Learning latent features with infinite non-negative binary matrix tri-factorization

Non-negative Matrix Factorization (NMF) has been widely exploited to learn latent features from data. However, previous NMF models often assume a fixed number of features, saypfeatures, wherepis simply searched by experiments. Moreover, it is even difficult to learn binary features, since binary matrix involves more challenging optimization problems. In this paper, we propose a new Bayesian model called infinite non-negative binary matrix tri-factorizations model (iNBMT), capable of learning automatically the latent binary features as well as feature number based on Indian Buffet Process (IBP). Moreover, iNBMT engages a tri-factorization process that decomposes a nonnegative matrix into the product of three components including two binary matrices and a non-negative real matrix. Compared with traditional bi-factorization, the tri-factorization can better reveal the latent structures among items (samples) and attributes (features). Specifically, we impose an IBP prior on the two infinite binary matrices while a truncated Gaussian distribution is assumed on the weight matrix. To optimize the model, we develop an efficient modified maximization-expectation algorithm (ME-algorithm), with the iteration complexity one order lower than another recently-proposed Maximization-Expectation-IBP model[9]. We present the model definition, detail the optimization, and finally conduct a series of experiments. Experimental results demonstrate that our proposed iNBMT model significantly outperforms the other comparison algorithms in both synthetic and real data

Hardware implementation of a spiking neural network for fast synchronization

In this master thesis, we present two different hardware implementations of the Oscillatory Dynamic Link Matcher (ODLM). The ODLM is an algorithm which uses the synchronization in a network of spiking neurons to realize different signal processing tasks. The main objective of this work is to identify the key design choices leading to the efficient implementation of an embedded version of the ODLM. The resulting systems have been tested with image segmentation and image matching tasks. The first system is bit-slice and time-driven. The state of the whole network is updated at regular time intervals. The system uses a bit-slice architecture with a large number of processing elements. Each processing element, or slice, implements one neuron of the network and takes the form of a column on the hardware. The columns are placed side by side and they are locally connected to their 2 neighbors. This local hardware connection scheme makes the system scalable, which means that columns can be easily added to increase the capacity of the system. Each column consists of a weight vector, a synapse model unit and a membrane model unit. The system can implement any network topology, making it very flexible. The function governing the time evolution of the neurons' membrane potential is approximated by a piece-wise linear function to reduce the amount of logical resources required. With this system, a fully-connected network of 648 neurons can be implemented on a Virtex-5 Xilinx XC5VSX5OT FPGA clocked at 100 MHz. The system is designed to process simultaneous spikes in parallel, reaching a maximum processing speed of 6 Mspikes/s. It can segment a 23×23 pixel image in 2 seconds and match two pre-segmented 90×30 pixel images in 550 ms. The second system is event-driven. A single processing element sequentially processes the spikes. This processing element is a 5-stage pipeline which can process an average of 1 synapse per 7 clock cycles. The synaptic weights are not stored in memory in this system, they are computed on-the-fly as spikes are processed. The topology of the network is also resolved during operation, and the system supports various regular topologies like 8-neighbor and fully-connected. The membrane potential time evolution function is computed with high precision using a look-up table. On the Virtex-5 FPGA, a network of 65 536 neurons can be implemented and a 406×158 pixel image can be segmented in 200 ms. The FPGA can be clocked at 100 MHz. Most of the design choices made for the second system are well adapted to the hardware implementation of the ODLM. In the original ODLM, the weight values do not change over time and usually depend on a single variable. It is therefore beneficial to compute the weights on the fly rather than saving them in a huge memory bank. The event-driven approach is a very efficient strategy. It reduces the amount of computations required to run the network and the amount of data moved in and out of memory. Finally, the precise computation of the neurons' membrane potential increases the convergence speed of the network

Robustness in Dimensionality Reduction

Dimensionality reduction is widely used in many statistical applications, such as image analysis, microarray analysis, or text mining. This thesis focuses on three problems that relate to the robustness in dimension reduction. The first topic is the performance analysis in dimension reduction, that is, quantitatively assessing the performance of a algorithm on a given dataset. A criterion for success is established from the geometric point of view to address this issues. A family of goodness measures, called \textsl{local rank correlation}, is developed to assess the performance of dimensionality reduction methods. The potential application of the local rank correlation in selecting tuning parameters of dimension reduction algorithms is also explored. The second topic is the sensitivity analysis in dimension reduction. Two types of influence functions are developed as measures of robustness, based on which we develop graphical display strategies for visualizing the robustness of a dimension reduction method, and flagging potential outliers. In the third part of the thesis, a novel robust PCA framework, called \textsl{Performance-Weighted Bagging PCA}, is proposed from the perspective of model averaging. It obtains a robust linear subspace by weighted averaging a collection of subspaces produced by subsamples. The robustness against outliers is achieved by a proper weighting scheme, and possible choices of weighting scheme are investigated