A unifying probabilistic perspective for spectral dimensionality reduction: Insights and new models

We introduce a new perspective on spectral dimensionality reduction which views these methods as Gaussian Markov random fields (GRFs). Our unifying perspective is based on the maximum entropy principle which is in turn inspired by maximum variance unfolding. The resulting model, which we call maximum entropy unfolding (MEU) is a nonlinear generalization of principal component analysis. We relate the model to Laplacian eigenmaps and isomap. We show that parameter fitting in the locally linear embedding (LLE) is approximate maximum likelihood MEU. We introduce a variant of LLE that performs maximum likelihood exactly: Acyclic LLE (ALLE). We show that MEU and ALLE are competitive with the leading spectral approaches on a robot navigation visualization and a human motion capture data set. Finally the maximum likelihood perspective allows us to introduce a new approach to dimensionality reduction based on L1 regularization of the Gaussian random field via the graphical lasso

Spectral Sequence Motif Discovery

Sequence discovery tools play a central role in several fields of computational biology. In the framework of Transcription Factor binding studies, motif finding algorithms of increasingly high performance are required to process the big datasets produced by new high-throughput sequencing technologies. Most existing algorithms are computationally demanding and often cannot support the large size of new experimental data. We present a new motif discovery algorithm that is built on a recent machine learning technique, referred to as Method of Moments. Based on spectral decompositions, this method is robust under model misspecification and is not prone to locally optimal solutions. We obtain an algorithm that is extremely fast and designed for the analysis of big sequencing data. In a few minutes, we can process datasets of hundreds of thousand sequences and extract motif profiles that match those computed by various state-of-the-art algorithms.Comment: 20 pages, 3 figures, 1 tabl

Optimal set of EEG features for emotional state classification and trajectory visualization in Parkinson's disease

In addition to classic motor signs and symptoms, individuals with Parkinson's disease (PD) are characterized by emotional deficits. Ongoing brain activity can be recorded by electroencephalograph (EEG) to discover the links between emotional states and brain activity. This study utilized machine-learning algorithms to categorize emotional states in PD patients compared with healthy controls (HC) using EEG. Twenty non-demented PD patients and 20 healthy age-, gender-, and education level-matched controls viewed happiness, sadness, fear, anger, surprise, and disgust emotional stimuli while fourteen-channel EEG was being recorded. Multimodal stimulus (combination of audio and visual) was used to evoke the emotions. To classify the EEG-based emotional states and visualize the changes of emotional states over time, this paper compares four kinds of EEG features for emotional state classification and proposes an approach to track the trajectory of emotion changes with manifold learning. From the experimental results using our EEG data set, we found that (a) bispectrum feature is superior to other three kinds of features, namely power spectrum, wavelet packet and nonlinear dynamical analysis; (b) higher frequency bands (alpha, beta and gamma) play a more important role in emotion activities than lower frequency bands (delta and theta) in both groups and; (c) the trajectory of emotion changes can be visualized by reducing subject-independent features with manifold learning. This provides a promising way of implementing visualization of patient's emotional state in real time and leads to a practical system for noninvasive assessment of the emotional impairments associated with neurological disorders