3 research outputs found
Mismatch in the Classification of Linear Subspaces: Sufficient Conditions for Reliable Classification
This paper considers the classification of linear subspaces with mismatched
classifiers. In particular, we assume a model where one observes signals in the
presence of isotropic Gaussian noise and the distribution of the signals
conditioned on a given class is Gaussian with a zero mean and a low-rank
covariance matrix. We also assume that the classifier knows only a mismatched
version of the parameters of input distribution in lieu of the true parameters.
By constructing an asymptotic low-noise expansion of an upper bound to the
error probability of such a mismatched classifier, we provide sufficient
conditions for reliable classification in the low-noise regime that are able to
sharply predict the absence of a classification error floor. Such conditions
are a function of the geometry of the true signal distribution, the geometry of
the mismatched signal distributions as well as the interplay between such
geometries, namely, the principal angles and the overlap between the true and
the mismatched signal subspaces. Numerical results demonstrate that our
conditions for reliable classification can sharply predict the behavior of a
mismatched classifier both with synthetic data and in a motion segmentation and
a hand-written digit classification applications.Comment: 17 pages, 7 figures, submitted to IEEE Transactions on Signal
Processin
Accurate, very low computational complexity spike sorting using unsupervised matched subspace learning
This paper presents an adaptable dictionary-based feature extraction approach for spike sorting offering high accuracy and low computational complexity for implantable applications. It extracts and learns identifiable features from evolving subspaces through matched unsupervised subspace filtering. To provide compatibility with the strict constraints in implantable devices such as the chip area and power budget, the dictionary contains arrays of {<formula><tex></tex></formula> and the algorithm need only process addition and subtraction operations. Three types of such dictionary were considered. To quantify and compare the performance of the resulting three feature extractors with existing systems, a neural signal simulator based on several different libraries was developed. For noise levels <formula><tex></tex></formula> between 0.05 and 0.3 and groups of 3 to 6 clusters, all three feature extractors provide robust high performance with average classification errors of less than 8% over five iterations, each consisting of 100 generated data segments. To our knowledge, the proposed adaptive feature extractors are the first able to classify reliably 6 clusters for implantable applications. An ASIC implementation of the best performing dictionary-based feature extractor was synthesized in a 65-nm CMOS process. It occupies an area of 0.09 mm2 and dissipates up to about 10.48 &#x03BC;W from a 1 V supply voltage, when operating with 8-bit resolution at 30 kHz operating frequency.</p