Large-Margin Convex Polytope Machine
نویسندگان
چکیده
We present the Convex Polytope Machine (CPM), a novel non-linear learning algorithm for large-scale binary classification tasks. The CPM finds a large margin convex polytope separator which encloses one class. We develop a stochastic gradient descent based algorithm that is amenable to massive data sets, and augment it with a heuristic procedure to avoid sub-optimal local minima. Our experimental evaluations of the CPM on large-scale data sets from distinct domains (MNIST handwritten digit recognition, text topic, and web security) demonstrate that the CPM trains models faster, sometimes by several orders of magnitude, than stateof-the-art similar approaches and kernel-SVM methods while achieving comparable or better classification performance. Our empirical results suggest that, unlike prior similar approaches, we do not need to control the number of sub-classifiers (sides of the polytope) to avoid overfitting.
منابع مشابه
Decomposition Algorithm for the Single Machine Scheduling Polytope
Given an n-vector p of processing times of jobs, the single machine scheduling polytope C arises as the convex hull of completion times of jobs when these are scheduled without idle time on a single machine. Given a point x ∈ C, Carathéodory’s theorem implies that x can be written as convex combination of at most n vertices of C. We show that this convex combination can be computed from x and p...
متن کاملBlind Data Classification Using Hyper-Dimensional Convex Polytopes
A blind classification algorithm is presented that uses hyperdimensional geometric algorithms to locate a hypothesis, in the form of a convex polytope or hyper-sphere. The convex polytope geometric model provides a well-fitted class representation that does not require training with instances of opposing classes. Further, the classification algorithm creates models for as many training classes ...
متن کاملMultilabel Classification of Drug-like Molecules via Max-margin Conditional Random Fields
We present a multilabel learning approach for molecular classification, an important task in drug discovery. We use a conditional random field to model the dependencies between drug targets and discriminative training to separate correct multilabels from incorrect ones with a large margin. Efficient training of the model is ensured by conditional gradient optimization on the marginal dual polyt...
متن کاملAn Infinity-sample Theory for Multi-category Large Margin Classification
The purpose of this paper is to investigate infinity-sample properties of risk minimization based multi-category classification methods. These methods can be considered as natural extensions to binary large margin classification. We establish conditions that guarantee the infinity-sample consistency of classifiers obtained in the risk minimization framework. Examples are provided for two specif...
متن کاملEfficient edge-skeleton computation for polytopes defined by oracles
In general dimension, there is no known total polynomial algorithm for either convex hull or vertex enumeration, i.e. an algorithm whose complexity depends polynomially on the input and output sizes. It is thus important to identify problems (and polytope representations) for which total polynomial-time algorithms can be obtained. We offer the first total polynomial-time algorithm for computing...
متن کامل