Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer

Robust automated detection of microstructural white matter degeneration in Alzheimer’s disease using machine learning classification of multicenter DTI data

Diffusion tensor imaging (DTI) based assessment of white matter fiber tract integrity can support the diagnosis of Alzheimer’s disease (AD). The use of DTI as a biomarker, however, depends on its applicability in a multicenter setting accounting for effects of different MRI scanners. We applied multivariate machine learning (ML) to a large multicenter sample from the recently created framework of the European DTI study on Dementia (EDSD). We hypothesized that ML approaches may amend effects of multicenter acquisition. We included a sample of 137 patients with clinically probable AD (MMSE 20.6±5.3) and 143 healthy elderly controls, scanned in nine different scanners. For diagnostic classification we used the DTI indices fractional anisotropy (FA) and mean diffusivity (MD) and, for comparison, gray matter and white matter density maps from anatomical MRI. Data were classified using a Support Vector Machine (SVM) and a Naïve Bayes (NB) classifier. We used two cross-validation approaches, (i) test and training samples randomly drawn from the entire data set (pooled cross-validation) and (ii) data from each scanner as test set, and the data from the remaining scanners as training set (scanner-specific cross-validation). In the pooled cross-validation, SVM achieved an accuracy of 80% for FA and 83% for MD. Accuracies for NB were significantly lower, ranging between 68% and 75%. Removing variance components arising from scanners using principal component analysis did not significantly change the classification results for both classifiers. For the scanner-specific cross-validation, the classification accuracy was reduced for both SVM and NB. After mean correction, classification accuracy reached a level comparable to the results obtained from the pooled cross-validation. Our findings support the notion that machine learning classification allows robust classification of DTI data sets arising from multiple scanners, even if a new data set comes from a scanner that was not part of the training sample

Non-Negative Tensor Factorization Applied to Music Genre Classification

Music genre classification techniques are typically applied to the data matrix whose columns are the feature vectors extracted from music recordings. In this paper, a feature vector is extracted using a texture window of one sec, which enables the representation of any 30 sec long music recording as a time sequence of feature vectors, thus yielding a feature matrix. Consequently, by stacking the feature matrices associated to any dataset recordings, a tensor is created, a fact which necessitates studying music genre classification using tensors. First, a novel algorithm for non-negative tensor factorization (NTF) is derived that extends the non-negative matrix factorization. Several variants of the NTF algorithm emerge by employing different cost functions from the class of Bregman divergences. Second, a novel supervised NTF classifier is proposed, which trains a basis for each class separately and employs basis orthogonalization. A variety of spectral, temporal, perceptual, energy, and pitch descriptors is extracted from 1000 recordings of the GTZAN dataset, which are distributed across 10 genre classes. The NTF classifier performance is compared against that of the multilayer perceptron and the support vector machines by applying a stratified 10-fold cross validation. A genre classification accuracy of 78.9% is reported for the NTF classifier demonstrating the superiority of the aforementioned multilinear classifier over several data matrix-based state-of-the-art classifiers

Compact Random Feature Maps

Kernel approximation using randomized feature maps has recently gained a lot of interest. In this work, we identify that previous approaches for polynomial kernel approximation create maps that are rank deficient, and therefore do not utilize the capacity of the projected feature space effectively. To address this challenge, we propose compact random feature maps (CRAFTMaps) to approximate polynomial kernels more concisely and accurately. We prove the error bounds of CRAFTMaps demonstrating their superior kernel reconstruction performance compared to the previous approximation schemes. We show how structured random matrices can be used to efficiently generate CRAFTMaps, and present a single-pass algorithm using CRAFTMaps to learn non-linear multi-class classifiers. We present experiments on multiple standard data-sets with performance competitive with state-of-the-art results.Comment: 9 page

Score Function Features for Discriminative Learning: Matrix and Tensor Framework

Feature learning forms the cornerstone for tackling challenging learning problems in domains such as speech, computer vision and natural language processing. In this paper, we consider a novel class of matrix and tensor-valued features, which can be pre-trained using unlabeled samples. We present efficient algorithms for extracting discriminative information, given these pre-trained features and labeled samples for any related task. Our class of features are based on higher-order score functions, which capture local variations in the probability density function of the input. We establish a theoretical framework to characterize the nature of discriminative information that can be extracted from score-function features, when used in conjunction with labeled samples. We employ efficient spectral decomposition algorithms (on matrices and tensors) for extracting discriminative components. The advantage of employing tensor-valued features is that we can extract richer discriminative information in the form of an overcomplete representations. Thus, we present a novel framework for employing generative models of the input for discriminative learning.Comment: 29 page