In this paper, we present a new feature selection method that is suitable for both unsupervised and supervised problems. We build upon the recently proposed Infinite Feature Selection (IFS) method where feature subsets of all sizes (including infinity) are considered. We extend IFS in two ways. First, we propose a supervised version of it. Second, we propose new ways of forming the feature adjacency matrix that perform better for unsupervised problems. We extensively evaluate our methods on many benchmark datasets, including large image-classification datasets (PASCAL VOC), and show that our methods outperform both the IFS and the widely used "minimum-redundancy maximum-relevancy (mRMR)" feature selection algorithm.
Most filter methods rely on the concept of feature relevance @cite_26 @cite_2 @cite_14 . For a given learning task, a feature can be in one of the following three disjoint categories: strongly relevant, weakly relevant and irrelevant. Strongly relevant features contain information that is not present in any subset of other features and therefore they are always necessary for the underlying task. Weakly relevant features contains information which is already present in a subset of strongly or irrelevant features. These features can be unnecessary (redundant) or necessary (non-redundant) with certain conditions. Irrelevant features contain no useful information and are not necessary at all. An ideal feature selection algorithm should eliminate all the irrelevant features and weakly redundant features. However, constructing such an algorithm is computationally infeasible, as it requires to check exponentially many combinations of features to ascertain weak relevancy. Therefore, several heuristics are proposed in the literature, which consider limited combination sizes @cite_7 @cite_4 @cite_32 @cite_35 @cite_14 @cite_25 @cite_10 .
@cite_35 @cite_14 @cite_26 @cite_4 @cite_7 @cite_32 @cite_2 @cite_10 @cite_25
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In many prediction tasks, selecting relevant features is essential for achieving good generalization performance. Most feature selection algorithms consider all features to be a priori equally likely to be relevant. In this paper, we use transfer learning---learning on an ensemble of related tasks---to construct an informative prior on feature relevance. We assume that features themselves have meta-features that are predictive of their relevance to the prediction task, and model their relevance as a function of the meta-features using hyperparameters (called meta-priors). We present a convex optimization algorithm for simultaneously learning the meta-priors and feature weights from an ensemble of related prediction tasks which share a similar relevance structure. Our approach transfers the "meta-priors" among different tasks, which makes it possible to deal with settings where tasks have nonoverlapping features or the relevance of the features vary over the tasks. We show that learning feature relevance improves performance on two real data sets which illustrate such settings: (1) predicting ratings in a collaborative filtering task, and (2) distinguishing arguments of a verb in a sentence. The idea that many important classes of signals can be well-represented by linear combinations of a small set of atoms selected from a given dictionary has had dramatic impact on the theory and practice of signal processing. For practical problems in which an appropriate sparsifying dictionary is not known ahead of time, a very popular and successful heuristic is to search for a dictionary that minimizes an appropriate sparsity surrogate over a given set of sample data. While this idea is appealing, the behavior of these algorithms is largely a mystery; although there is a body of empirical evidence suggesting they do learn very eective representations, there is little theory to guarantee when they will behave correctly, or when the learned dictionary can be expected to generalize. In this paper, we take a step towards such a theory. We show that under mild hypotheses, the dictionary learning problem is locally well-posed: the desired solution is indeed a local minimum of the ‘ 1 norm. Namely, if A 2 R m n is an incoherent (and possibly overcomplete) dictionary, and the coecients X 2 R n p follow a random sparse model, then with high probability (A;X) is a local minimum of the ‘ 1 norm over the manifold of factorizations (A 0 ;X 0 ) satisfying A 0 X 0 = Y , provided the number of samples p = The paper presents an original filter approach for effective feature selection in classification tasks with a very large number of input variables. The approach is based on the use of a new information theoretic selection criterion: the double input symmetrical relevance (DISR). The rationale of the criterion is that a set of variables can return an information on the output class that is higher than the sum of the informations of each variable taken individually. This property will be made explicit by defining the measure of variable complementarity. A feature selection filter based on the DISR criterion is compared in theoretical and experimental terms to recently proposed information theoretic criteria. Experimental results on a set of eleven microarray classification tasks show that the proposed technique is competitive with existing filter selection methods. Despite the availability of a huge amount of video data accompanied by descriptive texts, it is not always easy to exploit the information contained in natural language in order to automatically recognize video concepts. Towards this goal, in this paper we use textual cues as means of supervision, introducing two weakly supervised techniques that extend the Multiple Instance Learning (MIL) framework: the Fuzzy Sets Multiple Instance Learning (FSMIL) and the Probabilistic Labels Multiple Instance Learning (PLMIL). The former encodes the spatio-temporal imprecision of the linguistic descriptions with Fuzzy Sets, while the latter models different interpretations of each description's semantics with Probabilistic Labels, both formulated through a convex optimization algorithm. In addition, we provide a novel technique to extract weak labels in the presence of complex semantics, that consists of semantic similarity computations. We evaluate our methods on two distinct problems, namely face and action recognition, in the challenging and realistic setting of movies accompanied by their screenplays, contained in the COGNIMUSE database. We show that, on both tasks, our method considerably outperforms a state-of-the-art weakly supervised approach, as well as other baselines.