar, where device physics dictates the measurements to be Fourier samples of the signal. Consequently the observation matrix comprises certain rows of the DFT matrix. To recover an arbitrary k-sparse signal, the spark of the observation matrix must exceed 2k + 1. The technical question addressed in this paper is how to choose the rows of the DFT matrix so that its spark equals the maximum possible value L + 1. We expose certain coprimeness conditions that guarantee such a property.

Optimum sensor placement for localization in three dimensional under log normal shadowing

In scenarios of wireless source localization using sensor networks, the geometry of the sensor nodes in the network heavily influences the accuracy of the source location estimate. This paper thus considers the optimal sensor placement in three dimensions so that a source can be localized optimally from the Received Signal Strength (RSS) at various non-coplanar sensors, under Lognormal Shadowing. We assume that the source is uniformly distributed in a sphere and the sensors must be placed outside a larger concentric sphere to avoid proximity to the hazards posed by the source. The mathematical problem becomes one of maximizing the smallest eigenvalue or the determinant of the expectation of an underlying Fisher Information Matrix (FIM), or minimizing the trace of the inverse of this matrix, subject to the above constraint. We show that the optimality is achieved if and only if the expectation of the underlying FIM is a scaled diagonal, and provide methods for achieving this condition.

A transfer learning approach for integrating biological data across platforms

Transfer learning refers to situations where a classifier is trained on one set of data and tested on another set of data that may have an entirely different probability distribution. Biological data derived from diverse platforms, and possibly using diverse technologies, is a natural candidate for applying transfer learning methodologies. In this paper, we adapt the ℓ1-norm SVM to fit into the paradigm of Transfer Learning, by using the importance weighting approach. Our aim is to integrate biological data from diverse platforms. To validate our approach, we applied the proposed algorithm to the problem of classifying breast cancer tumors as Estrogen- Receptor-positive (ER-positive) or Estrogen-Receptor-negative (ER-negative), which is the first step in personalizing therapy to the patient. The standard approach used in Biology is to convert data to Z-scores, that is, to subtract the mean and divide by the standard deviation. The algorithm proposed here shows better performance than using Z-scores to account for platform variations.

Modeling of Ionospheric Time Delay Using Anisotropic IDW With Jackknife Technique

Transionospheric signals are affected due to the existence of anisotropic plasma in the ionosphere. The precise estimation of ionospheric time delay will play a major role in achieving better positional accuracy. For the first time, a novel model based on anisotropic inverse distance weighting with “Jackknife” technique is proposed, and its performance is evaluated in the context of the Global Positioning System. The performance of the model is compared with three prominent models, namely, the modified planar fit, spline, and Kriging models. Multistation data of a GPS-aided geoaugmented navigation network are used to evaluate the fidelity and sensitivity of the proposed model in near real time. The results due to both quiet and disturbed days are encouraging.

Matrix design for optimal sensing

We design optimal 2 × N (2 <; N) matrices, with unit columns, so that the maximum condition number of all the submatrices comprising 3 columns is minimized. The problem has two applications. When estimating a 2-dimensional signal by using only three of N observations at a given time, this minimizes the worst-case achievable estimation error. It also captures the problem of optimum sensor placement for monitoring a source located in a plane, when only a minimum number of required sensors are active at any given time. For arbitrary N ≥ 3, we derive the optimal matrices which minimize the maximum condition number of all the submatrices of three columns. Surprisingly, a uniform distribution of the columns is not the optimal design for odd N ≥ 7.

A multi-view ℓ 1 -norm SVM algorithm for data integration in biological applications

A multi-view ℓ1-norm Support Vector Machine (SVM) for integrating data from different views to improve binary classification performance in a given view is proposed. The performance of the proposed algorithm is evaluated by integrating biological data from two different gene expression measurement technologies. The experimental results show that the data integration method proposed leads to a better classification performance in comparison to the traditional ℓ1-norm SVM.

The spark of Fourier matrices

We consider conditions under which L rows of an N point DFT matrix form a matrix with spark L + 1 , i.e. a matrix with full spark. A matrix has spark L + 1 if all L columns are linearly independent. This has application in compressed sensing for MRI and synthetic aperture radar, where measurements are under sampled Fourier measurements, and the observation matrix comprises certain rows of the DFT matrix. It is known that contiguous rows of the DFT matrix render full spark and that from such a base set one can build a suite of other sets of rows that maintain full spark. We consider an alternative base set of the form { 0 , 1 , ? , K } ? { n } , and derive conditions on K, n and the prime factors of N, under which full spark is retained. We show that such a matrix has full spark iff there are no K distinct N-th roots of unity whose n-products form a vanishing sum, and leverage recent characterizations of vanishing sums of N-th roots of unity to establish the stated conditions.

Recovery of Low Rank and Jointly Sparse Matrices with Two Sampling Matrices

We provide a two-step approach to recover a jointly k-sparse matrix X, (at most k rows of X are nonzero), with rank r <; <; k from its under sampled measurements. Unlike the classical recovery algorithms that use the same measurement matrix for every column of X, the proposed algorithm comprises two stages, in each of which the measurement is taken by a different measurement matrix. The first stage uses a standard algorithm, [4] to recover any r columns (e.g. the first r) of X. The second uses a new set of measurements and the subspace estimate provided by these columns to recover the rest. We derive conditions on the second measurement matrix to guarantee perfect subspace aware recovery for two cases: First a worst-case setting that applies to all matrices. The second a generic case that works for almost all matrices. We demonstrate both theoretically and through simulations that when r <; <; k our approach needs far fewer measurements. It compares favorably with recent results using dense linear combinations, that do not use column-wise measurements.

A distributed control law for optimum sensor placement for source localization.

We formulate a nonlinear distributed control law that guides the motion a group of sensors to achieve a configuration that permits them to optimally localize a hazardous source they must keep a prescribed distance from. Earlier work shows that such a configuration involves the sensors being placed in an equispaced manner on a prescribed circle. The nonlinear control law we propose assumes that each sensor resides and moves on the prescribed circle, by accessing only the states of its two immediate clockwise and counterclockwise neighbors. We theoretically prove and verify through simulations, that the law allows the sensors to achieve the desired configuration while avoiding collisions.

Integrating biological data across multiple platforms using importance-weighted transfer learning and applications to breast cancer data sets

Traditional machine learning approaches are based on the premise that the training and testing samples come from a common probability distribution. Transfer learning refers to situations where this assumption does not necessarily hold. Integrating biological data measured on diverse platforms is a major challenge. Transfer learning is a natural candidate for achieving such integration. In this paper, we adapt the ¿1 — norm SVM using the importance weighting approach to fit into the paradigm of Transfer Learning under Covariate Shift, with the aim of integrating biological data sources from diverse platforms. The conditional probability of the testing data with respect to the training data is estimated using a small number of testing samples. The weights of the ℓ1-norm SVM are adapted using this estimated conditional probability, also known as the importance weight. To validate our approach, we applied the proposed algorithm to the problem of classifying breast cancer tumors as ERpositive or ER-negative, which is the first step in personalizing therapy to the patient. Then we compared it against conversion to Z-scores, which is the current best practice. The ℓ1-norm SVM modified via importance weighting shows better performance than using Z-scores, on five different test data sets.