108,166 research outputs found
Relative Information Loss in the PCA
In this work we analyze principle component analysis (PCA) as a deterministic
input-output system. We show that the relative information loss induced by
reducing the dimensionality of the data after performing the PCA is the same as
in dimensionality reduction without PCA. Finally, we analyze the case where the
PCA uses the sample covariance matrix to compute the rotation. If the rotation
matrix is not available at the output, we show that an infinite amount of
information is lost. The relative information loss is shown to decrease with
increasing sample size.Comment: 9 pages, 4 figure; extended version of a paper accepted for
publicatio
On orthogonal projections for dimension reduction and applications in augmented target loss functions for learning problems
The use of orthogonal projections on high-dimensional input and target data
in learning frameworks is studied. First, we investigate the relations between
two standard objectives in dimension reduction, preservation of variance and of
pairwise relative distances. Investigations of their asymptotic correlation as
well as numerical experiments show that a projection does usually not satisfy
both objectives at once. In a standard classification problem we determine
projections on the input data that balance the objectives and compare
subsequent results. Next, we extend our application of orthogonal projections
to deep learning tasks and introduce a general framework of augmented target
loss functions. These loss functions integrate additional information via
transformations and projections of the target data. In two supervised learning
problems, clinical image segmentation and music information classification, the
application of our proposed augmented target loss functions increase the
accuracy
Electrocortical components of anticipation and consumption in a monetary incentive delay task
In order to improve our understanding of the components that reflect functionally important processes during reward anticipation and consumption, we used principle components analyses (PCA) to separate and quantify averaged ERP data obtained from each stage of a modified monetary incentive delay (MID) task. Although a small number of recent ERP studies have reported that reward and loss cues potentiate ERPs during anticipation, action preparation, and consummatory stages of reward processing, these findings are inconsistent due to temporal and spatial overlap between the relevant electrophysiological components. Our results show three components following cue presentation are sensitive to incentive cues (N1, P3a, P3b). In contrast to previous research, rewardârelated enhancement occurred only in the P3b, with earlier components more sensitive to breakâeven and loss cues. During feedback anticipation, we observed a lateralized centroparietal negativity that was sensitive to response hand but not cue type. We also show that use of PCA on ERPs reflecting reward consumption successfully separates the reward positivity from the independently modulated feedbackâP3. Last, we observe for the first time a new reward consumption component: a late negativity distributed over the left frontal pole. This component appears to be sensitive to response hand, especially in the context of monetary gain. These results illustrate that the time course and sensitivities of electrophysiological activity that follows incentive cues do not follow a simple heuristic in which reward incentive cues produce enhanced activity at all stages and substages
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