A novel sub-Kmeans based on co-training approach by transforming single-view into multi-view
15
Citation
52
Reference
10
Related Paper
Citation Trend
Keywords:
Co-training
K-Means Clustering
Economic shortage
This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and randomness is found. The properties of randomness are summarized from the perspective of interaction between systems, that is, the set composed of sequences generated by randomness has the property of asymptotic completeness. Finally, the importance of randomness in AI research is emphasized.
Completeness (order theory)
Infinity
Randomness tests
Cite
Citations (0)
Abstract We show that a computable function $f:\mathbb R\rightarrow \mathbb R$ has Luzin’s property (N) if and only if it reflects $\Pi ^1_1$ -randomness, if and only if it reflects $\Delta ^1_1({\mathcal {O}})$ -randomness, and if and only if it reflects ${\mathcal {O}}$ -Kurtz randomness, but reflecting Martin–Löf randomness or weak-2-randomness does not suffice. Here a function f is said to reflect a randomness notion R if whenever $f(x)$ is R -random, then x is R -random as well. If additionally f is known to have bounded variation, then we show f has Luzin’s (N) if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset '$ -Kurtz randomness. This links classical real analysis with algorithmic randomness.
Cite
Citations (1)
I investigate the trade-off between regularity and randomness in Bridget Riley's early Op art, focusing on White Discs 2 (1964) and Fragment 6/9 (1965). I build on this to investigate the trade-off more generally. I analyse these two works and undertake three experimental investigations based on my observations. I first consider different types of randomness and the effect they have on the generated artwork. I then look at whether the introduction of randomness can be left to the computer or needs the artist's direction. For best aesthetic effect, there is some evidence that the choices made are not truly random. Finally, I consider how much randomness needs to be added to a regular pattern in order to produce a work that balances regularity and randomness in an aesthetically pleasing way. There is evidence that around two-thirds of the pattern needs to be retained.
Cite
Citations (9)
We show that a computable function $f:\mathbb R\rightarrow\mathbb R$ has Luzin's property (N) if and only if it reflects $\Pi^1_1$-randomnes, if and only if it reflects $\Delta^1_1(\mathcal O)$-randomness, and if and only if it reflects $\mathcal O$-Kurtz randomness, but reflecting Martin-L\"of randomness or weak-2-randomness does not suffice. Here a function $f$ is said to reflect a randomness notion $R$ if whenever $f(x)$ is $R$-random, then $x$ is $R$-random as well. If additionally $f$ is known to have bounded variation, then we show $f$ has Luzin's (N) if and only if it reflects weak-2-randomness, and if and only if it reflects $\emptyset'$-Kurtz randomness. This links classical real analysis with algorithmic randomness.
Cite
Citations (0)
Abstract We prove that there exists a noncomputable c.e. real which is low for weak 2-randomness, a definition of randomness due to Kurtz, and that all reals which are low for weak 2-randomness are low for Martin-Löf randomness.
Randomness tests
Cite
Citations (28)
Abstract In a number of studies, tendencies toward nonrepetition in judgments of randomness of visually presented sequences of events have been attributed to a biased concept of randomness. The present study proposed that such bias is due to “bottom-up” visual processes rather than a concept of randomness. Experiment 1 showed that judgments of randomness were less biased when repetitions were made less conspicuous by increasing the distance between adjacent items. Experiment 2 produced comparable results for increasing dissimilarity of categorically identical items. A third experiment showed that the bias in the judgment task was not related to a more direct measure of knowledge of random processes, the assignment of probabilities of repetition to imagined random sequences. The results supported the view that judgments of randomness are determined to a high degree by the conspicuousness of repetitions and are independent of the concept of randomness.
Repetition (rhetorical device)
Random sequence
Degree (music)
Cite
Citations (10)
Randomness tests
Cite
Citations (6)
Abstract This paper is a concept paper, which discusses the definition of randomness, and the sources of randomness in the physical system (the Universe) as well as in the formal mathematical system. I discuss how randomness, through chaos, the second law, the quantum mechanical character of small scales, and stochasticity is an intrinsic property of nature. I then move to our formal mathematical system and show that even in this formal system we cannot do away with randomness and that the randomness in the physical world is consistent with the origins of randomness suggested from the study of mathematical systems. Rules and randomness are blended together and their interaction is shaping all observed forms and structures.
Formal description
Randomness tests
Cite
Citations (1)
This work starts from definition of randomness, the results of algorithmic randomness are analyzed from the perspective of application. Then, the source and nature of randomness is explored, and the relationship between infinity and randomness is found. The properties of randomness are summarized from the perspective of interaction between systems, that is, the set composed of sequences generated by randomness has the property of asymptotic completeness. Finally, the importance of randomness in AI research is emphasized.
Completeness (order theory)
Infinity
Randomness tests
Cite
Citations (0)